応用統計（ベイズ統計学入門）

• Schedule in 2020 (A1A2 term)

  • Lecture 1 (September 25)  Chapter 1 (Introduction to R) 1.2　

    • 1.2 Summary statistics, barplots, boxplots, histogram, scatterplots

  • Lecture 2 (October 2)  Chapter 1 (Introduction to R) 1.3, 2.1

    • 1.3 Comparison of two means, Generation of normal random variables

    • 1.3 How to define functions, How to input data, Monte Carlo simulation for normal and exponential populations

    • 2.1 Introduction to Bayes Theorem

  • Lecture 3 (October 9)  Chapter 2 (Introduction to Bayesian Statistics) 2.2, 2.3, 2.4

    • 2.2, 2.3 Binomial distribution and Discrete prior

    • 2.4 Binomial distribution and Beta prior

  • Lecture 4 (October 16) Chapter 2 (Introduction to Bayesian Statistics) 2.4, 2.6, 3.2

    • 2.4 Binomial distribution and Beta prior

    • 2.6 Prediction. Predictive density

    • 3.2 Normal distribution

    • Assignment #1

  • Lecture 5 (October 23) Chapter 3 (Single parameter model) 3.2, 3.3

    • 3.2 Normal distribution

    • 3.3 Heart transplant mortality rate (Poisson distribution)

  • Lecture 6 (October 30) Chapter 4 (Multi-parameter model)  4.2, 4.3

    • 4.2 Normal data

    • 4.3 Multinomial model

  • Lecture 7 (November 6) Chapter 4, 5 (Introduction to Bayesian computation) 4.4, 5.3,5.5

    • 4.3 Multinomial model

    • 5.3 Log posterior function in R

    • 5.5 Approximations Based on Posterior Modes

    • Assignment #1 submission due date　

  • Lecture 8 (November 27) Chapter 5, 6 (Markov chain Monte Carlo) 6.2, 6.3

    • 5.5 Approximations Based on Posterior Modes

    • 5.2, 5.7 Monte Carlo Integration

    • 6.2 Markov chain

    • 6.3 Metropolis-Hastings algorithm

    • Assignment #2

  • Lecture 9 (December 4) Chapter 6 (Markov chain Monte Carlo) 6.3, 6.4, 6.5

    • 6.3 Metropolis-Hastings algorithm

    • 6.4 Gibbs sampler

    • 6.5 Output analysis

    • Example using WinBUGS (NIMBLE)  (6.7) (6.8)

  • Lecture 10 (December 11) Chapter 6 (Markov chain Monte Carlo) 6.7, 6.8

    • Example using WinBUGS (NIMBLE)  (6.7) (6.8)

    • Normal distributions (4.2)

    • 6.5 Output analysis

  • Lecture 11 (December 18) Chapter 6 (Markov chain Monte Carlo) 2.4, 3.3, 6.9, 6.10

    • Example using WinBUGS (NIMBLE) 

    • Poisson distributions (3.3)

    • Binomial distributions (2.4)

    • Cauchy distribution (6.9)

    • Analysis of Stanford heart transplant data (6.10)

    • Assignment #2 submission due date

    • Empirical paper (Assignment #3 and Term paper)

  • Lecture 12 (December 25) 6.10, Chapter 7

    • Example using WinBUGS (NIMBLE) 

    • Analysis of Stanford heart transplant data (6.10)

    • Hierarchical modeling (7.4)

  • January 6 No class

  • Lecture 13 (January 8) Chapter7, Chapter 9, Chapter 11

    • Hierarchical modeling (7.5-7.10)

    • Regression model (9.2)

    • Robust regression using t-density  (Section 11.5) 

    • Change point model (Section 11.4) 

  • January 29  Empirical paper submission due date

Install R and RStudio: 

• • •  Visit R Homepage and download R from a mirror site.  

    •  R Studio (Free): a set of integrated tools for R. Very convenient.

“Bayesian Computation With R” by Jim Albert

• pdf is available at University

• Website for the book

• R scripts for examples in Second Edition (backup copy)

How to install “LearnBayes” library

• Start R Studio

• Tools -> Install packages…

• Type “LearnBayes” in "Packages" and click “Install"

Install NIMBLE

• Install R and Rstudio

• Visit the web page of https://r-nimble.org/  and see Documentation

• Install Rtools (Windows users) or Xcode (Mac users) . See Chapter 4 of Manual (https://r-nimble.org/html_manual/cha-welcome-nimble.html )

• Install packages: igraph, coda, R6

• Install package: nimble

NIMBLE Examples

Install WinBUGS

• Visit the web page of the BUGS Project

• Download WinBUGS (winbugs143_unrestricted.zip)

• Go to WinBUGS folder and double-click on WinBUGS14.exe to start WinBUGS.

• File -> Open and choose “WinBUGS14_immortality_key.txt” among Text (*.txt) files．

• Tools -> Decode and “Decode All”.

• File -> Open and choose “WinBUGS14_cumulative_patch_No3_06_08_07_RELEASE.txt” among Text (*.txt) files．

• Tools -> Decode and “Decode All”

• Done!

WinBUGS Examples

OpenBUGS for Mac and Windows users

• Overview

• Download

Stata

• Bayesian analysis