Dynamical Systems, Stochastic Processes and Bayesian Inference

Path Integral Method for Estimation of Time Series

author: Juan Restrepo, Mathematics Department, University of Arizona

Categories

Top: Computer Science: Machine Learning: Markov Processes
Top: Computer Science: Data Mining: Time Series Analysis

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*Slides*
0:00	Data Assimilation
1:01	Collaborators
1:15	Three Estimation Problems
3:08	Turning a model into a state estimation problem
4:52	Statement of the Problem
6:50	GOAL: estimate moments
7:25	A Nonlinear Example
9:45	Observations
10:18	Extended Kalman Filter
13:46	Alternative Approaches
15:37	Observations
15:40	KSP Filter Results
18:02	Why not KSP?
18:42	A Statistical-Mechanical Digression
20:04	Fact: log n! ¼ n log n - n
20:30	BAYESIAN STATEMENT
21:22	Path Integral Method
23:21	Path Integral Method01
24:39	Path Integral Method02
25:39	Path Integral Method03
27:08	Otherwise use sampling
27:41	Hybrid Monte Carlo
29:42	The HMC algorithm
33:07	What’s going on?
34:05	What’s going on?01
34:51	Unigrid Monte Carlo
35:19	Generalized HMC
37:14	PIMC Results
38:06	RESULTS: decorrelation time
39:07	Conclusions (Sampling)
39:46	OVERALL CONCLUSIONS
41:06	Further Information

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