Bayesian Computation
Andrew Gelman
Department 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. 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 multiplicative
constant)
2. Program one-dimensional Metropolis jumps
3. Program the accept/reject rule
4. Fit generalized linear models in R
5. Display and summarize results
I
And more . . .
Andrew Gelman
Bayesian Computation
Implementing Gibbs and Metropolis and improving their
efficiency
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 their
efficiency
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 their
efficiency
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 multiplicative
constant)
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 multiplicative
constant)
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 multiplicative
constant)
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 multiplicative
constant)
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 multiplicative
constant)
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 multiplicative
constant)
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
Next class:
I
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
Next class:
I
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
Next class:
I
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
Next class:
I
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
Next class:
I
I
Student presentation on missing-data imputation
Andrew Gelman
Bayesian Computation