Bayesian Computation
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Bayesian Computation Andrew Gelman Department of Statistics and Department of Political Science Columbia University Class 4, 28 Sept 2011 Andrew Gelman Bayesian Computation Review of homework 4 I Skills: 1. Write the joint posterior density (up to a multiplicative constant) 2. Program two-dimensional Metropolis jumps 3. Program the accept/reject rule 4. Tune the parameters of your algorithm Andrew Gelman Bayesian Computation Review of homework 4 I Skills: 1. Write the joint posterior density (up to a multiplicative constant) 2. Program two-dimensional Metropolis jumps 3. Program the accept/reject rule 4. Tune the parameters of your algorithm Andrew Gelman Bayesian Computation Review of homework 4 I Skills: 1. Write the joint posterior density (up to a multiplicative constant) 2. Program two-dimensional Metropolis jumps 3. Program the accept/reject rule 4. Tune the parameters of your algorithm Andrew Gelman Bayesian Computation Review of homework 4 I Skills: 1. Write the joint posterior density (up to a multiplicative constant) 2. Program two-dimensional Metropolis jumps 3. Program the accept/reject rule 4. Tune the parameters of your algorithm Andrew Gelman Bayesian Computation Review of homework 4 I Skills: 1. Write the joint posterior density (up to a multiplicative constant) 2. Program two-dimensional Metropolis jumps 3. Program the accept/reject rule 4. Tune the parameters of your algorithm Andrew Gelman Bayesian Computation Review of homework 4 I Skills: 1. Write the joint posterior density (up to a multiplicative constant) 2. Program two-dimensional Metropolis jumps 3. Program the accept/reject rule 4. Tune the parameters of your algorithm Andrew Gelman Bayesian Computation Optimization of Gibbs and Metropolis algorithms I Conclusion of presentation by Wei Wang, Ph.D. student in statistics I You can interrupt and discuss . . . Andrew Gelman Bayesian Computation Optimization of Gibbs and Metropolis algorithms I Conclusion of presentation by Wei Wang, Ph.D. student in statistics I You can interrupt and discuss . . . Andrew Gelman Bayesian Computation Optimization of Gibbs and Metropolis algorithms I Conclusion of presentation by Wei Wang, Ph.D. student in statistics I You can interrupt and discuss . . . Andrew Gelman Bayesian Computation Missing-data imputation I Presentation by Ido Rosen, M.S. student in computer science I You can interrupt and discuss . . . Andrew Gelman Bayesian Computation Missing-data imputation I Presentation by Ido Rosen, M.S. student in computer science I You can interrupt and discuss . . . Andrew Gelman Bayesian Computation Missing-data imputation I Presentation by Ido Rosen, M.S. student in computer science 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 Tuning the algorithm I Shape of jumping kernel I Scale of jumping kernel I Objective function to optimize I Trying different tuning parameters I Stochastic optimization Andrew Gelman Bayesian Computation Tuning the algorithm I Shape of jumping kernel I Scale of jumping kernel I Objective function to optimize I Trying different tuning parameters I Stochastic optimization Andrew Gelman Bayesian Computation Tuning the algorithm I Shape of jumping kernel I Scale of jumping kernel I Objective function to optimize I Trying different tuning parameters I Stochastic optimization Andrew Gelman Bayesian Computation Tuning the algorithm I Shape of jumping kernel I Scale of jumping kernel I Objective function to optimize I Trying different tuning parameters I Stochastic optimization Andrew Gelman Bayesian Computation Tuning the algorithm I Shape of jumping kernel I Scale of jumping kernel I Objective function to optimize I Trying different tuning parameters I Stochastic optimization Andrew Gelman Bayesian Computation Tuning the algorithm I Shape of jumping kernel I Scale of jumping kernel I Objective function to optimize I Trying different tuning parameters I Stochastic optimization Andrew Gelman Bayesian Computation For next week’s class I Homework 5 due 5pm Tues I All course material is at http: //www.stat.columbia.edu/~gelman/bayescomputation Next class: I I I present weakly informative priors Andrew Gelman Bayesian Computation For next week’s class I Homework 5 due 5pm Tues I All course material is at http: //www.stat.columbia.edu/~gelman/bayescomputation Next class: I I I present weakly informative priors Andrew Gelman Bayesian Computation For next week’s class I Homework 5 due 5pm Tues I All course material is at http: //www.stat.columbia.edu/~gelman/bayescomputation Next class: I I I present weakly informative priors Andrew Gelman Bayesian Computation For next week’s class I Homework 5 due 5pm Tues I All course material is at http: //www.stat.columbia.edu/~gelman/bayescomputation Next class: I I I present weakly informative priors Andrew Gelman Bayesian Computation For next week’s class I Homework 5 due 5pm Tues I All course material is at http: //www.stat.columbia.edu/~gelman/bayescomputation Next class: I I I present weakly informative priors Andrew Gelman Bayesian Computation
