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Models and statisticsModels and statistics

Statistical estimation methods, FinseFriday 10.9.2010, 9.30–10.00

Andreas Lindén

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OutlineOutline• What are models?

• Kinds of models

• Stochastic models

• Basic concepts: parameters and variables

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What are modelsWhat are models• A model is a description of reality

– Models ≠ reality– Usually a simplification– Helps to understand reality

• “All models are wrong, but some are useful” (Box)

• The suitable complexity of models can depend on the purpose (e.g. understanding, prediction)

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Examples of modelsExamples of models

http://education.jlab.org/qa/atom_model_02.gif

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http://plaza.fi/s/f/editor/images/model_expo_08_galleria_3.jpg

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http://images.askmen.com/galleries/model/claudia-schiffer/pictures/claudia-schiffer-picture-3.jpg

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http://www.symscape.com/files/images/navier_stokes_equation.png

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Anything can be modelledAnything can be modelled• “My research system is complex and can not

be described in terms of any model”• The thoughts about how a system works

produce a model• In science mathematics is a common language

used to express these thoughts as models• Mathematical modelling is not always easy or

successful

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Stochastic modelsStochastic models• In deterministic models there are no randomness and the

outcome is totally predictable

• Stochastic models include both deterministic and random (stochastic) components

• Statistical inference based on data — reverse engineering– Based on stochastic models– Trying to quantify the role of chance– Any stochastic model can in principle be confronted with data

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VariablesVariables• A variable is some quantity of interest that shows variation

– Different replicates– Different individuals– Varies in time– Spatial variation

• Typically measurable• Subject to data collection• In a statistical model:

– Explanatory variables– Response variable

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Examples of variablesExamples of variables• The number of migrating sparrowhawks

counted on a particular day

• The number of breeding pairs in a nestbox population of pied flycatchers

• The clutch size (number of eggs) in each nestbox

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ParametersParameters• Defines model properties

• Underlying approximating metrics

• The prefix para- (Ancient Greek). Wiktionary:– 1) beside, near, alongside, beyond;– 2) abnormal, incorrect;– 3) resembling

• In statistics usually unknown and estimated

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Examples of parametersExamples of parameters• Population characters of the flycatcher

population– Intrinsic growth rate– Carrying capacity

• The average clutch size

• The variance of clutch size

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Variables vs. parametersVariables vs. parameters• Important to distinguish…

– Variables are observable/measurable and varies– Parameters are often imaginary defining model properties

• In linear regression

• …but there are grey zones– Stochastic, time-varying parameters– Latent variables– State-variables (e.g. populations size)

Variable

Parameter