WinBUGS Training WinBUGS & linear regression

WinBUGS TrainingTricks & Tips – Interface with R

Catherine Dettori & Jonathan Jaeger

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WinBUGS & linear regression

Data:

Plot:

1 2 3 4 5

1 3 3 3 5

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WinBUGS & linear regression

1 – Regression model:

2 – Estimation of parameters

3 – Frequentist approach uses t-tests

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Frequentist approach

Result of the regression:

Prediction formula:

Estimate Std. error t-value P(>|t|)

0.6 0.7659 0.783 0.4906

0.8 0.2309 3.464 0.0405

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1. a model giving the likelihood

and the prior

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2. some data

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3. initials values to start the

MCMC algorithm

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Use the WinBUGS command

“model”

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Don’t forget to embrace the

model with {…}

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Define the likelihood

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Specify the priors

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Monitor any other parameter

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Use “list” structures … (R syntax)

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… and “vector” structures … (R syntax)

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WinBUGS

1- check model

2- load data

3- specify the number of MCMC chains

4- compile model

5- load initials values

6- generate burn-in value

7- parameters to be monitored

8- perform the sampling to generate posteriors

9- check convergence and display results

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WinBUGS – Node Statistics

95% credibility intervals

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WinBUGS – Node Statistics

Estimate Std. error t-value P(>|t|)

0.6 0.7659 0.783 0.4906

0.8 0.2309 3.464 0.0405

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WinBUGS – Trace

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WinBUGS – Autocorrelation function

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WinBUGS – Density

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WinBUGS – Quantiles

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WinBUGS

A way to identify non-convergence is to simulate multiple

sequences for over-dispersed starting points.

Intuitively, the behavior 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).

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WinBUGS – Gelman Rubin Statistic

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.

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Script in WinBUGS

Another mean to use WinBUGS : script.

Advantages :

Faster (only a script for all the instructions).

Put all the graph and statistical results in one file.

Easy to modify the script to solve a new problem.

Disadvantages :

Difficult to manipulate the outputs.

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Script in WinBUGS

check the model

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Script in WinBUGS

load the data

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Script in WinBUGS

number of chains & initials

values

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Script in WinBUGS

update & thin

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Script in WinBUGS

set the parameters

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Script in WinBUGS

statistical output

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Script in WinBUGS

Save the log file with all the

output

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Running WinBUGS using R

WinBUGS : uneasy to read complex sets of data and

initial values.

Quite boring to specify the parameters to be monitored

in each run.

Interesting to save the output and read it into R for

further analyses :

R2WinBUGS allows WinBUGS to be run from R

Possibility to have the results of the MCMC and work with

them (plot, convergence diagnostics…)

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R2WinBUGS

1- Create a .txt file with the model.

2- In R, load coda and R2WinBUGS packages.

3- Load the data in a list.

4- Load the initials values in a list.

5- Specify the parameters in a vector.

6- Create a bugs object using:

data,

initials values,

parameters,

model,

…

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R2WinBUGS

load the R2WinBUGS and

coda packages

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R2WinBUGS

load the data in a list

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R2WinBUGS

initials values in a list

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R2WinBUGS

Parameters of the model in a

list

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R2WinBUGS

create a bugs object

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R2WinBUGS

Using the command plot

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R2WinBUGS

With the option codaPkg=TRUE:

Use the command read.bugs to work with this object:coda.sim1 <- read.bugs(sim1)

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R2WinBUGS

Using the command plot:

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R2WinBUGS

Using the command autocorr.plot:

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R2WinBUGS

Using the command gelman.diag & gelman.plot:

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R2WinBUGS

Other convergence diagnostics are possible :

Geweke (1992)

geweke.diag & geweke.plot

Heidelberger and Welch (1983)

heidel.diag & heidel.plot

Raftery and Lewis

raftery.diag

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