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1. Edit the Dim statement in this file from Dim c 5 2 to Dim c 2 5 The file is now in the correct format to input the required 2 5 dimensional matrix into WinBUGS Smoothing Smoothing is an option in Winbugs There are radio buttons that are used to specify whether the reference line if it is to be displayed should be linear or whether an exponentially weighted smoother should be fitted instead In the case where a linear line is required its intercept and gradient should be entered in the two numeric fields to the right of the linear radio button in that order If a smoother is required then the desired degree of smoothing should be entered in the numeric field to the right of the smooth radio button To save unnecessary redrawing of the plot as the various numeric parameters are changed the Redraw line command button is used to inform WinBUGS of when all alterations to the parameters have been completed From previous listing of functions we may notice some basic functions which used a lot in statistics like nested variable random effect chi squared testing factor analysis could not be done by using Winbugs at least we could not find the command to do these directly More sophisticated programming Gibbs Sampling As we discussed before when doing basic functions Winbugs is not a good choice But it is designed for Gibbs sampling here is the advantage Go to the model menu and select Update A small dialog called the Update To
2. and transformations We suggest doing data manipulation or transformation before using Winbugs Since Winbugs is not designed to do usual statistical analysis it is especially for sampling it is convenient to finish the entire data step before start to exam the model Of course it is also possible to try various transformations of dependent variables within a model description Some simple transformation can be done directly We use square root for example The BUGS language permits the following type of structure to occur for i in 1 N z i lt sart yli We emphasize that this construction is only possible when transforming observed data with no missing values Formatting of data Data can be S Plus format for data in arrays in rectangular format Missing values are represented as NA All variables in a data file must be defined in a model even if just left unattached to the rest of the model WlinBUGS reads data into an array by filling the right most index first whereas the S Plus program fills the left most index first Hence WinBUGS reads the string of numbers c 1 2 3 4 5 6 7 8 9 10 into a 2 5 dimensional matrix in the order i jth element of matrix value 1 1 1 1 2 2 1 3 3 1 5 5 2 1 6 2 5 10 For example consider the 2 5 dimensional matrix 1 2 3 4 5 6 7 8 9 10 will then produce the following data file list M structure Data c 1 2 3 4 5 6 7 8 9 10 Dim c 5 2
3. Winbugs Introduction This document is intended to introduce some basic information about Winbugs We hope by reading this introductory report users can have a first look at this statistical software and get familiar with Winbugs in a short time Most of the examples used in the report and function codes are coming from the user s manual of Winbugs What is Winbugs WinBUGS is statistical software for Bayesian analysis using Markov chain Monte Carlo MCMC methods It is based on the BUGS Bayesian inference Using Gibbs Sampling project started in 1989 It runs under Microsoft Windows Winbugs has some specialty in the following area Its ability to fit complex statistical models using MCMC methods Its flexibility to program two different ways to specify model DoodleBUGS Direct graphics BUGS language Interface of Winbugs WinBUGS has an option of a graphical user interface the standard point and click windows interface Using this interface some of the functions can be done by pull down command However most of the time model fitting must be done by using command lines This means some coding work Generally speaking Winbugs is not entry level statistical software and it requires some knowledge of programming If the user has some background or experience using R or S plus it will be easier for user to get familiar with Winbugs Graph in Winbugs Plotting is not the best part of Winbugs Compared with so
4. bugs However if the user do not doing MCMC it is better to use other software to do the basic functions that is much easier than learning this new one Let us look at some example functions Linear Regression We use the heights and weights dataset to fit a linear regression model This example can be found in the file regression odc and loaded from the File menu The Winbugs code is as follows MODEL Definition model for i in 1 N height i dnorm mu i tau mufi lt beta0 beta1 weight i beta0 dnorm 0 1 beta1 dnorm 0 1 0E 6 tau dgamma 1 0E 3 1 0E 3 sigma2 lt 1 0 tau tau lt 1 0 sigma sigma sigma dunif 0 1000 sigma2 lt sigma sigma Initial values file list betaO 0 beta1 0 tau 1 list betaO 0 beta1 0 sigma 1 Data File list N 10 height c 169 6 166 8 157 1 181 1 158 4 165 6 166 7 156 5 168 1 165 3 weight c 71 2 58 2 56 0 64 5 53 0 52 4 56 8 49 2 55 6 77 8 When specifying the parameters to be sampled users need to input each of three parameters in turn and click on the set button Histograms In Winbugs histogram is not an independent command It exists under the density button Also it is affected by the type of variables When the density button on the Sample Monitor Tool is pressed the output depends on whether the specified variable is discrete or c
5. dom effect as normally distributed We then specify the prior of each coefficient and the hyper prior of the precision model N observations for i in 1 N hospital i dbern p i logit p i lt beta0 beta1 loginc i beta2 distance i beta3 educ 1 i beta4 educ3 i u group i M groups for j in 1 M u j dnorm 0 tau Priors betaO dnorm 0 0 1 0E 6 beta1 dnorm 0 0 1 0E 6 beta2 dnorm 0 0 1 0E 6 beta3 dnorm 0 0 1 0E 6 beta4 dnorm 0 0 1 0E 6 Hyperprior tau dgamma 0 001 0 001 Sample size calculation There is no sample size calculation function in Winbugs However we can use Winbugs to calculate power The data we use is e list prop1 25 prop2 35 size1 250 size2 150 N 100 alpha val 1 96 Node statistics node mean sd MC error 2 5 median 97 5 start sample power 0 5705 0 04899 0 001392 0 47 0 57 0 67 1001 1000 Read in data Data files are entered as lists or can be embedded as sub documents From previous examples we can notice that this method of data input is quite tedious Output is listed in a separate window but can be embedded in the compound document to help maintain a paper trail of the analysis Any part of the compound document can be folded out of sight to make the document easier to work with Data can be expressed in list structures or as rectangular tables in plain text format however WinBUGS cannot read data from an external file Data Manipulation
6. me other statistical software it is relatively inconvenient to draw some simple graphics It doesn t have simple command to do some basic graphs Meanwhile it could not do some complicated graphing either General properties for plotting Generating graphs are usually done by using the scatterplot option from the Inference Compare menu When the user have already finished the plot one thing WinBUGS graphics can do is it has a set of basic properties that can be modified using the Plot Properties dialog box Remember user must have finished the plot first This is opened as follows First focus the relevant plot by left clicking on it then select Object Properties from the Edit menu Alternatively right clicking on a focused plot will reveal a pop up menu from which Properties may equivalently be selected The Plot Properties dialogue box comprises a tab view and two command buttons namely Apply and Special The tab view contains five tabs that allow the user to make different types of modification The Apply command button applies the properties displayed in the currently selected tab to the focused plot And Special opens any special property editors that have been designed so that the user may further interact with specific types of plot The Margins tab displays the plot s left right top and bottom margins in mm The left and bottom margins are used for drawing the y and x axes respectively The top margin provides r
7. ol will pop up Often analysts start with a burn in run intended to discard the first few hundred samples If you want to do this enter 500 or 1000 on the updates box and click on update The status bar will read updating Now go to the Inference menu and select Samples A small dialog called the Sample Monitor Tool will pop up Under node type each of the parameters you want to monitor and click set for example you must type beta0 beta eta Remember to click on set after each one WinBUGS will now store the sampled values of each parameter Note that you can specify a beginning iteration so this is another way of discarding a burn in A window will pop up with graphs that can show the values of all parameters as they are generated Now go to the update tool select 1000 and click on update Click on history on the Sample Monitor Tool to get the complete trace Click on stats on the Sample Monitoring Tool to see statistics on the nodes you have monitored Conclusion Winbugs is designed for more sophisticated programming tasks Choose Winbugs wisely when you need it We assume most of Winbugs information can be found in the user manual document and examples with Winbugs But when users have questions and could not find the answers try to use the BUGS project online will be a good choice Discussion with the project members can help a lot
8. ontinuous If the variable is discrete then a histogram is produced whereas if it is continuous a kernel density estimate is produced instead The specialized property editor that appears when Special on the Plot Properties dialogue box is selected also differs slightly depending on the nature of the specified variable In both cases the editor comprises a numeric field and two command buttons apply and apply all but in the case of a histogram the numeric field corresponds to the bin size whereas for kernel density estimates it is the smoothing parameter fA Histogram prope i bin size apply apply all 83 Density properties smooth 0 2 apply apply all QQ plot QQ plot is not the same name in Winbugs Here it is called caterpillar plots for the QQ plot can be produced in Winbugs using the appropriate options from the Inference Compare menu Produce plots of residuals versus covariates and fitted values as well use the scatterplot option from the Inference Compare menu The caterpillar plot property editor looks like below Caterpillar plot V show baseline 5 2490864320 IV show labels vert bar show means horiz bar show medians J tank I log scale Random effect Model For each of the N observations we say the outcome is Bernoulli and specify the logit og the probability which depends on the x s and a random effect u For each of the M groups we specify the ran
9. oom for the plot s title and the right margin is typically used for plots that require a legend Note that top margins and hence titles are always inside the plotting rectangle x Margins Axis Bounds Titles All Plots Fonts left 20 right fo top 5 bottom fi2 Apply Special The user may specify new minimum and maximum values for either or both axes using the Axis Bounds tab Some advantage of Winbugs graphics is it has the All Plots tab The idea behind the All Plots tab is to allow the user to apply some or all of the properties of the focused plot to all plots of the same type in the same window The user should first configure the focused plot in the desired way and then decide which of the plot s various properties are to be applied to all plots It is easy to make mistakes here and there is no undo option It is suggested by the user manual that the best advice for users who go wrong is to reproduce the relevant graphics window via the Sample Monitor Tool or the Comparison Tool Some functions in Winbugs As we mentioned before Winbugs is specially designed for Bayesian inference using Gibbs sampling Thus it is not surprising that some simple and basic statistical functions can not be easily done by Winbugs It is quite possible for users to spend some time before they can figure out how to implement some functions The user manual provides some first step introduction and there are some good examples with Win

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