Statistics and Statistical Science

Statistics and Statistical ScienceAuthor(s): J. DurbinSource: Journal of the Royal Statistical Society. Series A (General), Vol. 150, No. 3 (1987), pp.177-191Published by: Wiley for the Royal Statistical SocietyStable URL: http://www.jstor.org/stable/2981472 .

Accessed: 25/06/2014 07:03

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Wiley and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access toJournal of the Royal Statistical Society. Series A (General).

http://www.jstor.org

This content downloaded from 91.229.229.101 on Wed, 25 Jun 2014 07:03:25 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=black

http://www.jstor.org/action/showPublisher?publisherCode=rss

http://www.jstor.org/stable/2981472?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


... ... . .. ..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.:. : : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. . ....

..... .. . .. ..a . . . .. . . .. . .. .

t.~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ....... ..

.. . ... . . . . .



J. R. Statist. Soc. A (1987) 150, Part 3, pp. 177-191

Statistics and Statistical Science

By J. DURBIN

London School of Economics and Political Science, UK

[The Address of the President, delivered to the Royal Statistical Society on Wednesday, March 18th, 1987]

SUMMARY The distinction is made between statistics in its original sense of the collection and dissemination of quantitative information for the investigation of economic and social problems, and statistical science in the modern sense of the techniques and methodology of statistical analysis. The impact of the development of computing technology on both statistics and statistical science will be considered from a general point of view. Some questions of statistical policy are discussed. A plea is made for the development of a unified philosophy for statistical science in which competing schools of statistical thought can be accommodated in a spirit of tolerance.

1. INTRODUCTION In electing me as President, the Society has conferred on me a considerable honour which I deeply appreciate. While contemplating my inadequacy for the task it occurred to me that one reason why I was selected might have been that my work has been done mainly within the context of the social sciences and it has been a number of years since we had a President from that area. With this in mind, I thought it might be of interest to go back to the nineteenth century meaning of the word statistics, namely the collection and dissemination of data for the study of economic and social problems, and to consider how this aspect of our subject is being affected by current explosive developments in computing and information technology.

A number of questions of policy and public concern are raised by such a review and I shall consider these briefly, without, I hasten to say, taking it upon myself to make specific recommendations. No-one can doubt that we live in a society in which knowledge and information, regarded as an economic e ltity, are increasing rapidly in value relative to other commodities in the national economy. What I hope to do is draw attention to some specific examples of the increasing availability of economic and social data through the use of modern electronic technology, and then ask some questions about how our society is to achieve the right balance between the public and private provision of data for government, research, education and for the private sector.

1.1. Statistical Science Academic statisticians are concerned primarily with statistical techniques and methodology

derived from probability theory and they develop applications of their techniques and methods to a wide range of problems, particularly in science and technology. This group of topics constitutes an academic discipline of great breadth and depth which is not only an excellent educational subject for students that is Qf great practical value in the world but is also intellectually fascinating to those who wcrk in it. However, names are important and it is unfortunate that the name statistics that we normally use to refer to the discipline has a somewhat different connotation in the minds of the general public, namely the compilation and presentation, usually in tabular form, of numerical data. The name obviously fails to be sufficiently suggestive of the real fascination of the subject. While this may not be a matter of any great concern to the public, I think it has some importance to statisticians in terms of attracting students into the discipline. The competition for the limited pool of mathematically qualified students has been increasing steadily for many years. We have to compete for students

t Addess for correspondence: London School of Economics, Houghton St., London WC2A 2AE, UK.

@D 1987 Royal Statistical Society 0035-9238/87/150177 $2.00



178 DURBIN [Part 3,

not only with our traditional rivals in mathematics, science and technology but also with newer subjects with names that may possibly seem more glamorous to students such as computer science, operational research and management science.

I do not know who invented the name statistical science but its introduction seems to me a useful contribution. Two recent examples of the use of the name that spring immediately to mind are the name of the statistics department at University College London (The Department of Statistical Science) and the new journal Statistical Science published by the Institute of Mathematical Statistics; there must be many others. The idea is that under the broad umbrella profferred by the name statistics, which could for example be regarded as covering all the topics dealt with by the Royal Statistical Society, we need a specific term for the specialist academic discipline which provides the theoretical and methodological underpin- ning for the work done by professional statisticians. The name statistical science seems apt for the purpose since the inclusion of the word science is suggestive of the intellectual rigour which is the basis of the discipline. It provides a useful differentiation from the everyday use of the word statistics in the sense of the compilation and presentation of numerical data.

1.2. The Philosophy of Statistical Science With this nomenclature I now move to the next main theme of this address which is to

review some of the changes that appear to be taking place in statistical science at the present time. Once again, the main agent of change, direct or indirect, is the rapid increase of computational capability. I shall not be concerned so much with forecasts of developments in specific techniques as with the changes in the set of ideas and theories which determine the selection and use of statistical techniques and methodology. For want of a better collective term I shall refer to this set of ideas and theories as the philosophy of statistical science. I am not using the word philosophy here with any abstruse or ethereal interpretation in mind but in a more down to earth sense.

Because of the increasing practical importance of problems involving statistical variability, the search was begun early in this century for a comprehensive mathematical theory of statistical inference from uncertain data. I think it is important that the historical context within which this enterprise was begun should be properly appreciated. There is no question in my mind that the dominating factor which determined the limits of what was considered as achievable in the first half of this century was the primitive state of computing technology at the time.

My first attempt at research on a methodological problem was done jointly with G. S. Watson and I can remember the discussions we had about what we felt we had to do as theoreticians if we were to make a non-trivial contribution to the subject. We thought that two elements were needed. Firstly, whatever the mathematical difficulties encountered on the way, it was essential to finish up with a neatly stated result, the essence of which could be explained to and accepted by an applied worker who took no interest in the mathematical details of the derivation. Secondly, any statistical procedure advocated should be capable of implementation by an applied worker with at most the support of a computing assistant using a desk calculator. The desk calculators of the time were expensive, noisy and slow. Thus the implementation of any newly suggested statistical procedure required a great deal of determination and commitment on the part of the person using the technique in practice.

My contention is that the rigid, almost ritualistic, statistical procedures advocated at the time were determined as much by the exigencies of computational feasibility as by intellectual conviction. Techniques were derived on the basis of mathematical models whose form was simple, usually linear, and which depended only on a small number of parameters. Such models were adopted primarily because it would not have been realistic to set up more complicated models with any hope of implementation.

Undoubtedly most applied workers have always been aware that any statistical model is at best an approximation to reality. There is in real life no such thing as a "true model". Yet much of the discussion of the foundations of statistical inference that has taken place over the past half century has been predicated on the assumption that the model is "true". The



1987] Presidential Address 179

alternative formulations of the inference problems that have been considered relate mainly to the properties of models and there has been too little discussion of the interaction with the underlying statistical reality. Statements about parameter values have been discussed as if parameters had a clearly-defined tangible existence, whereas in most cases they are at best mathematical artefacts introduced only in order to provide the most useful approximation available to the behaviour of the underlying reality. It is all too easy to lose sight of the fact that the real purpose of the analysis is to make statements about this reality rather than about the models that approximate it.

Of course I appreciate that a standard procedure in science is to postulate a model and make inferences about the behaviour of the phenomena under study on the assumption that the model is an accurate one. My point is that because of the manifest imperfections of many statistical models as descriptions of the reality under investigation, this process has been carried a bit too far. The obsessional desire to make "best possible" statements about parameter values in artificially small models has been over-indulged to an extent that seems out of proportion to the true interests of users of statistical methods.

I have suggested that computational limitations were a powerful factor in determining the size and form of the mathematical models used in statistical science. The same can be claimed for the structure given to formal rules of statistical inference. It seemed essential to Fisher and his followers that a complete package of procedures covering collection, analysis and interpretation of data should be provided that was computationally feasible for applied workers. This package had to be laid out as a set of clearcut rules since numerical experimentation with a variety of procedures was not an option that was normally available to the investigator.

I shall argue later that the immense computing power that will be available for almost all statistical work from now on ought to change the perspective from which the role of formal systems of inference in statistical investigations is perceived. My claim will be that in the light of modern techniques of exploratory data analysis, graphical presentation, model selection and model validation a broad eclectic approach on the part of statistical scientists as a professional group is becoming increasingly desirable when discussing procedural options with students and clients. I shall go on to express the hope that the profession will move towards a unified philosophy of statistics in which alternative and even competing ideas and procedures will be accommodated and presented to users of statistics in a spirit of tolerance and objectivity.

2. DISSEMINATION OF ECONOMIC AND SOCIAL DATA In this section I wish to consider some of the changes that are taking place in the organisation

and dissemination of economic and social data as a result of the current explosive developments in computer technology. We have now reached the situation where in western industrial societies micro-computers or computer terminals are widely available to school children, university students and people in jobs. Data are already being disseminated by magnetic tapes, floppy discs, optical discs and by national and international computer networks as well as by the printed page. What I plan to do is refer first to a number of developments in the area that are of interest to me and then raise some related questions of public policy.

2.1. ESRC's Contributions to Data Dissemination The first major step in the exploitation of computer technology for data dissemination in

the social field in this country was the founding of the ESRC Data Archive in 1967. This was established jointly by the Social Science Research Council (now the Economic and Social Research Council or ESRC) and the University of Essex to preserve computer-readable information about British society for research workers. The Archive is still financed substantially by ESRC. Originally most of the material stored came from commercial polling organisations and from academic social surveys and the idea was that this repository of information would provide a rich stock of data which would be available for future social research. Subsequently, various government departments came to realise the value to government itself as well as to the academic community in storing their own data in a readily



180 DURBIN [Part 3. accessible form in a public respository. As a result, many of the large data sets compiled by government such as those from the Family Expenditure Survey, the General Household Survey and Census Small Area Statistics are deposited in the Archive and are routinely available for research purposes at handling cost only. Indeed, data from the public sector now constitute the greater part of the input to the Archive. Now that the funds available for direct collection of data from individuals and households for academic research have almost vanished, the Archive supplies a vital need for economic and social research.

Data are still mainly distributed by magnetic tape though floppy and optical discs can also be used. The system has recently been connected to JANET, the university computer network, so in principle large amounts of data can be distributed to research workers throughout the country via the network; however, in the short run the network will probably be more useful for use interactively for such things as key-word searches, interrogation of the file catalogue, and so on.

This is not the occasion to go any deeper into the Archive's work except to refer to the Domesday project which it has just completed jointly with the BBC. This was intended to celebrate the 900th anniversary in 1986 of the Domesday Book and makes use of up-to-date interactive video disc technology. A vast amount of spatial and other data including 24,000 maps, 250,000 pages of information, 50,000 photographs and 200 megabytes of data, as well as movie and sound recordings, is held on only two video discs. These are deployed interactively on a microcomputer connected to a video recorder of a type expected to be available in schools throughout the country. The project is a brilliant success and it has enormous potential value for the statistical education of schoolchildren as well as providing a useful data source for workers in both the public and private sectors. It can be recommended as a good example of interactive visual interrogation of a phenomenally large data set.

Another data source is the Central Statistical Office's computerised data base. This consists of the more important economic and social time series and in addition to its use in government it has been available for some time to private sector users through a commercial computer bureau and to academic users through the Essex archive. The ESRC has recently set up a Centre in Economic Computing at the London School of Economics and this has developed software which provides research workers with easy access to a rearranged form of the CSO database as well as to the Bank of England databank and the CRONOS databank of the European communities. This facility is available online to academic research workers through the JANET network and a floppy disc version for mail distribution is being developed for use on microcomputers.

A major use of economic time series data is for the construction and use of macroeconomic models. The ESRC has set up a Macroeconomic Modelling Bureau at Warwick University for the purpose of facilitating access by research workers to the major models that have been database as well as to the Bank of England databank and the CRONOS databank of the Bank of England Model as well as five models of various types supported by ESRC at various academic centres. These models together with various supporting services are kept up to data and are available for research including forecasting to workers throughout the country through JANET.

2.2. Dissemination of Small Area Statistics Progress in computerised dissemination of survey and time series data has undoubtedly

been impressive. Even more dramatic, however, has been the impact of the computerised dissemination of small-area statistics. At the heart of this development is the concept of the decennial Census of Population as a multi-purpose socio-economic data base. Computerised small-area statistics from the 1981 Census giving detailed social and economic data for enumeration districts, say about 150 households in each, are sold by the Office of Population Censuses and Surveys (OPCS) and by various commercial agencies and are available for research purposes through the ESRC Archive.

This rich data set is in process of rapid exploitation but only a few brief points can be made




here. Geographers at Durham University have developed two important systems on behalf of public sector users. The first, SASPAC, was produced for the Local Authorities Management Services and Computing Committee (LAMSAC) by organising the basic data set together with other relevant data in a form which facilitates use in local government. The other system, NOMIS, was developed jointly with the Centre for Urban and Regional Development Studies of Newcastle University for the Manpower Services Commission. It is an online system kept continuously up to date and constructed by adding to the small area data set local information on unemployment, vacancies etc. together with other relevant data, the whole being organised for instant online access. It requires little imagination to appreciate the value of rapid access to computerised information of this kind for intelligent local administration as well as for commercial work in a complex modern society. The data resources of both systems are also available for research purposes at marginal cost.

A second key database for small areas is the postcode directory, held in various computerised forms by the Post Office and other organisations including OPCS. The postcode consists of up to seven letters and numbers which define the location of an address and permit four different levels of geographical aggregation. The advantages of postcodes over census enumeration districts is they are much smaller-leaving aside business and institutions there are only about fifteen addresses per postcode. By adding a map reference for position finding and addresses from the Post Office, the Electoral Register or elsewhere, a statistical tool is created which can be linked with other local economic and social data from Census local area statistics and other sources to give very precise information about local characteristics. This information can then be linked to households and individuals by microeconomic and microsocial statistical modelling of individual behaviour. The addition of information to the data by modelling adds considerably to the value of the basic area statistics.

I need not dwell on the potential commercial value of this kind of information, not only for the direct target mailing business but also for other commercial applications such as the organisation of the retail trade and indeed the planning of the provision of regional and local facilities of all kinds. It is not therefore surprising that the main impetus for the development of computerised databases at this level of disaggregation is coming from the private sector. Further prospects for organisations with access to the relevant information are inclusion of credit rating data, shopper's card data, credit card transfers, particularly when these become automated under the electronic point of sales system, and so on. While there is no reason at the moment to believe that confidentiality as regards individuals will be breached it is clear that market pressures for trade in local information will be very strong. From the standpoint of the rights of the individual it appears that vigilance is going to be called for in the years to come. A further question is the extent to which valuable data of this kind obtained by commercial interests will be made available for legitimate academic research and on what terms. Some of these issues have been subjected to a detailed scrutiny from the standpoint of academic geographers by Openshaw and Goddard (1987).

Finally I should mention that the Department of Trade and Industry has started up very recently a Tradeable Information Initiative under which statistical information held by government can be made available to firms in the private sector at production cost or market value depending on the circumstances. However, it is too early to say how successful the scheme will be or what the spin-off will be for academic research.

3. SOME POLICY QUESTIONS

3.1. Government Statistical Policy This brief review of developments in data dissemination raises some important questions

of public policy. In a different world from the one we actually live in, government leaders might have been so excited by the opportunities for improving the efficiency of our society that are offered by technological change in information processing that they felt impelled to



182 DURBIN [Part 3,

expand expenditure on government statistics. In fact the reverse has happened and over the last six years or so the numbers employed in the Government Statistical Service have been reduced by over 25 per cent.

Government policy on statistics was set out in the 1981 White Paper (Cmnd 8236). This was discussed at a special meeting of this Society and a summary of the discussion has been reported by Hoinville and Smith (1982); the main parts of the White Paper are quoted in the appendix to their paper. I think that most statisticians would take it as self evident that government has an obligation to collect and publish statistical data not only for its own purposes but also to inform the public about conditions in society. Yet there is virtually no mention of any such obligation in the White Paper.

The main purpose of the White Paper was not to consider matters of general statistical policy but to announce cost-cutting measures arising from Sir Derek Rayner's review of statistical services in government. The nearest that the document comes to a statement of general principle on the matters I am discussing is in quoting, presumably with approval, one of Sir Derek Rayner's thirty recommendations (paragraph 17.1) which reads as follows:

Information should not be collected primarily for publication. It should be collected primarily because government needs it for its own business.

This recommendation encapsulates in stark form the shift of emphasis that occurred as a result of the Rayner review towards the specific purposes of government. While it is obvious that governmental statistical services should be efficiently run and should serve the needs of government well, the public also have an interest in the dissemination of data about society and it should be openly accepted that government has an obligation to collect and publish statistical information in the interests of society as a whole.

None of these remarks should be interpreted as criticism of the statistical civil servants themselves. Britain has a good system of statistical publications by international standards and within the manpower and other constraints determined by ministers the government statisticians have done a good job in maintaining and developing the system. My main concern has been with the impact of developments of computer technology on dissemination and I imagine that one of the consequences of both the staff cuts and the policy emphasis could have been that initiatives that would otherwise have been pursued in the public dissemination of data may have been inhibited.

Looking to the future, most statisticians and users of statistics would no doubt wish to see greater resources devoted to official statistics together with a shift of emphasis towards publication for the public benefit. However, in the British system there is no clearcut way in which pressure for changes in overall statistical policy can be organised. In most European countries there is a national statistical council or commission composed of representatives of government and of broad areas of interest outside government which either determine or closely influence national statistical policy. Indeed in a paper to the 1986 European Conference of Statisticians by the Netherlands Bureau of Statistics on legal aspects of statistics it is stated that only eleven of twenty-nine European countries surveyed did not have such a commission. Sir Claus Moser (1980) in his Presidential Address to this Society proposed the creation of a National Statistics Council, one of the main functions of which would be to advise government on statistical policy. However, when the RSS Council pursued the matter it found there was not enough support for the proposal and the idea was dropped.

The nearest British equivalent to a national commission is the Statistics Users' Council which is a voluntary body consisting of representatives from interested groups including this Society and the Government Statistical Service. It has organised a successful series of annual one-day conferences on various aspects of official statistics but it has no responsibility for policy matters and has no official status so far as government is concerned. Thus in many respects it is a typically British institution.

Another relevant consideration is that the British statistical system is more decentralised




than that of most other countries. Production of statistical data is largely the responsibility of the individual government departments concerned and is not under direct control of the Central Statistical Office. Thus in order to influence policy on particular items representations need to be channelled to the appropriate departments. So far as overall policy on the scale and direction of statistical services is concerned it appears that there is no obvious channel for representations from outside government except through the usual parliamentary and political processes. Whether this is as it should be remains a matter for continuing debate. Meantime the problem of finding the right forum for discussion of overall statistical policy remains unresolved.

3.2. Funding of ESRC I will conclude this section by referring briefly to the role of the Economic and Social

Research Council. It will be clear from what was said earlier that ESRC plays an important part in the dissemination of economic and social statistics for research purposes through the Data Archive, the Modelling Bureau and the Centre in Economic Computing. Yet the financial basis of the Council's existence remains precarious. At the present time the ESRC's budget is more than 25 per cent less after deflation by the retail price index than it was eight years ago. During this time the Council's allocation as a percentage of the total science vote has gone down from 5.5 per cent to 3.8 per cent.

ESRC's income is determined by the Secretary of State for Education and Science acting on the advice of the Advisory Board for Research Councils (ABRC), a body which consists of independent members, heads of research councils, chief scientists of government departments and the Chairman of the UGC. ESRC's financial difficulties arose initially from the well known scepticism of the former Secretary of State for Education and Science about the value of research in the social sciences, a view shared by some other members of ABRC. It is likely that this scepticism will persist in the future to some degree.

Part of the problem arises from a misunderstanding of what the social sciences are about. I have discussed with people from science and technology on a number of occasions what they regard as the comparative failure of the social sciences relative to the spectacular success of natural science. This is sometimes attributed either to lack of proper scientific rigour on the part of social scientists or to the use of defective methodology. There is of course always room for further exchanges of methodology between the natural and social sciences but I do not personally believe that either of these explanations accounts for what might appear to the outside observer to be the disappointing performance of some of the social sciences when assessed relative to the performance of natural science. The true explanation is that all the social sciences are directed one way or another towards the study of human behaviour and this depends on processes in the human mind. Unlike, say, the physiology of the brain, these mental processes cannot be reduced ultimately to physics and chemistry and they necessarily involve a substantial amount of variability and unpredictability.

There is in fact no essential difference between the basic methodological approaches of the natural and the social sciences. Both are based on objectivity, intellectual rigour and dispassionate analysis of observations. The justification of the social sciences is not to be found in measuring their performance relative to various branches of the natural sciences; it is rather that the progressive betterment of society depends to an important degree on the state of our knowledge both as regards facts and also as regards the processes underlying behaviour. Thus the extent to which economic and social research should be supported from public funds depends largely on the extent to which the research helps society to understand itself.

This brings me back to the ABRC which, as I indicated earlier, advises the Secretary of State on the allocation of the science vote. Most of the members of ABRC are natural scientists and technologists so there is a natural anxiety among some social scientists that under the heavy pressure on the science vote from other research councils ESRC's allocation might be cut even further. If this is done there is a risk that ESRC will no longer be viable. In defence



184 DURBIN [Part 3,

of ESRC's claim for funding I would argue that research in the social sciences is needed today in order to generate the ideas and knowledge that will be required for the development of policy and institutions in the economic and social fields in the future. The debate about the extent to which the social sciences can be regarded as true sciences in the sense in which this term is used in the natural sciences seems to me less important. I have discussed earlier the increased scope for dissemination of economic and social data through the use of modern information technology and I have referred to some of the contributions that ESRC has been making in the field. It would be regrettable if the scale of these and other contributions had to be reduced because of further reductions in ESRC's budget.

4. DEVELOPMENTS IN STATISTICAL SCIENCE I shall now jump from the hard ground of economic and social data to the rarefied air in

which statistical ideas are debated. However, my intention is not to discuss ideas in the abstract but to review some current developments in statistical practice and to go on from this to consider what the ideological needs of applied statistics will be in the future. Although I shall finish up by discussing philosophical ideas my orientation will be practical and pragmatic rather than ideological in any purist sense.

4.1. Current Developments in Statistical Practice I expressed earlier the view that the rather rigid form in which inference procedures were

laid out in earlier decades arose partly because of the severe computational restrictions of the times. Clearcut numerical techniques had to be laid down which were capable of implementation on desk calculators and there was very little scope for flexible manipulation of data by the investigator. The position today is entirely different. The applied statistician can sit at a micro-computer, a work station or a mainframe terminal with a vast range of graphical and analytical techniques at his disposal. He can analyse immensely larger and more varied data sets than could be coped with in earlier times. He can proceed interactively step by step, examining the results at each stage before deciding what to do next. He can plot and examine the data in imaginative ways, adjust outliers and transform the observations into more manageable forms. Most importantly, he can adopt a highly flexible attitude towards model selection, checking the performance of a variety of models, linear and non-linear, against his particular data set. For each tentative model he can compute a variety of diagnostic statistics, not necessarily interpretable in any parametric sense but each intended to measure the discrepancy between the model and the data in some particular direction.

Having got the model that he regards as the most suitable for his purpose, the sophisticated worker will be aware that it represents at best only an approximation to the real situation he is investigating, and perhaps not a very good approximation either. He will therefore be wary of rushing straight into an "optimal" analysis based on the assumption that the model is "correct". IHe may wish to carry out sensitivity tests intended to reveal the effects on the analysis of particular types of departure from the assumptions of the model, and he will almost certainly prefer an analysis that is slightly suboptimal but robust against departures from the assumptions, to an optimal analysis that is highly sensitive to these departures. The best workers will always be conscious of the fact that the ultimate purpose of their analysis is to make statements about the real situation they are investigating and not about properties of models. Finally, if alternative package programs are available from different schools of inference, he might wish to experiment with these in order to form a judgement about which appears to provide the most informative analysis for his particular problem and data set.

All this is far removed from the picture of the statistician as one who conceives the design, analysis and inference of a statistical investigation as a single operation. Yet this simplistic concept has dominated most discussions of statistical inference for many years. In addition, the data are usually assumed in such discussions to be generated by a model which is true, has a simple form and is determined by a small number of parameters each of which




is to be thought of as having a credible real existence. Discussions of the merits of competing systems of inference on the basis of oversimplified assumptions of this kind do not seem to have much relevance to practical needs.

The distinguishing characteristics of statistical investigations arise from variability and uncertainty in the observations. Everyone is agreed that an intellectual framework is needed within which the problems arising from variability and uncertainty can be discussed in appropriately disciplined ways. My view is that current systems of inference are too narrowly focussed to be adequate for the diversity of useful techniques of statistical analysis that are currently emerging. An appropriate ideological framework ought to take proper account of the fact that practical statistical work is not done in a single stage after which the probabilities of various outcomes can be definitively calculated once and for all. Rather, it is a sequential process in which the data are looked at from a variety of viewpoints at different stages and where at each stage it may be helpful to make assessments based on probabilistic calculations even though it is recognised that these assessments interact in complicated ways.

I shall argue that no monolithic system of inference can meet these practical needs and that what is required instead is a flexible, pragmatic and eclectic system of ideas and theories which I call a philosophy of statistical science. This will need to embrace a wide range of inferential procedures regarded as legitimate for use in different circumstances by the majority of professional statistical methodologists. It seems evident that a broadly based philosophy of this kind would need to accommodate inferential techniques based on sampling theory, likelihood and Bayesian approaches of various kinds. However, before claiming that the case for such a philosophy has already been established I wish to discuss some further points in the argument.

4.2. Objective and Subjective Probability Statistical inference is based on probability theory and it was obvious when the theory

originated with games of chance in the 17th century that it had two aspects. One was the objective behaviour of the chance mechanism in the real world and the other was the subjective assessment of probability by the gambler. It would therefore seem quite natural to have two distinct but consistent models of probability, one an objective model governing the observed behaviour of the mechanism and the other a subjective or personalist model reflecting the beliefs of the observer.

However, it is not universally accepted that an objective probability model can legitimately be constructed for a game of chance. If one takes a simple game such as tossing a coin, some people claim that the outcome is not a matter of chance but is determined by the initial conditions and the laws of motion. It is quite true that if the tossing were done by a precisely constructed machine and the average number of rotations of the coin was small then the distribution of outcomes need not be consistent with the predictions of the binomial distribution. It is therefore claimed that the postulation of an objective probability model lacks scientific validity; the randomness that we attribute to the outcomes is a purely subjective phenomenon arising from the inadequacy of our powers of observation and our imperfect knowledge of physical laws. Since the source of the randomness is subjective it is suggested that the appropriate response is to represent randomness by a subjective model.

Until recently there has undoubtedly been a gap in theory between the deterministic behaviour of physical bodies at the micro level and the apparent randomness they exhibit at the macro level. This has created a difficulty in the understanding of the behaviour of physical phenomena which, while obeying the laws of deterministic physics, appear to exhibit stochastic behaviour. However, it appears that theories of chaotic behaviour have recently been developed which effectively bridge the gap in the sense that it has been shown using the modern theory of nonlinear dynamics that deterministic systems containing only a few elements can exhibit genuinely stochastic behaviour obeying the laws of probability. This behaviour arises from exponential build-up of small errors in finite systems and has nothing to do with limiting



186 DURBIN [Part 3,

behaviour in large aggregates as in statistical mechanics. I hasten to disclaim any expert knowledge of the area and quote two relatively non-technical papers (Crutchfield et al., 1986, and Ford, 1983) in justification. Nevertheless if one puts these theories together with Kolmogorov and Martin-Lof's theory of randomness it appears that the case for the postulation of objective probability models in physical situations such as games of chance has been strengthened.

Of course, many statisticians and scientists have been unconcerned about the transition from micro to macro behaviour and have been content to accept objective probability models as providing an adequate approximation to the observed behaviour of macro physical systems, such as games of chance, in the same spirit as mathematical models are accepted in other branches of physics. In this approach, models are taken as valid to the extent that predictions of the model are consistent with observations of behaviour; if discrepancies are found the model is modified. Some critics object to the fact that probability is involved in assessing the significance of the discrepancies, but most statisticians do not find their objections compelling. Similar considerations apply to objective probabilistic modelling in other areas such as genetics. In all these areas objective probability models have been used successfully and this adds to their vindication. It is therefore evident that a comprehensive philosophy of statistical science should include provision for objective probability models.

There have been many subjective theories of probability going back as far as Leibnitz and Jacques Bernoulli and an interesting review of their historical origins has been given by Hacking (1984). For simplicity I shall restrict myself to the Ramsey- de Finetti- Savage (RDS) theory of personal probability since this is the dominant subjective theory in contemporary statistics. There has been a great deal of controversy over several decades about the use of personal probability for statistical analysis in scientific contexts. However, I imagine that few would object to its use in decision analysis where the object of the analysis is to assist in the process of decision taking under uncertainty. Leaving aside controversial aspects for the moment it is clear that statisticians can either often, or at least occasionally, expect to be professionally involved in decision situations either as individuals or in advising other individuals or organisations. It follows that our philosophy should be broad enough to include subjective probability models including the RDS model.

Enthusiastic RDS adherents sometimes claim that de Finetti has shown that objective probability is a "special case" of personal probability and can therefore be dispensed with. However, the situation is rather that he showed how objective probabilistic phenomena can be handled within the personalistic theory. In opposition to this claim, many people believe that objectivity is the basic principle of science; when objectivity is kept constantly in mind as a guiding principle, it helps in the discovery of the truth and in communicating the truth to others. Thus if the data are objective and the purpose of the analysis is objective, many statisticians feel that the model should be objective and the discussion of the results should also be objective. From this point of view it does not seem relevant to be told that objective elements can be incorporated within an overall subjective framework.

4.3. Statistical Procedures I now turn to consider the range of analytical procedures that should be admitted as

legitimate within a unified philosophy of statistical science. It follows from my earlier remarks on the iterative nature of statistical work that I regard it as fruitless to attempt to embody these procedures within a single coherent logical framework. The diversity of needs is too great for that to be feasible.

Let us begin by considering significance tests. Now that exploratory model selection and evaluation is becoming more widely practised a great variety of diagnostic test statistics are becoming available. These statistics measure the discrepancies in various directions between the postulated model and the data and so are highly informative to the investigator in the task of choosing between models. The significance of these statistics is tested by comparing




their observed values with their sampling distributions and there is no reason why this process should not be found helpful and illuminating even if likelihood or Bayesian inference is used at a later stage. Many such statistics cannot be parametrised in any meaningful way so they cannot readily be accommodated in a full Bayesian analysis. I conclude that a unified philosophy should include significance tests.

Similarly a unified philosophy should include Bayesian techniques of various kinds beginning with the full RDS treatment for decision situations and other circumstances where the requisite preconditions are applicable. There is sometimes an unfortunate tendency to equate the word Bayesian with strict adherence to RDS theory but of course the range of applications of Bayes theorem is much wider than this. First there is the case where the analysis emerges directly from an objective model with known prior as in quality control. Secondly there is the use of the technique for cases where an objective probability model is used but the statistician wishes to regard the observed sample as fixed and the parameters as variable; the prior can be of a Jeffreys type or it can reflect prior knowledge or it can be hypothetical. Thirdly there is the pragmatic use by an eclectic statistician in cases where package programs are available; he may wish to try out different types of non-Bayesian or Bayesian analysis on his data set in order to discover the technique that seems to suit his particular situation best.

It will be obvious that part of my objective in advocating the adoption of an ecumenical philosophy as the basis for inferential aspects of statistics is to assist in de-fusing the controversy between "Bayesians" and "non-Bayesians". While the controversy has become tedious to most methodological statisticians, it remains unresolved and as a result the credibility of the subject with people outside remains damaged. I find myself returning constantly to the following transparent truism. If two capable statisticians with different ideological preconcep- tions are confronted with the same data set, and if the data set is informative about the questions at issue, then it is scarcely credible that they can emerge with conclusions which are essentially different from a practical point of view; on the other hand if the data set is uninformative then this ought to be revealed by both analyses. The reason this is truism is that the statistician's job is to extract relevant information from data and I assume that, whatever their ideologies, each of two capable statisticians would perform this task in an effective way.

What I am seeking is to display this controversy against the perspective of current statistical practice. I have claimed that the typical statistical investigation is a messy multistage process for which a wide variety of tools is potentially available. It is unrealistic to expect that there could exist a flawless logical system that would chart out a unique path for the analysis. Moreover, it would be counterproductive to try to force a person to commit himself in advance to any particular ideology since this might deprive him of access to potentially useful techniques. The practitioner should be free to exploit whatever techniques are available and to select from among them that combination which appears to him best suited to the task of extracting relevant information from his data. From this point of view we see Bayesian and non-Bayesian techniques not as irreconcilable antagonists facing each other across an unbridgeable divide but in a more humble spirit as alternative procedures for analysing statistical data.

Thus I am suggesting that the profession should sink its differences, accept the main features of the major probability and inference models as legitimate within a unified philosophy and agree to present the alternatives to students and clients in a spirit of tolerance and objectivity. Within the system, individual methodologists would be encouraged to develop new techniques of analysis from their own ideological standpoints and to attempt to persuade others to use them. What would be discouraged would be the denial of legitimacy to other inferential standpoints. The idea would be that in the long run, success of any technique or approach would be determined more by its perceived value in applications than by a priori arguments about its ideological purity.

Of course I am not suggesting there should be a free for all in which applied workers would be free to use techniques incorrectly through ignorance of their proper applicability. On the



188 DURBIN [Part 3,

contrary, the need for sound education and strong leadership from professional statisticians on legitimacy of usage would remain a matter of considerable importance.

One final point. My claim that there is no single logically coherent system of ideas that can satisfy all the needs of modern applied statistics should not be taken as an indication that I am against work on the logic of inferential systems. On the contrary I think it most important for the healthy development of the subject that work on the internal and external logic of these systems should be prosecuted with vigour.

I have expounded the case for a unified philosophy from a slightly different point of view in Durbin (1987). The arguments there were illustrated by referring to a particular piece of applied work, namely the study of the effects of seat belt legislation on road casualties.

4.4. Evolutionary Aspects As the final theme of this address I wish to introduce a rather different element into the

perspective from which the status of logical systems in statistical science is perceived. I do so in a spirit of diffidence and trepidation since I am aware that some people will regard the ideas I am about to expound as irrelevant to my main thesis while others will regard them as eccentric. Nevertheless, if one takes the long view I believe that the ideas are both relevant and valid, so on the principle that a president ought to be allowed to address adventurous thoughts to interested minorities as well as sober thoughts to the majority, let me proceed.

I start with the proposition that a statisticians's attitude to basic philosophical questions, such as the relation between human thought and external reality, will affect his posture in relation to the foundations of statistical science. The belief is growing that ideas about philosophical questions are bound to change fundamentally over the coming years due to the recent growth in understanding of the mechanisms of evolutionary biology. It is becoming evident that a fruitful way of improving our understanding of these questions is to think in terms of the origins and development of the human mind during the process of biological evolution. By studying the evolutionary development of the mechanisms which control the behaviour of organisms in relation to such matters as gaining food, reproduction and avoiding predators, we can gain insight into the way the human mind has evolved and hence improve our understanding of the philosophical basis of reasoning.

Taking for granted the biological consensus on the evolution of the human species by the neo-Darwinian process, let us consider what this approach can tell us about the nature of human logical thought and its relation to the external world. The first point is that whatever the transcendental logic that may exist in the vastness of the universe, there does not seem to have been any necessity for the human species to have mastered the full essence of this during the evolutionary process. It seems more reasonable to suppose that humans acquired just enough thinking capacity to ensure survival as primitive hominids millenia ago. Fortunately the universe appears to be so constructed that the thought mechanisms that evolved for the needs of our remote ancestors have proved powerful enough to enable humans to achieve the extraordinary level of understanding of their environment that they possess today. However, this success does not contain any explicit or implicit guarantee that human logical thought has an absolute or total validity in any transcendental sense. Like the models of natural science it is at best an approximative tool which we may use in a pragmatic way to get as close to the truth as we can; fortunately with a considerable degree of success.

What is the relevance of these thoughts to the philosophy of statistical science? I think that as speculative philosophy becomes increasingly permeated by ideas from evolutionary biology, perspectives on the role of abstract logical systems in science will change. In statistical science, models of probability and systems of inference will be seen less as imperatives and more in the spirit of scientific models which are useful to the extent that they fit the situation under investigation. This is not to suggest that the importance of abstract logical systems should be downgraded; only that there will be a shift towards pragmatism in the perspectives from




which they are perceived. The function of logical systems in ensuring disciplined thought will remain paramount.

Some of these ideas are developed in more detail in my paper (1985) in the International Statistical Institute Centenary volume. Starting from the standpoint of statistical science, the paper attempts to develop a plausible explanation of why humans can do mathematics as well as they can, given that our mental equipment was developed primarily for survival during the evolutionary process. While I wrote the paper in a spirit of intellectual adventure, I believe that the basic arguments in it are sound and I documented them as well as I could. Thus I hope the paper will provide a useful source for statisticians wishing to pursue these questions further.

The quest for an understanding of the relation between human intellectual achievement and human evolutionary origins is a fascinating challenge. While I believe that the case for a unified philosophy of statistical science is largely practical and down to earth, I would like to end by suggesting that our thoughts about this challenge have some modest relevance since they will affect the perspectives from which the theories of statistical science will ultimately be perceived.

REFERENCES

Crutchfield, J. P., Farmer, J. D., Packarad, N. H. and Shaw, R. S. (1986) Chaos. Scientific American, December, 1986, 38-49.

Durbin, J. (1985) Evolutionary origins of statisticians and statistics. A Celebration of Statistics: The ISI Centenary Volume. (A. C. Atkinson and S. E. Fienberg, eds). New York: Springer Verlag.

(1987) Is a unified pilosophy of statistics attainable? J. Econometrics, to appear. Ford, J. (1983) How random is a coin toss? Physics Today, April, 1983, 40-47. Hacking, I. (1984) The Emergence of Probability. (Paperback edition). Cambridge University Press. Hoinville, G. and Smith, T. M. F. (1982) The Rayner review of government statistical services. J. R. Statist. Soc. A,

145, 195-207. Moser, Sir Claus (1980) Statistics and Public Policy (with discussion). J. R. Statist. Soc. A, 143, 1-32. Openshaw, S. and Godard, J. B. (1987) Some implications of the commodification of information and the emerging

information economy for applied geographical analysis in the U.K. Environment andPlanning Series A (forthcoming). White Paper (1981) Government Statistical Services. Cmnd 8236. London: HMSO.

The two last Presidents of the Society responded as follows:

Professor J. A. Nelder: We are fortunate this year in having as President someone who is not only eminent in the social sciences, an area of growing importance, but who is also prepared to tackle major theoretical questions that underlie our subject. In the ISI centenary volume he tackled what is perhaps the most fundamental question of all, namely, the evolutionary origins of statistics-how did the brain that served our hunter-gatherer ancestors on the African savannah go on to develop the idea of, say, characteristic functions and to prove theorems about them?

Today, on the theoretical side, he has raised the question of the unification of the, at present, disparate theories of inference. Those of us who have been campaigning against the rigid view of analysis implicit in too many statistical texts will welcome his description of what a good analysis is like, multi-stage, iterative, and highly flexible. The influence of the computer here cannot be overestimated, particularly in the field of model-checking techniques. Most of these techniques did not exist 15 years ago, and they often need substantial computing. Now we can offer them in GLIMPSE, the front end we are developing for GLIM, with assistance in their use. Such knowledge-enhancement techniques, to use Dr Hand's phrase, represent a new use of computers. What part they will play in a unification of inference remains to be seen. Professor Dawid believes-in fact believes he has proved-"that no approach to statistical inference, Bayesian or not, can ever be entirely satisfactory". I would only remove that qualification "Bayesian or not". The President also asserts "that no monolithic system of inference can meet these practical needs ... ", and he calls for a philosophy, rather than a logic, of statistical science. I look forward eagerly to further arguments from this starting point; in particular, the important activity of model checking needs to be firmly integrated in any framework. At present I don't think it is. The other main component of the address has an equal importance, namely the social consequences of the



190 Presidential Address [Part 3,

information explosion and the implications for public policy. There is a story of a mandarin who said that you should always resist any call for the publication of figures, because next year there would be two sets of such figures, people would compare them, and then they would start asking questions. Exactly. There is a real sense in which information is power, and some kinds of it are more informative than others.

A danger of the information explosion is that of people being buried in statistics, and some institutions are already showing signs of failure to cope with the ever-rising tide of information. While at the ISI meeting in Washington DC I bought a paper at the local kiosk. The man in charge saw my badge, and on being told that it was the ISI conference said "well, I reckon we've got more statistics than we know what to do with". He had a point.

The capacity of a compact disc is alarming-one of them can hold the whole of the big Oxford Dictionary. The power of statistical science to summarize, to fit models which reduce many figures to a few relevant parameter estimates is going to be more and more needed, as a liferaft to keep our heads above the sea of data. As a society, we need to ensure that the President's wise words are not lost, and that we continue to have a voice in public affairs. It is a great pleasure to propose the vote of thanks for this Presidential address.

Sir Walter Bodmer: I was sorry that last year I could not fulfil my obligation as an ex-president to propose a vote of thanks. It is a great pleasure this year to be able to second the vote of thanks to a very thoughtful and stimulating address that really probes the roots of our subject and the basis of the philosophy of statistics. As we have heard, also, from the proposer of the vote of thanks, statistics as a science contrasts with its original use in terms of data gathering, a sense that sometimes distorts the public view of our subject.

I wonder, however, whether academic statistics is primarily the study of statistical techniques and methodologies. Perhaps that has to be accepted, when defined in a narrow sense. However, I do hope that those, such as myself, who became embedded in a subject of application, although trained as statisticians, are not forgotten, and so lost to statistics. When seeking to encourage more people to go into statistics in competition with all these other exciting areas of operational research, information technology and so on, it seems to me that a great effort should be made to keep those trained as statisticians who have become embedded in other subjects in the community of statistics. We should make the case that statistics provides an appropriate-if not perhaps a more appropriate-fundamental quantitative basis for applications in many other fields, in biology, medicine, the social sciences and other areas. We should, in other words, make a special plea to bring people from statistics into other subjects, without detracting from the value of statistics per se.

I was intrigued by the view that computation had limited the sophistication of earlier statistical methodology in applied areas. I would rather have to agree with that. I remember that the great Sir Ronald Fisher, who was my first teacher, certainly always liked neat solutions and simple methods. Yet any of you who knew him (and there are many here who did) will realise what a fiend he was with a calculator. If you ever watched him, you could never follow what he was doing. He seemed to be doing it half on the machine and half in his head. This represented an apparently new and particularly advanced form of parallel processing, which is now commonplace in all sorts of computing! Perhaps that accounts for why some of his statistical methodology in genetics was certainly rather complicated, and led to some of the earliest applications of computing in statistics.

It is not only complexity but also just the large amount of data to be handled and analysed that meant that computing was necessary to obtain useful results. That was certainly true in my endeavours, for example, in the definition of the human tissue typing system.

There is, however, danger, as we have heard, in the uses of computers in this way. There can be too many parameters and too many models, so that we are spoilt for choice. We may no longer understand or have a feeling for what is in that sausage machine of the model builder. The problems of the extreme deviates may be ignored, problems that come with multiple comparisons. That, again, is why I would go back to emphasising the value of statisticians who become embedded in a subject. I think they will have more of a 'feel' for the reality of models-even accepting the fact that models may never truly be real.

Variability is as important in areas outside the social sciences, including biology, as anywhere else. In the written part of Professor Durbin's text there is an interesting comment on the bridge between deterministic models and variability, suggesting that chaos may to some extent fill that gap.

However, that is not necessarily the case. Genetics is a classical example of the applications of statistics. Mendelian ratios are the result of scrambling the immediate products of meiosis, which have no statistical basis-they are an exact 1:1. We could imagine setting up detailed dynamic models of sperm behaviour




to try to account for Mendelism, but I do not think that we would ever get (or ever expect to get) a better result than from the application of the simple statistical aproach to the subject.

There is no doubt that the range and complexity of accessible data is increasing enormously, and one must agree with the importance of this. The whole of the human genome (a subject I am rather fond of discussing) could fit on to much less than one small optical disk, and it is a rather fundamental piece of information.

I very strongly support, as I am sure we all must, the value of, and the need for, comprehensive social data for planning as well as for basic research. It does seem incredibly short-sighted of government not to recognise this. It seems that the Rayner view of what should be done is somewhat analogous to the rather short-term view of an industry that should depend on its research and development, but which often spends far too little on it, with the obvious results that follow.

As a member of the Advisory Board for Research Councils (ABRC), I have to declare a certain interest in the comments on the ABRC. I have to say that the ABRC did actually support the value of the collection of data. The need for government support in that way is highly analogous to the need for support of basic and fundamental research in other areas of science. As in all basic research, although the specific outcomes may be unpredictable, it is clearly predictable that there will be outcomes that will be of value to understanding society, and that therefore some of those outcomes are bound to have economic benefit. Data on a large scale are really the raw material, it seems to me, for basic social science research, whose support is as important as that of any other area of science.

I think that importance is fully accepted, even by the members of the ABRC. But it must also be accepted that the social sciences are the most difficult of the sciences. This is because they put the social problems on top of biology, which in turn is on top of the chemistry, which in its turn is on top of the physics. It is often the physical scientists I believe, who have the greatest difficulty in seeing how anything can be done in such a complex area. They are used to rather cut-and-dried models that give them what they feel is a realistic, simple, mathematically valid picture of the universe. That is not true for biology, let alone for the social sciences.

I think that there is a problem there, in the ABRC and elsewhere, not in a lack of appreciation of the importance of what social science can do but in a lack of familiarity with the approaches and the fact that there are approaches that can be carried out with some success.

I do not think, though, that I need to go into the fact that no research council, even the Economic and Social Research Council (ESRC), is totally perfect. There are problems. One problem that I would particularly mention is that if one agrees, as the President says, that there is no essential difference between basic methodological approaches of the natural and social sciences, then the research organisation should reflect that. There should be some parallelism in the research organisation for social sciences research and that for the physical and biological sciences. I think that there is perhaps some need for thought as to how, in that context, the ways that social science research is carried out might be improved.

Conflicting approaches to statistical analysis must in the end, as has been said, be resolved by the fact that the outcome of an interpretation of data should be the same whatever approach is used. My experience perhaps, admittedly a generation ago, was that the criterion for the validity of any Bayesian approach was that it actually matched and gave the same answer as any other approach. I am sure that nowadays the situation would be slightly more symmetrical.

I am reminded of the variety of different approaches that exists for constructing phylogenetic trees. Notwithstanding how much the supporters of any one approach argue for it as compared to another, they all give essentially the same result.

As in all good discussions, evolution stands on top of everything. It is an intriguing question that our President has looked into, namely the origin of the mathematical and statistical ability that we have. Perhaps we are channelled by our evolution so that all the approaches we take will give the same answer. Would not that be a nice way of thinking about things?

Certainly, we must assume that finding a valid and rational model for the world of the hunter-gatherer is as relevant as finding a rational model for how to deal with modern industrial homo sapiens.

I do, though, wonder a little about how closely related mathematical and statistical abilities are. Does a statistician need slightly more of a touch of reality than a mathematician? In my day, anyone going from mathematics into statistics was considered a mathematical failure-or vice-versa. Perhaps there is still a need to change that.

It is certainly a challenging thought that the ultimate reality may be determined by our evolutionary origin. As our President has put it elsewhere, there are no philosophical imperatives, only biological ones.

I have great pleasure in seconding the Vote of Thanks to the Presidential address.



Documents

Statistics and Statistical Science