Introduction to WinBUGS Olivier Gimenez. A brief history 1989: project began with a Unix version called BUGS 1998: first Windows version, WinBUGS

Introduction to WinBUGS

Olivier Gimenez

A brief history

1989: project began with a Unix version called BUGS

1998: first Windows version, WinBUGS was born

Initially developed by the MRC Biostatistics Unit in Cambridge and now joint work with Imperial College School of Medicine at St Mary's, London.

Windows Bayesian inference Using Gibbs Sampling Software for the Bayesian analysis of complex statistical

models using Markov chain Monte Carlo (MCMC) methods

Nicky Best

Imperial College Faculty of Medicine, London (UK)

Thomas Andrew

University of Helsinki, Helsinki (Finland)

David Spiegelhalter

MRC Biostatistics Unit Institute of Public Health

Cambridge (UK)

Wally Gilks

MRC Biostatistics Unit Institute of Public Health

Cambridge (UK)

Who?

How to obtain and install WinBUGS

1. downloadable from:

http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml

(... see section Obtaining the File to download WinBUGS14.exe)

2. to install WinBUGS:

Exit all other programs currently running (particularly if using Windows XP); Copy WinBUGS14.exe to your computer; Double click on WinBUGS14.exe and follow the instructions in the dialog box; You should have a new directory called WinBUGS14 within Program Files;

Inside the WinBUGS14 directory is a program called WinBUGS14.exe; Right-click on the pretty WinBUGS icon, select `create shortcut', then drag this shortcut to the desktop;

Double click on WinBUGS14.exe to run WinBUGS14.

How to obtain and install WinBUGS To obtain the key for unrestricted use:

Fill in the registration form

~1h later, you will receive an email from Bugs with subject

WinBUGS registration - AUTOMATIC RESPONSE!

Follow the instructions...

Congratulations, you're ready to use WinBUGS

Principle You specify the prior and build up the likelihood

WinBUGS computes the posterior by running a Gibbs sampling algorithm, based on:

(|D) / L(D|) ()

WinBUGS computes some convergence diagnostics that you have to check

Demographic components (fecundity, breeding success,

survival, etc…)

A biological example throughoutWhite stork (Ciconia ciconia) in Alsace 1948-1970

Climate(Temperature, rainfall, etc…)

15.1 67 13.3 52 15.3 88 13.3 61 14.6 32 15.6 36 13.1 72 13.1 43 15.0 92 11.7 32 15.3 86 14.4 28 14.4 57 12.7 55 11.7 66 11.9 26 15.9 28 13.4 96 14.0 48 13.9 90 12.9 86 15.1 7813.0 87

2.551.852.052.883.132.212.432.692.552.842.472.692.522.312.072.352.981.982.532.212.621.782.30

WinBUGS & Linear Regression

YNumber of chicks per pairs

T Temp. May (°C)R Rainf. May (mm)

1. Do temperature and rainfall affect the number of chicks?

Yi = + r Ri + t Ti + i , i=1,...,23i i.i.d. ~ N(0,2)

2. Regression model:

3. Estimation of parameters: , r, t,

4. Frequentist inference uses t-tests

Yi i.i.d. ~ N(i,2), i=1,...,23

i = + r Ri + t Ti

WinBUGS & Linear Regression

15.1 67 13.3 52 15.3 88 13.3 61 14.6 32 15.6 36 ... ...13.0 87

2.551.852.052.883.132.21 ...

2.30



Estimate Std. Error t value Pr(>|t|) temperature 0.031069 0.054690 0.568 0.57629 rainfall -0.007316 0.002897 -2.525 0.02011 *

Linear Regression using Frequentist approach

Y = 2.451 + 0.031 T - 0.007 R

15.1 67 13.3 52 15.3 88 13.3 61 14.6 32 15.6 36 ... ...13.0 87

2.551.852.052.883.132.21 ...

2.30



Linear Regression using Frequentist approach

Influence of Rainfall only


Y = 2.451 + 0.031 T - 0.007 R

Running WinBUGSWhat do you need?

1 - a model giving the likelihood and the priors

2 - some data of course

3 - initial values to start the MCMC algorithm

Running WinBUGSThe model

use the WinBUGS command 'model'

don't forget to embrace the model with {...}

Define the likelihood...Yi ~ N( + r Ri + t Ti ,2)

Note: 2 = 1/

Specify the priors

We use noninformative or vague or flat priors

here

Monitor any other parameter you'd like to... e.g. 2 = 1/

Running WinBUGSData and initial values

Use 'list' structures (R/Splus syntax)......and 'vector' structures (R/Splus syntax)

Running WinBUGSOverall

1 - a model giving the likelihood and the priors

2 - data

3 - initial values

1- check model

2- load data

3- compile model

4- load initial values

5- generate burn-in values

6- parameters to be monitored

7- perform the sampling to generate posteriors

8- check convergence and display results

Running WinBUGSAt last!!

Running WinBUGS1. Check model

Running WinBUGS1. Check model: highlight 'model'

Running WinBUGS1. Check model: open the Model Specification

Tool

Running WinBUGS1. Check model: Now click 'check model'

Running WinBUGS1. Check model: Watch out for the confirmation at the

foot of the screen

Running WinBUGS2. Load data: Now highlight the 'list' in the data

window

Running WinBUGS2. Load data: then click 'load data'

Running WinBUGS2. Load data: watch out for the confirmation at the foot of

the screen

Running WinBUGS3. Compile model: Next, click 'compile'

Running WinBUGS3. Compile model: watch out for the confirmation at the

foot of the screen

Running WinBUGS4. Load initial values: highlight the 'list' in the

data window

Running WinBUGS4. Load initial values: click 'load inits'

Running WinBUGS4. Load initial values: watch out for the confirmation at

the foot of the screen

Running WinBUGS5. Generate Burn-in values: Open the Model

Update Tool

Running WinBUGS5. Generate Burn-in values: Give the number of burn-in

iterations (1000)

Running WinBUGS5. Generate Burn-in values: click 'update' to do the

sampling

Running WinBUGS6. Monitor parameters: open the Inference Samples Tool

Running WinBUGS6. Monitor parameters: Enter 'intercept' in the node box

and click 'set'

Running WinBUGS6. Monitor parameters: Enter 'slope_temperature' in the node box

and click 'set'

Running WinBUGS6. Monitor parameters: Enter 'slope_rainfall' in the node box and

click 'set'

Running WinBUGS7. Generate posterior values: enter the number of samples you want

to take (10000)

Running WinBUGS7. Generate posterior values: click 'update' to do the sampling

Running WinBUGS8. Summarize posteriors: Enter '*' in the node box and

click 'stats'

Running WinBUGS8. Summarize posteriors: mean, median and credible

intervals

Running WinBUGS8. Summarize posteriors: 95% Credible intervals

tell us the same story


Running WinBUGS8. Summarize posteriors: 95% Credible intervals

tell us the same story


Running WinBUGS8. Summarize posteriors: click 'history'

Running WinBUGS8. Summarize posteriors: click 'auto cor'

Problem of autocorrelation

Coping with autocorrelationuse standardized covariates

Coping with autocorrelationuse standardized covariates

slope.rainfall

lag

0 20 40

-1.0 -0.5 0.0 0.5 1.0

slope.temperature

lag

0 20 40

-1.0 -0.5 0.0 0.5 1.0

Re-running WinBUGS1,2,...7, and 8. Summarize posteriors: click 'auto cor'

autocorrelation OK

slope.rainfall sample: 1000

-0.6 -0.4 -0.2

0.0 2.0 4.0 6.0 8.0

slope.temperature sample: 1000

-0.4 -0.2 0.0 0.2

0.0 2.0 4.0 6.0 8.0

Re-running WinBUGS1,2,...7, and 8. Summarize posteriors: click 'density'

slope.rainfall

iteration

1041 1250 1500 1750

-0.4 -0.3 -0.2 -0.1

-2.77556E-17

slope.temperature

iteration

1041 1250 1500 1750

-0.2 -0.1 0.0 0.1 0.2 0.3

Re-running WinBUGS1,2,...7, and 8. Summarize posteriors: click 'quantiles'

Running WinBUGS8. Checking for convergence using the Brooks-Gelman-

Rubin criterion

• A way to identify non-convergence is to simulate multiple sequences for over-dispersed starting points

• Intuitively, the behaviour of all of the chains should be basically the same.

• In other words, the variance within the chains should be the same as the variance across the chains.

• In WinBUGS, stipulate the number of chains after 'load data' and before 'compile' (obviously, as many sets of initial values as chains have to be loaded, or generated)

Running WinBUGS8. Checking for convergence using the Brooks-Gelman-

Rubin criterion

slope.temperature chains 1:2

iteration

1 5000 10000

0.0

0.5

1.0

1.5

slope.rainfall chains 1:2

iteration

1 5000 10000

0.0

0.5

1.0

The normalized width of the central 80% interval of the pooled runs is green

The normalized average width of the 80% intervals within the individual runs is blue

Re-running WinBUGS1,2,...7, and 8. Summarize posteriors: others...

• Click 'coda' to produce lists of data suitable for external treatment via the Coda R package

• Click 'trace' to produce dynamic history changing in real time

15.1 67 13.3 52 15.3 88 13.3 61 14.6 32 15.6 36 13.1 72 13.1 43 15.0 92 11.7 32 15.3 86 14.4 28 14.4 57 12.7 55 11.7 66 11.9 26 15.9 28 13.4 96 14.0 48 13.9 90 12.9 86 15.1 7813.0 87

151 / 173 105 / 164 73 / 103 107 / 113 113 / 122 87 / 112 77 / 98 108 / 121 118 / 132 122 / 136 112 / 133 120 / 137 122 / 145 89 / 117 69 / 90 71 / 80 53 / 67 41 / 54 53 / 58 31 / 39 35 / 42 14 / 23 18 / 23

Another example: logistic regression

YProportion

of nests with success

(>0 youngs)


Performing a logistic regression with WinBUGS

model

# succ. in year i ~ Bin(pi, total # couples in year i)

where pi the probability of success in year i

logit(pi)= + r Ri + t Ti, i=1,...,23


noninformative priors


data & initial values


Performing a logistic regression with WinBUGSthe results

• influence of rainfall, but not temperature (see credible intervals)

lower upper

• additional parameters as a by-product of the MCMC samples: just add them in the model as parameters to be monitored

- geometric mean:

geom <- pow(prod(p[]),1/N)

- odds-ratio:

odds.rainfall <- exp(slope.rainfall)

odds.temperature <- exp(slope.temperature)


• additional parameters as a by-product of the MCMC samples

- geom. mean probability of success around 82% [81%;84%]

- odds-ratio: -16% for an increase of rainfall of 1 unit


Climatic conditions affect survival in the wilda) European dippers in Eastern France (1981-1987)

Practical session 1

• Estimating survival using capture-recapture models

• CJS model: time-dependent survival and detection rates

• Case study a): A flood occured in the 1983 breeding season so that survival rates are expected to differ between flood (f) and non-flood (n) years

use constraints to estimate parameters f and n

Climatic conditions affect survival in the wildb) Lapwings in UK (1980-1993)

Practical session 2

• Estimating survival using ring-recovery models

• Case study b): Number of days that the mean temperature is below freezing in central England (fdays) is expected to affect Lapwings survival

use fdays as a covariate

• Strong assumption: variation in survival is totally explained by the covariate alone

incorporate random effects

Documents

Introduction to WinBUGS Olivier Gimenez. A brief history 1989: project began with a Unix version called BUGS 1998: first Windows version, WinBUGS