R Tutorial: The posterior model

you now have the pieces in place to construct a posterior model of P your underlying support in the upcoming election first the beta 4555 prior model suggested that your support hovered around 45% subsequently you pulled N equals 10 voters and recorded the number X that support you conditioned on your support P the likelihood model of X is binomial upon observing x equals 6 the corresponding likelihood function indicates the values of support P near 0.6 are the most compatible with your pool the prior and likelihood scaled here for comparison don't completely agree yet both are valuable to a Bayesian analysis the prior contributes knowledge that you built prior to the most recent poll the likelihood provides insight into the values of P that are most compatible with the current polling data the posterior model combines the insights from the prior and likelihood here the posterior reflects increased optimism about your election chances in light of the small but optimistic polling data in the previous course you learned that the exact specification of the posterior can be obtained through Bayes rule specifically the posterior is proportional to the product of the likelihood and prior however in more sophisticated model settings tidy closed form solutions to this formula might not exist thus in this course will focus on approximating posterior models using ardex our jegs combines the power of r with the just another Gibbs sampler or Jegs engine to get started first download the jags program outside r then within our install the most recent version of the archives package there are three essential steps to all our jives analyses define compile and simulate to begin we define the Bayesian model by a model string and store this as boat model the two lines of code within the curly brackets to find the two important pieces of your model the D bin function specifies that the likelihood structure or the dependence of Exxon P is modeled by the binomial NP distribution similarly the D beta function specifies a beta a B prior model for P if you're familiar with the D binome function and base are you might think that there's a typo in the D bin call the order of N and P are reversed this isn't a typo it's important to keep in mind that probability functions work differently in our jigs than they do in bass our next we compiled a model using the jags model function very loosely speaking the goal here is to send information out to the jags program which will then design an algorithm to sample from the posterior in the first argument we provide a text connection to the defined vote model string in the data argument we supply the values of the a and B prior shaped parameters as well as the observed values of polling data x and n the annette's argument ensures the reproducibility of our simulation results well elaborate on this in Chapter two finally we simulate the posterior using coda samples to draw 10,000 approximate samples from the posterior code samples takes three arguments model your compiled vote Jegs model variable names here your parameter of interest P and n itter your desired sample size our number of iterations the results stored in vote sim are an MCMC list object we can take a quick peek at the distribution of the resulting 10,000 code samples using the plot function importantly this approximates the posterior model of your election support P it's your turn to define compile and simulate and the remaining chapter 1 exercises you'll play around with our jegs while exploring the impact the different priors and different data can have on the posterior election model