Computing with R & Bayesian Statistical Inference P548: Intro Bayesian Stats with Psych Applications Instructor: John Miyamoto 01/11/2016: Lecture 02-1 Note: This Powerpoint presentation may contain macros that I wrote to help me create the slides. The macros aren’t needed to view the slides. You can disable or delete the macros without any change to the presentation.

When Do We Use R in a Bayesian Statistical Analysis? Data manipulation (data preparation step) ♦ Put the data into a form that is easy to work with or easy to understand. Pass the Bayesian inference problem from R to JAGS (inference step) Result of Bayesian inference =Approximation to the posterior distribution over the parameters of a model. Use R to make a statistical or graphical analysis of the approximate posterior distribution (interpretation step). Psych 548:, Miyamoto, Win ‘16 2 General Pattern of Bayesian Inference

Background to the Analysis General Pattern of Bayesian Statistical Inference Psych 548, Miyamoto, Win '16 3 Define Prior Distribution over the Parameters of the Model Define Likelihoods Conditional on Parameters Data Define the Class of Statistical Models (Reality is Assumed to Lie within this Class of Models Infer and Interpret the Posterior Distribution over the Parameters of the Model Three Strategies for Bayesian Inference

Three Strategies of Bayesian Statistical Inference Psych 548, Miyamoto, Win '16 4 Define Prior Distributions Define Likelihoods Conditional on Parameters Data Compute Posterior from Conjugate Priors (if possible) Compute Approximate Posterior by MCMC Algorithm (if possible) Compute Posterior with Grid Approximation (if practically possible) Define the Class of Statistical Models (Reality is Assumed to Lie within this Class of Models Same Slide – Summary Representation

Psych 548, Miyamoto, Win '16 General Strategy of Bayesian Statistical Inference 5 Define Prior Distributions Define Likelihoods Conditional on Parameters Data Compute Posterior from Conjugate Priors (if possible) Compute Approximate Posterior by MCMC Algorithm (if possible) Compute Posterior with Grid Approximation (if practically possible) Define the Class of Statistical Models (Reality is Assumed to Lie within this Class of Models Outline of Today's Lecture - END

Today's Class Basic data types in R Needed for data preparation Needed for analysis of results Writing functions in R Makes it easier to solve complex problems or problems that come up repeatedly. Psych 548: Miyamoto, Win ‘16 6 END