Time Dependent Stick Breaking Processes

author: Jim Griffin, University of Kent

Description

The stick breaking construction of the Dirichlet process has been a popular starting point for many dependent nonparametric processes. This talk considers a temporal version of the Order-Based Dependent Dirichlet Process, which can be extended to more general stick-breaking marginal processes. Interestingly, the simplest constructions lead to marginal Dirichlet and Poisson-Dirichlet processes. Usefully, the first process also has a “Chinese restaurant”-type representation which will be described. Applications to time-dependent mixture modelling will be presented.

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*Slides*
0:00	Time Dependent Stick Breaking Processes
0:28	Outline
1:29	Introduction (1)
4:39	Introduction (2)
6:35	Stick Breaking Processes
8:29	Examples
9:15	Random Walks on Discrete Distributions (1)
14:50	Random Walks on Discrete Distributions (2)
15:17	Random Walks on Discrete Distributions (1)
15:52	Random Walks on Discrete Distributions (2)
17:56	DPAR process (1)
22:21	DPAR process (2)
23:31	DPAR process (3)
24:16	Properties
25:01	Chinese restaurant representation (1)
28:32	Chinese restaurant representation (2)
32:22	Chinese restaurant representation (3)
32:52	П-AR processes (1)
33:40	П-AR processes (2)
34:07	A stochastic process for V
35:05	PDAR (1)
35:16	A stochastic process for V
35:35	PDAR (1)
35:53	PDAR (2)
37:21	Computation
38:03	Stochastic volatility (1)
38:43	Stochastic volatility (2)
38:57	Stochastic volatility (3)
38:59	- Questions
39:16	Stochastic volatility (3)
39:46	Stochastic volatility (4)
40:04	Stochastic volatility (5)
40:41	Time-dependent density estimation (1)
41:18	Time-dependent density estimation (2)
41:33	Time-dependent density estimation (3)
41:48	Time-dependent density estimation (4)
42:13	Discussion

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