A First Course in Bayesian Statistical Methods

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introduction staistics
Contents
1  
Belief probability and exchangeability  13 
Oneparameter models  31 
Monte Carlo approximation  53 
The normal model  67 
Posterior approximation with the Gibbs sampler  88 
The multivariate normal model  105 
Group comparisons and hierarchical modeling  125 
Linear regression  148 
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Common terms and phrases
autocorrelation Bayes Bayesian inference beliefs beta Chapter compute confidence interval conjugate prior correlation covariance matrix dataset described distri empirical distribution estimate example full conditional distribution function gamma Gibbs sampler given hierarchical model independent iteration joint posterior distribution Markov chain math score mean and variance Metropolis algorithm MetropolisHastings algorithm Monte Carlo approximation Monte Carlo samples multivariate normal distribution number of children obtained panel of Figure plot Poisson distribution Poisson model population mean posterior density posterior distribution posterior expectation posterior mean posterior predictive distribution posterior probability Pr(Y prior distribution prior expectation prior information probability density probability distribution proposal distribution q q q q q quantilebased quantiles random variable rank likelihood regression coefficients regression model regressors sample mean sampling distribution sampling model second panel sequence Springer Science+Business Media standard deviation theta unit information prior vector yi,j zero