Simon Jackman:Bayesian Analysis for the Social Sciences(Using JAGS)

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Bayesian Analysis for the Social Sciences

Simon Jackman

ISBN: 978-0-470-01154-6

598 pages

November 2009

Bayesian Analysis for the Social Sciences provides a thorough yet accessible treatment of Bayesian statistical inference in social science settings.

The first part of this book presents the foundations of Bayesian inference, via simple inferential problems in the social sciences: proportions, cross-tabulations, counts, means and regression analysis. A review of modern, simulation-based inference is presented with a detailed examination of the suite of computational tools (Markov chain Monte Carlo algorithms) that underlie the “Bayesian revolution” in contemporary statistics. Furthermore, the book introduces the general purpose Bayesian computer programs BUGS and JAGS along with numerous examples, and a detailed consideration of the art of using these programs in real-world settings.

The second half of the book focuses on intermediate to advanced applications in the social sciences, including hierarchical or “multi-level” models, models for discrete responses (binary, ordinal, and multinomial data), measurement models (factor analysis, item-response models, dynamic linear models), and mixture models, along with models that are interesting hybrids of these models.  Each model is accompanied by worked examples using BUGS/JAGS, using data from political science, sociology, psychology, education, communications, economics and anthropology.

Each chapter is accompanied with exercises to further the students' understanding of Bayesian methods and applications.  Extensive appendices provide important technical background and proofs of key theoretical propositions.

http://bcs.wiley.com/he-bcs/Books?action=index&bcsId=5422&itemId=0470011548

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关键词：Sciences Analysis Bayesian Analysi Jackman accessible problems provides science simple

[victory]

1. require(rjags)
   
2. foo <- jags.model(file="regression.bug",
   
3.                   data=forJags,
   
4.                   inits=inits)
   
5. out <- coda.samples(model=foo,
   
6.                     variable.names=c("beta","sigma"),
   
7.                     n.iter=50000,thin=5)

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1. library(pscl)
   
2. data(absentee)
   
3. attach(absentee)
   
4. ## create variables for regression analysis
   
5. y <- (absdem - absrep)/(absdem + absrep)*100
   
6. x <- (machdem - machrep)/(machdem + machrep)*100
   
7. 
   
8. ## environment for passing to JAGS
   
9. forJags <- list(y=y[1:20],x=x[1:20],n=20,xstar=x[21])
   
10. 
    
11. ## initial values, one chain
    
12. inits <- list(list(beta=c(0,0),sigma=5,
    
13.                    .RNG.seed=1234,
    
14.                    .RNG.name="base::MersenneTwister"))

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1. require(rjags)
   
2. foo <- jags.model(file="negbin.bug",
   
3.                   data=forJags,
   
4.                   inits=inits)
   
5. 
   
6. update(foo,5000)
   
7.                   
   
8. out <- coda.samples(foo,
   
9.                     variable.names=c("beta","r"),
   
10.                     n.iter=50000)

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1. require(pscl)
   
2. data(bioChemists)
   
3. 
   
4. forJags <- list(n=dim(bioChemists)[1],  ## sample size
   
5.                 fem=as.numeric(bioChemists$fem=="Women"),    ## covariates
   
6.                 mar=as.numeric(bioChemists$mar=="Married"),
   
7.                 kid5=bioChemists$kid5,
   
8.                 phd=bioChemists$phd,
   
9.                 ment=bioChemists$ment,
   
10.                 y=bioChemists$art,    ## response
    
11.                 b0 = rep(0,6),        ## prior hyperparameters
    
12.                 B0 = diag(.0001,6))
    
13. 
    
14. inits <- list(list(beta=rep(0,6),
    
15.                    r=1))

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1. forJags <- list(y=y,
   
2.                 x=x,
   
3.                 b0=rep(0,7),
   
4.                 B0=diag(.0001,7))
   
5. 
   
6. inits <- list(list(beta=matrix(0,7,2),       ## two sets of initial values
   
7.                    s=runif(n=2,0,.5),
   
8.                    rho=runif(n=1,-1,1),
   
9.                    nu=4),
   
10.               list(beta=matrix(0,7,2),
    
11.                    s=runif(n=2,0,.5),
    
12.                    rho=runif(n=1,-1,1),
    
13.                    nu=29))
    
14. require(rjags)
    
15. foo <- jags.model(file="92plain.bug",
    
16.                   data=forJags,
    
17.                   inits=inits,
    
18.                   nchain=2,
    
19.                   n.adapt=10e3)
    
20. 
    
21. out <- coda.samples(foo,
    
22.                     variable.names=c("beta","Sigma","nu"),
    
23.                     n.iter=50e3)

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1. ## map into space of identified parameters
   
2. remap <- function(x){
   
3.   foo <- x                         ## copy MCMC output
   
4.   int <- x[,"beta[1,1]"]
   
5.   k <- cbind(x[,"beta[4,1]"],      ## subset of parameters we need
   
6.              x[,"beta[5,1]"],
   
7.              x[,"beta[6,1]"],
   
8.              x[,"beta[7,1]"])
   
9.   kbar <- apply(k,1,mean)          ## mean at each iteration
   
10.   k <- sweep(k,1,kbar)             ## subtract out
    
11.   foo[,"beta[1,1]"]  <- int + kbar
    
12.   foo[,"beta[4,1]"] <- k[,1]       ## write mean-differenced to output
    
13.   foo[,"beta[5,1]"] <- k[,2]
    
14.   foo[,"beta[6,1]"] <- k[,3]
    
15.   foo[,"beta[7,1]"] <- k[,4]
    
16. 
    
17.   int <- x[,"beta[2,1]"]
    
18.   k <- cbind(x[,"beta[4,2]"],      ## repeat for 2nd set of regression coefficients
    
19.              x[,"beta[5,2]"],
    
20.              x[,"beta[6,2]"],
    
21.              x[,"beta[7,2]"])
    
22.   kbar <- apply(k,1,mean)
    
23.   k <- sweep(k,1,kbar)
    
24.   foo[,"beta[1,2]"] <- int + kbar
    
25.   foo[,"beta[4,2]"] <- k[,1]
    
26.   foo[,"beta[5,2]"] <- k[,2]
    
27.   foo[,"beta[6,2]"] <- k[,3]
    
28.   foo[,"beta[7,2]"] <- k[,4]
    
29. 
    
30.   return(foo)
    
31. }
    
32. 
    
33. z <- lapply(out,remap)             ## apply to each chain in out

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1. inits <- list(list(sigma1=3,sigma2=3,rho=.99),
   
2.               list(sigma1=.25,sigma2=.25,rho=-.99))
   
3. foo <- jags.model(file="bimodal3.bug",
   
4.                   data=forJags,
   
5.                   n.adapt=5000,
   
6.                   nchain=2,
   
7.                   inits=inits)
   
8. 
   
9. out <- coda.samples(foo,
   
10.                     n.iter=250000,
    
11.                     thin=50,
    
12.                     variable.names=c("Sigma","rho"))

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1. model{
   
2.   for (i in 1:12){
   
3.     y[i,1] ~ dnorm(0.0,tau[1,1]);  ## y1 marginal model
   
4.     y[i,2] ~ dnorm(mu[i],tau21);   ## y2 conditional on y1
   
5.     mu[i] <- beta*y[i,1];          ## E(y2|y1)
   
6.   }
   
7. 
   
8.   ## priors  
   
9.   sigma[1] ~ dunif(0,6)
   
10.   sigma[2] ~ dunif(0,6)
    
11.   rho ~ dunif(-1,1)                   ## correlation
    
12.   Sigma[1,1] <- pow(sigma[1],2)       ## variance
    
13.   Sigma[2,2] <- pow(sigma[2],2)       ## variance
    
14.   Sigma[1,2] <- rho*sigma[1]*sigma[2] ## covariance        
    
15.   Sigma[2,1] <- Sigma[1,2]            ## covariance
    
16. 
    
17.   ## convert covariance matrix to precision matrix
    
18.   tau <- inverse(Sigma)
    
19. 
    
20.   ## conditional variance
    
21.   Sigma21 <- Sigma[2,2] - pow(Sigma[1,2],2)/Sigma[1,1]
    
22.   tau21 <- 1/Sigma21                  ## conditional precision
    
23.   
    
24.   beta <- Sigma[1,2]/Sigma[1,1]       ## regression coefficient
    
25. }

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1. y <- matrix(c(-1, -1, 1, 1, 2, -2, 2, -2, NA, NA, NA, NA,
   
2.               -1, 1, -1, 1, NA, NA, NA, NA, 2, -2, 2, -2),
   
3.             12, 2)
   
4. forJags <- list(y=y)

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