Bayesian Computation

Andrew GelmanDepartment of Statistics and Department of Political Science

Columbia University

Class 3, 21 Sept 2011

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Review of homework 3

I Skills:

1. Write the joint posterior density (up to a multiplicativeconstant)

2. Program one-dimensional Metropolis jumps3. Program the accept/reject rule4. Fit generalized linear models in R5. Display and summarize results

I And more . . .

Andrew Gelman Bayesian Computation

Implementing Gibbs and Metropolis and improving theirefficiency

I Presentation by Wei Wang, Ph.D. student in statistics

I You can interrupt and discuss . . .

Andrew Gelman Bayesian Computation

Implementing Gibbs and Metropolis and improving theirefficiency

I Presentation by Wei Wang, Ph.D. student in statistics

I You can interrupt and discuss . . .

Andrew Gelman Bayesian Computation

Implementing Gibbs and Metropolis and improving theirefficiency

I Presentation by Wei Wang, Ph.D. student in statistics

I You can interrupt and discuss . . .

Andrew Gelman Bayesian Computation

1. Write the joint posterior density (up to a multiplicativeconstant)

I Binomial model for #deaths given #rats

I Logistic model for Pr(death)

I Prior distribution for the logistic regression coefficients

I Discuss extensions to the model

I Steps 2, 3, 4 5 are straightforward

Andrew Gelman Bayesian Computation

1. Write the joint posterior density (up to a multiplicativeconstant)

I Binomial model for #deaths given #rats

I Logistic model for Pr(death)

I Prior distribution for the logistic regression coefficients

I Discuss extensions to the model

I Steps 2, 3, 4 5 are straightforward

Andrew Gelman Bayesian Computation

1. Write the joint posterior density (up to a multiplicativeconstant)

I Binomial model for #deaths given #rats

I Logistic model for Pr(death)

I Prior distribution for the logistic regression coefficients

I Discuss extensions to the model

I Steps 2, 3, 4 5 are straightforward

Andrew Gelman Bayesian Computation

1. Write the joint posterior density (up to a multiplicativeconstant)

I Binomial model for #deaths given #rats

I Logistic model for Pr(death)

I Prior distribution for the logistic regression coefficients

I Discuss extensions to the model

I Steps 2, 3, 4 5 are straightforward

Andrew Gelman Bayesian Computation

1. Write the joint posterior density (up to a multiplicativeconstant)

I Binomial model for #deaths given #rats

I Logistic model for Pr(death)

I Prior distribution for the logistic regression coefficients

I Discuss extensions to the model

I Steps 2, 3, 4 5 are straightforward

Andrew Gelman Bayesian Computation

1. Write the joint posterior density (up to a multiplicativeconstant)

I Binomial model for #deaths given #rats

I Logistic model for Pr(death)

I Prior distribution for the logistic regression coefficients

I Discuss extensions to the model

I Steps 2, 3, 4 5 are straightforward

Andrew Gelman Bayesian Computation

And more . . .

I Check convergence

I Debug program

I Check fit of model to data

I Understand model in context of data and alternative models

Andrew Gelman Bayesian Computation

And more . . .

I Check convergence

I Debug program

I Check fit of model to data

I Understand model in context of data and alternative models

Andrew Gelman Bayesian Computation

And more . . .

I Check convergence

I Debug program

I Check fit of model to data

I Understand model in context of data and alternative models

Andrew Gelman Bayesian Computation

And more . . .

I Check convergence

I Debug program

I Check fit of model to data

I Understand model in context of data and alternative models

Andrew Gelman Bayesian Computation

And more . . .

I Check convergence

I Debug program

I Check fit of model to data

I Understand model in context of data and alternative models

Andrew Gelman Bayesian Computation

Optimizing the algorithm

I Scale of jumps in α and β

I Jumping distributions

I One-dimensional or two-dimensional jumps

I How to implement Gibbs here??

I Other computational strategies??

Andrew Gelman Bayesian Computation

Optimizing the algorithm

I Scale of jumps in α and β

I Jumping distributions

I One-dimensional or two-dimensional jumps

I How to implement Gibbs here??

I Other computational strategies??

Andrew Gelman Bayesian Computation

Optimizing the algorithm

I Scale of jumps in α and β

I Jumping distributions

I One-dimensional or two-dimensional jumps

I How to implement Gibbs here??

I Other computational strategies??

Andrew Gelman Bayesian Computation

Optimizing the algorithm

I Scale of jumps in α and β

I Jumping distributions

I One-dimensional or two-dimensional jumps

I How to implement Gibbs here??

I Other computational strategies??

Andrew Gelman Bayesian Computation

Optimizing the algorithm

I Scale of jumps in α and β

I Jumping distributions

I One-dimensional or two-dimensional jumps

I How to implement Gibbs here??

I Other computational strategies??

Andrew Gelman Bayesian Computation

Optimizing the algorithm

I Scale of jumps in α and β

I Jumping distributions

I One-dimensional or two-dimensional jumps

I How to implement Gibbs here??

I Other computational strategies??

Andrew Gelman Bayesian Computation

For next week’s class

I Homework 4 due 5pm Tues

I All course material is at http://www.stat.columbia.edu/~gelman/bayescomputation

I Next class:I Student presentation on missing-data imputation

Andrew Gelman Bayesian Computation

For next week’s class

I Homework 4 due 5pm Tues

I All course material is at http://www.stat.columbia.edu/~gelman/bayescomputation

I Next class:I Student presentation on missing-data imputation

Andrew Gelman Bayesian Computation

For next week’s class

I Homework 4 due 5pm Tues

I All course material is at http://www.stat.columbia.edu/~gelman/bayescomputation

I Next class:I Student presentation on missing-data imputation

Andrew Gelman Bayesian Computation

For next week’s class

I Homework 4 due 5pm Tues

I All course material is at http://www.stat.columbia.edu/~gelman/bayescomputation

I Next class:I Student presentation on missing-data imputation

Andrew Gelman Bayesian Computation

For next week’s class

I Homework 4 due 5pm Tues

I All course material is at http://www.stat.columbia.edu/~gelman/bayescomputation

I Next class:I Student presentation on missing-data imputation

Andrew Gelman Bayesian Computation