General Bayesian estimation using MHadaptive
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If you can write the likelihood function for your model, MHadaptive will take care of the rest (ie. all that MCMC business). I wrote this R package to simplify the estimation of posterior distributions of arbitrary models. Here’s how it works:
1) Define your model (ie the likelihood * prior). In this example, lets build a simple linear regression model.
(log)Likelihood:
li_reg<-function(pars,data)
{
a<-pars[1] #intercept
b<-pars[2] #slope
sd_e<-pars[3] #error (residuals)
if(sd_e<=0){return(NaN)}
pred <- a + b * data[,1]
log_likelihood<-sum( dnorm(data[,2],pred,sd_e, log=TRUE) )
prior<- prior_reg(pars)
return(log_likelihood + prior)
}
Prior:
prior_reg<-function(pars)
{
a<-pars[1] #intercept
b<-pars[2] #slope
epsilon<-pars[3] #error
prior_a<-dnorm(a,0,100,log=TRUE) ## non-informative (flat) priors on all
prior_b<-dnorm(b,0,100,log=TRUE) ## parameters.
prior_epsilon<-dgamma(epsilon,1,1/100,log=TRUE)
return(prior_a + prior_b + prior_epsilon)
}
Now lets just simulate some data to give it a test run:
x<-runif(30,5,15) y<-x+rnorm(30,0,5) ##Slope=1, intercept=0, epsilon=5 d<-cbind(x,y) plot(x,y)
2) The function Metro_Hastings() does all the work. Just pass your model to this function, sit back and let MC Emmcee take it away.
mcmc_r<-Metro_Hastings(li_func=li_reg,pars=c(0,1,1),
par_names=c('a','b','epsilon'),data=d)
3) You can view the posteriors of all model parameters using plotMH()
plotMH(mcmc_r)
By default, this will also plot the pair-wise correlation between all parameters.
4) Print posterior Credible Intervals.
BCI(mcmc_r) # 0.025 0.975 # a -5.3345970 6.841016 # b 0.4216079 1.690075 # epsilon 3.8863393 6.660037
Tadda! Easy-Peasy.
For a more introductory look at Bayesian modeling, check out the slides and script file from an R workshop I gave at McGill on the subject. There are some additional optional arguments you can pass to Metro_Hastings() which you can read all about in the package manual. You can get the package source from cran, or from my github page.
*notes: MHadaptive is only recommended for relatively low dimensional models. Mixing can be quite slow for higher order models.
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