bayesian statistics, modeling & reasoning what is this course about? p548: intro bayesian stats...

Bayesian Statistics, Modeling & ReasoningWhat is this course about?

P548: Intro Bayesian Stats with Psych ApplicationsInstructor: John Miyamoto

01/04/2016: Lecture 01-1

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Outline

• What is Bayesian inference?

• Why are Bayesian statistics, modeling & reasoning relevant to psychology?

• What is Psych 548 about?

• Explain Psych 548 website

• Intro to R

• Intro to RStudio

• Intro to the R to BUGS interface

Psych 548, Miyamoto, Win '16 2

Lecture probably ends here

3

Bayes Rule – What Is It?

• Reverend Thomas Bayes, 1702 – 1761English Protestant minister & mathematician

• Bayes Rule is fundamentally important to:♦ Bayesian statistics♦ Bayesian decision theory♦ Bayesian models in psychology

Psych 548, Miyamoto, Win '16

P Data|Hypothesis P(Hypothesis)P(Hypothesis|Data)

P(Data)=

n

i ii 1

P(Data) P Data | Hypothesis P Hypothesis

Bayes Rule – Why Is It Important?

4Psych 548, Miyamoto, Win '16

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 conceptso Concept 1: Bayesian inference is a model of optimal learning

from experience.o Concept 2: Bayesian decision theory describes optimal strategies

for taking actions in an uncertain environment. Optimal gambling strategies.

o 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.

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?

o 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.

Four Roles for Bayesian Reasoning in Psychology Research


Four Roles for Bayesian Reasoning in Psychology

1. Bayesian statistics: Analyzing datao E.g., is the slope of the regression of grades on IQ the same for boys as

for girls?o E.g., are there group differences in an analysis of variance?

Four Roles …. (Continued)



1. Bayesian statistics: Analyzing data

2. Bayesian decision theory – a theory of strategic action.How to gamble if you must.

3. Bayesian modeling of psychological processes

4. Bayesian reasoning – Do people reason as if they are Bayesian probability analysts? (At macro & neural levels)

o Judgment and decision making – This is a major issue.o Human causal reasoning – is it Bayesian or quasi-Bayesian?o Modeling neural decision making – many proposed models have a

strong Bayesian flavor.

Four Roles …. (Continued)



1. Bayesian statistics: Analyzing data

2. Bayesian decision theory – a theory of strategic action.How to gamble if you must.

3. Bayesian modeling of psychological processes

4. Bayesian reasoning – Do people reason as if they are Bayesian probability analysts? (At macro & neural levels)

Graphical Representation of Psych 548 Focus on Stats/Modeling

Psych 548: Focus on Topics (1) and (3). Include a little bit of (4).


Graphical Representation of Psych 548

Bayesian Statistics& Modeling:

R & JAGS

Bayesian Models in Cognitive Psychology

& Neuroscience

Psych 548

Graph & Text Showing the History of S, S-Plus & R


Brief History of S, S-Plus, & 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)

o currently the standard computing framework for statisticians worldwideMany contributors to its development

o Excellent general computation. Powerful & flexible.

o Great graphics.o Multiplatform: Unix, Linux, Windows, Maco User must like programming

BUGS, WinBUGS, OpenBUGS, JAGS

S

S-PlusR

Ancestry of R


BUGS, WinBUGS, OpenBUGS & JAGS

• Gibbs Sampling & Metropolis-Hastings AlgorithmTwo algorithms for sampling from a hard-to-evaluate probability distribution.

• BUGS – Bayesian inference Under Gibbs Sampling (circa 1995)

• WinBUGS - Open source (circa 1997)o Windows only

• OpenBUGS – Open source (circa 2006) o Mainly Windows. Runs within a virtual Windows machine on a Mac.

• JAGS – Open source (circa 2007)o Multiplatform: Windows, Mac, Linux

• STAN – Open source (circa 2012) Multiplatform: Windows, Mac, Linux

Basic Structure of Bayesian Computation with R & OpenBUGS

“BUGS” includes all of these.


Basic Structure of Bayesian Computation

R

data preparation

analysis of results

JAGSComputes

approximation to the posterior distribution.Includes diagnostics.

rjags functions

rjags functions

rjagsrunjags

OpenBUGS/WinBUGS/

StanR BRugs functions

Brugs functions

BRugsR2WinBUGS

rstan

Outline of Remainder of the Lecture: Course Outline & General Information

RStudio

• Run RStudio

• Run R from within RStudio

Psych 548, Miyamoto, Win '16 13


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

5 Minute Break

5 Minute Break

• Introduce selves upon return

Psych 548, Miyamoto, Win '16 15Course Goals


Course Goals

• Learn the theoretical framework of Bayesian inference.

• Achieve competence with R, OpenBUGS and JAGS.

• Learn basic Bayesian statisticso Learn how to think about statistical inference from a Bayesian standpoint. o Learn how to interpret the results of a Bayesian analysis. o Learn basic tools of Bayesian statistical inference - testing for

convergence, making standard plots, examing samples from a posterior distribution.

---------------------------------------------------------------

Secondary Goalso Bayesian modeling in psychologyo Understand arguments about Bayesian reasoning in the psychology

of reasoning. The pros and cons of the heuristics & biases movement.

Kruschke Textbook

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 ($90 from Amazon)

• Emphasis on classical statistical test problems from a Bayesian perspective. Not so much modeling per se.

♦ Binomial inference problems, anova problems, linear regression problems.

Computational Requirements

• R & JAGS (or OpenBUGS)

• A programming editor like Rstudio is useful.

Psych 548, Miyamoto, Win '16 17Chapter Outline of Kruschke Textbook

Kruschke, Doing Bayesian Data Analysis

• Ch 1 – 4: Basic probability background (pretty easy)

• Ch 5 – 8: Bayesian inference with simple binomial models♦ Conjugate priors, Gibbs sampling & Metropolis-Hastings algorithm♦ OpenBUGS or JAGS

• Ch 9 – 12: Bayesian approach to hierarchical modeling, model comparison, & hypothesis testing.

• Ch 13: Power & sample size (omit )

• Ch 14: Intro generalized linear model

• Ch 15 – 17: Intro linear regression

• Ch 18 – 19: Oneway & multifactor anova

• Ch 20 – 22: Categorical data analysis, logistic regression, probit regression, poisson regression

Psych 548, Miyamoto, Win '16 18Lee & Wagenmakers, Bayesian Graphical Modeling


Bayesian Cognitive Modeling

Lee, M. D., & Wagenmakers, E. J. (2014). Bayesian cognitive modeling: A practical course. Cambridge University Press.

o Michael Lee: http://www.socsci.uci.edu/~mdlee/bgm.html o E. J. Wagenmaker: http://users.fmg.uva.nl/ewagenmakers/BayesCourse/BayesBook.html

o Equivalent Matlab & R code for book are available at the Psych 548 website and at Lee or Wagenmaker's website.

• Emphasis is on Bayesian models of psychological processes rather than on methods of data analysis. Lots of examples.

Chapters in Lee & Wagenmakers

Table of Contents in Lee & Wagenmakers

20Psych 548:, Miyamoto, Win ‘16 Computer Setup in CSSCR


CSSCR Network & Psych 548 Webpage

• 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 o Note that Ctrl-D takes you to your Desktop.

• Run R or RStudio.

Psych 548 Website - END

Is this information obsolete?

Psych 548 Website

• Point out where to download the material for today’s class

• Point out pdf’s for the textbooks.

Psych 548, Miyamoto, Win '16 22NEXT: Time Permitting ......


General Characteristics of Bayesian Inference

• The decision maker (DM) is willing to specify the prior probability of the hypotheses of interest.

• DM can specify the likelihood of the data given each hypothesis.

• Using Bayes Rule, we infer the probability of the hypotheses given the data

Comparison Between Bayesian & Classical Stats - END

How Does Bayesian Stats Differ from Classical Stats?

Bayesian: Common Aspects• Statistical Models

• Credible Intervals – sets of parameters that have high posterior probability

Bayesian: Divergent Aspects• Given data, compute the full posterior

probability distribution over all parameters

• Generally null hypothesis testing is nonsensical.

• Posterior probabilities are meaningful; p-values are half-assed.

• MCMC approximations to posterior distributions.

Classical: Common Aspects• Statistical Models

• Confidence Intervals – which parameter values are tenable after viewing the data.

Classical: Divergent Aspects• No prior distributions in general, so

this idea is meaningless or self-deluding.

• Null hypothesis te%sting• P-values• MCMC approximations are

sometimes useful but not for computing posterior distributions.

Psych 548, Miyamoto, Win '16 24Sequential Presentation of the Common & Divergent Aspects













• Null hypothesis te%sting• P-values• MCMC approximations are


Psych 548, Miyamoto, Win '16 25END











Classical: Divergent Aspects• No prior distributions in general,

so this idea is meaningless or self-deluding.

• Null hypothesis testing• P-values• MCMC approximations are















• Null hypothesis testing• P-values• MCMC approximations are



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