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Dirichlet Processes and Nonparametric Bayesian Modelling
Published on Feb 25, 200732254 Views
Bayesian modeling is a principled approach to updating the degree of belief in a hypothesis given prior knowledge and given available evidence. Both prior knowledge and evidence are combined using Bay
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Chapter list
Dirichlet Processes and Nonparametric Bayesian Modelling00:00
Motivation00:38
Gaussian Processes: Modeling Functions01:17
Dirichlet Processes: Modeling Probability measures02:36
Outline04:23
I: Introduction to Bayesian Modeling05:57
Statistical Approaches to Learning and Statistics05:59
Review of Some Laws of Probability07:42
Multivariate Distribution07:46
Conditional Distribution08:15
Product Decomposition and Chain Rule08:38
Bayes’ Rule10:00
Marginal Distribution10:22
Bayesian Reasoning and Bayesian Statistics10:52
Bayesian Reasoning10:56
Bayesian Reasoning: Example12:15
Bayesian Reasoning: Debate13:20
Bayesian Reasoning: Subjective Probabilities15:15
Technicalities in Bayesian Statistics16:43
Basic Approach in Statistical Bayesian Modeling17:08
Basic Approach in Statistical Bayesian Modeling (2)20:37
Approximating the Integrals in Bayesian Modeling23:02
Conclusion on Bayesian Modeling24:51
II: Multinomial Sampling with a<br> Dirichlet Prior26:09
Likelihood, Prior, Posterior, and Predictive <br>Distribution26:37
Multinomial Sampling with a Dirichlet Prior26:40
Example: Tossing a Loaded Dice27:28
Multinomial Likelihood29:02
Multinomial Likelihood for a Data Set31:14
Dirichlet Prior32:48
Posterior Distribution36:15
Dirichlet Distributions for Dir(·| 1, 2, 3)38:14
Generating Samples from g and 42:04
Generative Model42:22
First Approach: Sampling from g43:56
Second Approach: Sampling from directly45:01
Second Approach: Sampling from directly (2)47:00
P(N+1 = k|D) = 0 k+Nk<br> 0+N with 0 ! 0: A Paradox?47:13
Beta-Distribution49:47
Noisy Observations50:37
Noisy Observations 0151:05
Noisy Observations 0252:07
Inference based on Markov Chain Monte Carlo Sampling53:52
Gibbs Sampling56:43
Gibbs Sampling (2)59:11