My Office Hours I will stay after class on both Monday and Wednesday, i.e., 1:30 Mon/Wed in MGH 030. Can everyone stay if they need to? Psych 548, Miyamoto, Win '17

Computing with R & Bayesian Statistical Inference P548: Intro Bayesian Stats with Psych Applications Instructor: John Miyamoto 01/11/2017: Lecture 02-2 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.

What Tasks Does R Perform in a Bayesian Statistical Analysis? 1. Data manipulation (data preparation step) Put the data into a form that is easy to work with or easy to understand. 2. 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. 3. Use R to make a statistical or graphical analysis of the approximate posterior distribution (interpretation step). General Pattern of Bayesian Inference Psych 548:, Miyamoto, Win '17

General Pattern of Bayesian Statistical Inference Background to the Analysis Define the Class of Statistical Models (Reality is Assumed to Lie within this Class of Models Define Likelihoods Conditional on Parameters Define Prior Distribution over the Parameters of the Model Data Infer and Interpret the Posterior Distribution over the Parameters of the Model Psych 548, Miyamoto, Win '17 Three Strategies for Bayesian Inference

Three Strategies of Bayesian Statistical Inference Define the Class of Statistical Models (Reality is Assumed to Lie within this Class of Models Define Likelihoods Conditional on Parameters Define Prior Distributions Data Compute Posterior from Conjugate Priors (if possible) Compute Posterior with Grid Approximation (if practically possible) Compute Approximate Posterior by MCMC Algorithm (if possible) Psych 548, Miyamoto, Win '17 Same Slide – Summary Representation

General Strategy of Bayesian Statistical Inference Define the Class of Statistical Models (Reality is Assumed to Lie within this Class of Models Define Likelihoods Conditional on Parameters Define Prior Distributions Data Compute Posterior from Conjugate Priors (if possible) Compute Posterior with Grid Approximation (if practically possible) Compute Approximate Posterior by MCMC Algorithm (if possible) Psych 548, Miyamoto, Win '17 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. Use R function to compute This is a conceptually useful a grid approximation to exercise; once in awhile it is useful the posterior in a binomial in actual research. inference problem. Use conjugate priors to This is a conceptually useful compute the posterior in a exercise, and it can be extremely binomial inference problem useful in actual research. END Psych 548: Miyamoto, Win '17

Set Up for Instructor Turn off your cell phone. Close web browsers if they are not needed. Classroom Support Services (CSS), 35 Kane Hall, 206-543-9900 If the display is odd, try setting your resolution to 1024 by 768 Run Powerpoint. For most reliable start up: Start laptop & projector before connecting them together If necessary, reboot the laptop Psych 548, Miyamoto, Aut ‘16