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Approximate Bayesian computation (ABC): advances and questions
Published on 2012-08-2212519 Views
The lack of closed formlikelihoods has been the bane of Bayesian computation for many years and, prior to the introduction of MCMC methods, a strong impediment to the propagation of the Bayesian para
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Presentation
Approximate Bayesian Computation: how Bayesian can it be?00:00
This talk is dedicated to the memory of our dear friend and fellow Bayesian, George Casella, 1951{201202:17
Outline02:57
Approximate Bayesian computation03:47
General issue04:08
Monte Carlo basics (1)04:29
Monte Carlo basics (2)04:48
Importance Sampling (1)05:04
Importance Sampling (2)05:29
Importance Sampling (convergence) (1)05:44
Importance Sampling (convergence) (2)05:50
Self-normalised importance Sampling (1)06:05
Self-normalised importance Sampling (2)06:18
Self-normalised importance Sampling (3)06:25
Perspectives (1)06:58
Perspectives (2)07:38
Perspectives (3)07:42
Econom'ections09:03
Simulated method of moments (1)10:08
Simulated method of moments (2)10:57
Method of simulated moments11:13
Indirect inference12:10
Indirect inference (PML vs. PSE) (1)13:24
Indirect inference (PML vs. PSE) (2)13:56
Consistent indirect inference (1)14:05
Consistent indirect inference (2)14:09
Choice of pseudo-model15:21
Empirical likelihood (1)16:56
Empirical likelihood (2)18:56
ABCel19:47
A?B?C? (1)20:58
A?B?C? (2)21:08
A?B?C? (3)21:19
How much Bayesian?21:31
Genetic background of ABC23:14
Demo-genetic inference (1)24:01
Demo-genetic inference (2)24:21
A genuine example of application24:37
Alternative scenarios25:10
Untractable likelihood (1)25:36
Untractable likelihood (2)25:56
Untractable likelihood (3)25:59
Untractable likelihood (4)26:49
ABC methodology (1)27:01
ABC methodology (2)27:04
ABC methodology (3)27:15
Why does it work?!29:01
A as A...pproximative (1)29:52
A as A...pproximative (2)30:15
ABC algorithm30:19
Output (1)31:31
Output (2)31:35
Output (3)31:59
Convergence of ABC ( first attempt) (1)32:01
Convergence of ABC ( first attempt) (2)32:04
Convergence of ABC ( first attempt) (3)32:19
Convergence of ABC ( first attempt) (4)32:20
Convergence of ABC (second attempt) (1)32:21
Convergence of ABC (second attempt) (2)32:22
Convergence (do not attempt!) (1)32:22
Convergence (do not attempt!) (2)32:32
Convergence (do not attempt!) (3)32:42
Convergence (do not attempt!) (4)33:01
Probit modelling on Pima Indian women (1)33:27
Probit modelling on Pima Indian women (2)33:30
Probit modelling on Pima Indian women (3)33:31
Probit modelling on Pima Indian women (4)33:32
Pima Indian benchmark33:33
MA example (1)33:34
MA example (2)34:10
MA example (3)34:23
MA example (4)34:52
Comparison of distance impact (1)36:14
Comparison of distance impact (2)37:41
Comparison of distance impact (3)38:29
Comments38:44
ABC (simul') advances (1)40:46
ABC (simul') advances (2)41:04
ABC (simul') advances (3)41:05
ABC (simul') advances (4)41:06
ABC-NP41:15
ABC-NP (regression) (1)42:07
ABC-NP (regression) (2)42:33
ABC-NP (density estimation) (1)43:06
ABC-NP (density estimation) (2)43:19
ABC-NP (density estimations) (1)43:20
ABC-NP (density estimations) (2)43:37
ABC inference machine44:17
How much Bayesian? (1)44:35
How much Bayesian? (2)46:02
ABCμ (1)46:14
ABCμ (2)46:14
ABCμ (3)46:15
ABCμ details (1)47:21
ABCμ details (2)47:24
ABCμ multiple errors48:19
ABCμ for model choice48:59
Questions about ABCμ [and model choice] (1)49:01
Questions about ABCμ [and model choice] (2)49:02
Wilkinson's exact BC (not exactly!) (1)49:03
Wilkinson's exact BC (not exactly!) (2)50:12
How exact a BC? (1)51:20
How exact a BC? (2)51:44
ABC for HMMs (1)52:10
ABC for HMMs (2)52:11
ABC-MLE for HMMs (1)53:22
ABC-MLE for HMMs (2)53:24
ABC-MLE is biased (1)54:28
ABC-MLE is biased (2)54:44
Noisy ABC-MLE55:16
Consistent noisy ABC-MLE56:16
Which summary? (1)56:49
Which summary? (2)56:59
Which summary? (3)57:06
Which summary for model choice? (1)58:06
Which summary for model choice? (2)58:15
Semi-automatic ABC58:44
Summary [of F&P/statistics) (1)59:15
Summary [of F&P/statistics) (2)01:00:23
Details on Fearnhead and Prangle (F&P) ABC01:00:24
Errors, errors, and errors01:00:27