Bayesian Statistics, Modeling & Reasoning What is this course about? P548: Bayesian Stats with Psych Applications Instructor: John Miyamoto 01/05/2017: Lecture 01-2 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.

Lecture probably ends here Outline What is Bayesian inference? Why is Bayesian statistics, modeling & reasoning relevant to psychology? What is Psych 548 about? Familiarize students with the set up for using MGH 030 Explain Psych 548 website Intro to R Intro to RStudio Intro to the R to BUGS interface Lecture probably ends here Psych 548, Miyamoto, Win '17 What Is Bayes Rule?

Bayes Rule – What Is It? Reverend Thomas Bayes, 1702 – 1761 English Protestant minister & mathematician Bayes Rule is fundamentally important to: Bayesian statistics Bayesian decision theory Bayesian models in psychology Psych 548, Miyamoto, Win '17 Bayes Rule – Why Is It Important?

Bayes Rule – Why Is It Important? Bayes Rule is the optimal way to update the probability of hypotheses given data. The concept of "Bayesian reasoning“: 3 related concepts Concept 1: Bayesian inference is a model of optimal learning from experience. Concept 2: Bayesian decision theory describes optimal strategies for taking actions in an uncertain environment. Optimal gambling. Concept 3: Bayesian reasoning represents the uncertainty of events as probabilities in a mathematical calculus. Concepts 1, 2 & 3 are all consistent with the use of the term, "Bayesian", in modern psychology. Psych 548, Miyamoto, Win '17 Bayesian Issues in Psychology

Bayesian Issues in Psychological Research Does human reasoning about uncertainty conform to Bayes Rule? Do humans reason about uncertainty as if they are manipulating probabilities? These questions are posed with respect to infants & children, as well as adults. Do neural information processing systems (NIPS) incorporate Bayes Rule? Do NIPS model uncertainties as if they are probabilities? Bruno de Finetti (great 20th century Bayesian theorist): A probability is a measure of the rational degree of belief in a proposition.Subjective probability – are human judgments of uncertainty as if they are applying a probability calculus? Four Roles for Bayesian Reasoning in Psychology Research Psych 548, Miyamoto, Win '17

Four Roles for Bayesian Reasoning in Psychology 1. Bayesian statistics: Analyzing data E.g., is the slope of the regression of grades on IQ the same for boys as for girls? E.g., are there group differences in an analysis of variance? These topics can blur together, e.g., Roles 2 & 4 overlap; Roles 3 & 4 overlap. Four Roles …. (Continued) Psych 548, Miyamoto, Win '17

Four Roles for Bayesian Reasoning in Psychology 1. Bayesian statistics: Analyzing data 2. Bayesian decision theory – a theory of strategic action. How to gamble if you must. Bayesian modeling of psychological processes Bayesian reasoning – Do people reason as if they are Bayesian probability analysts? (At macro & neural levels) Judgment and decision making – This is a major issue. Human causal reasoning – is it Bayesian or quasi-Bayesian? Modeling neural decision making – many proposed models have a strong Bayesian flavor. These topics can blur together, e.g., Roles 2 & 4 overlap; Roles 3 & 4 overlap. Psych 548, Miyamoto, Win '17 Four Roles …. (Continued)

Four Roles for Bayesian Reasoning in Psychology 1. Bayesian statistics: Analyzing data 2. Bayesian decision theory – a theory of strategic action. How to gamble if you must. Bayesian modeling of psychological processes Bayesian reasoning – Do people reason as if they are Bayesian probability analysts? (At macro & neural levels) Focus is on Topic (1). Psych 548: Some Topic (3) will be discussed. A little bit of Topic (4) will be discussed. These topics can blur together, e.g., Roles 2 & 4 overlap; Roles 3 & 4 overlap. Psych 548, Miyamoto, Win '17 Graphical Representation of Psych 548 Focus on Stats/Modeling

Graphical Representation of Psych 548 Bayesian Statistics & Modeling: R, JAGS & Stan Bayesian Models in Child & Adult Psychology & Neuroscience Psych 548, Miyamoto, Win '17 Graph & Text Showing the History of S, S-Plus & R

Brief History of S, S-Plus, & R Ancestry of R S – open source statistics program created by Bell Labs (1976 – 1988 – 1999) S-Plus – commercial statistics program, refinement of S (1988 – present) R – free open source statistics program (1997 – present) Currently the standard computing framework for statisticians worldwide Many contributors to its development Excellent general computation. Powerful & flexible. Great graphics. Multiplatform: Unix, Linux, Windows, Mac User must like programming Psych 548, Miyamoto, Win '17 BUGS, WinBUGS, OpenBUGS, JAGS, Stan

BUGS, WinBUGS, OpenBUGS & JAGS Gibbs Sampling & Metropolis-Hastings Algorithm Two algorithms for sampling from a hard-to-evaluate probability distribution. BUGS – Bayesian inference Under Gibbs Sampling (circa 1995) WinBUGS - Open source (circa 1997) Windows only OpenBUGS – Open source (circa 2006) Mainly Windows. Runs within a virtual Windows machine on a Mac. JAGS – Open source (circa 2007) Multiplatform: Windows, Mac, Linux STAN – Open source (circa 2012) “BUGS” includes all of these. Basic Structure of Bayesian Computation with R & OpenBUGS Psych 548, Miyamoto, Win '17

Basic Structure of Bayesian Computation data preparation analysis of results JAGS Computes approximation to the posterior distribution. rjags functions rjags runjags OpenBUGS/ WinBUGS/ Stan R BRugs functions Brugs functions BRugs R2WinBUGS rstan Psych 548, Miyamoto, Win '17 Outline of Remainder of the Lecture: Course Outline & General Information

RStudio Run RStudio Run R from within RStudio Psych 548, Miyamoto, Win '17

Remainder of This Lecture Take 5 minute break Introduce selves Psych 548: What will we study? Briefly view the Psych 548 webpage. Introduction to the computer facility in CSSCR. Introduction to R, BUGS (OpenBUGS & JAGS), and RStudio Psych 548, Miyamoto, Win '17 5 Minute Break

5 Minute Break Introduce selves upon return Course Goals Psych 548, Miyamoto, Win '17 Course Goals

Course Goals Learn the theoretical framework of Bayesian inference. This slide was skipped on 1/4/17. It will be discussed on 1/9/17. Learn the theoretical framework of Bayesian inference. Achieve competence with R and JAGS. Learn basic Stan. Learn basic Bayesian statistics Learn how to think about statistical inference from a Bayesian standpoint. Learn how to interpret the results of a Bayesian analysis. Learn basic tools of Bayesian statistical inference - testing for convergence, making standard plots, examing samples from a posterior distribution. --------------------------------------------------------------- Secondary Goals Bayesian modeling in psychology Understand arguments about Bayesian reasoning in the psychology of reasoning. The pros and cons of the heuristics & biases movement. Psych 548, Miyamoto, Win '17 Kruschke Textbook

Main Text: Kruschke, Doing Bayesian Data Analysis Kruschke, J. K. (2014). Doing bayesian data analysis, second edition: A tutorial with R, JAGS, and Stan. Academic Press. Excellent textbook – worth the price ($77 from Amazon) Emphasis on classical statistical problems from a Bayesian perspective. Not so much modeling per se. Binomial inference problems, anova problems, linear regression problems. Bayesian statistical inference requires new tricks (but it eliminates a lot of trickery from classical statistics). Computational Requirements R & JAGS. Use a bit of Stan after Week 6. A programming editor like Rstudio is useful. Psych 548, Miyamoto, Win '17 Chapter Outline of Kruschke Textbook

Main Text: Kruschke, Doing Bayesian Data Analysis This slide was skipped on 1/4/17. It will be discussed on 1/9/17. Ch 1 – 4: Basic probability background (pretty easy) Ch 5 – 8: Bayesian inference with simple binomial models Conjugate priors, Gibbs sampling & Metropolis-Hastings algorithm JAGS Ch 9 – 10: Bayesian approach to hierarchical modeling, model comparison, & hypothesis testing. OMIT Ch 11 - 12: Compare Bayesian stats to classical stats OMIT Ch 13: Power & sample size Ch 14: Intro generalized linear model Ch 15 – 17: Intro simple linear & multiple regression Ch 18 – 19: Oneway & multifactor anova Ch 20 – 22: Categorical data analysis, logistic regression, probit regression, poisson regression Probably won't have the time for this. Lee & Wagenmakers, Bayesian Graphical Modeling Psych 548, Miyamoto, Win '17

Workbook on Bayesian Graphical Modeling Lee, M. D., & Wagenmakers, E. J. (2014). Bayesian cognitive modeling: A practical course. (Abbreviate as LW) Michael Lee: http://www.socsci.uci.edu/~mdlee/bgm.html E. J. Wagenmaker: http://users.fmg.uva.nl/ewagenmakers/BayesCourse/BayesBook.html Equivalent Matlab & R code for book is available at the Psych 548 website and at Lee or Wagenmaker's website. LW uses WinBUGS instead of JAGS. It is very easy to convert WinBUGS code to JAGS code. Emphasis is on Bayesian models of psychological processes rather than on statistical theory. Lots of examples. Computer Setup in MGH 030 Psych 548, Miyamoto, Win '17

MGH Network & Psych 548 Webpage REVISE: Click on /Start /Computer. The path & folder name for your Desktop is: C:\users\NetID\Desktop (where "NetID" refers to your NetID) Double click on MyUW on your Desktop. Find Psych 548 under your courses and double click on the Psych 548 website. Download files that are needed for today's class. Save these files to C:\users\NetID\Desktop Note that Ctrl-D takes you to your Desktop. Run R. Run RStudio. This slide was skipped on 1/4/17. It will be discussed on 1/9/17. Psych 548 Website - END Psych 548, Miyamoto, Win '17

Psych 548 Website This slide was skipped on 1/4/17. It will be discussed on 1/9/17. Point out where to download the material for today’s class Point out pdf’s for the textbooks. END Psych 548, Miyamoto, Win '17

Assignment and Exams This slide was skipped on 1/4/17. It will be discussed on 1/9/17. Look at Course Description Look at schedule – mention exams Look at Assignment 1 Psych 548, Miyamoto, Win '17