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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