Approximate Inference in Stochastic Processes and Dynamical Systems

On stratified path sampling of the Thermodynamic Integral: computing Bayes factors for nonlinear dynamical systems models

author: Mark Girolami, University of Glasgow

Description

Bayes factors provide a means of objectively ranking a number of plausible statistical models based on their evidential support. Computing Bayes factors is far from straightforward and methodology based on thermodynamic integration can provide stable estimates of the integrated likelihood. This talk will consider a stratified sampling strategy in estimating the thermodynamic integral and will consider issues such as optimal paths and the variance of the overall estimator. The main application considered will be the computation of Bayes factors for dynamical biochemical pathway models based on systems of nonlinear ordinary differential equations (ODE). A large scale study of the ExtraCellular Regulated Kinase (ERK) pathway will be discussed where recent Small Interfering RNA (siRNA) experimental validation of the predictions made using the computed Bayes factors is presented.

You might be experiencing some problems with Your Video player.

*Slides*
0:00	On Stratified Path Sampling of the Thermodynamic Integral: Computing Bayes Factors for Nonlinear ODE Models of Biochemical Pathways
1:07	Talk Outline (1)
1:20	Talk Outline (2)
1:50	Talk Outline (3)
2:27	Talk Outline (4)
2:46	Talk Outline (5)
3:13	Talk Outline (6)
3:49	Talk Outline (7)
3:52	Identification of Parameters in Mechanistic Models
4:16	Identification of Parameters in Mechanistic Models
5:06	Assessing Evidential Support for Competing Mechanistic Descriptions
5:07	Assessing Evidential Support for Competing Mechanistic Descriptions
6:08	Assessing Evidential Support for Competing Mechanistic Descriptions
6:27	Assessing Evidential Support for Competing Mechanistic Descriptions
7:29	Statistical Inference over Mechanistic Models
8:22	Estimation of Bayes Factors (1)
9:00	Estimation of Bayes Factors (2)
9:36	Estimation of Bayes Factors (3)
10:08	Estimation of Bayes Factors (4)
10:09	Estimation of Bayes Factors (5)
10:30	Estimation of Bayes Factors (6)
10:58	Estimation of Bayes Factors (7)
11:44	Estimation of Bayes Factors (8)
12:38	Estimation of Bayes Factors (9)
12:47	Estimation of Bayes Factors (10)
13:06	Estimation of Bayes Factors (11)
13:42	Estimation of Bayes Factors (12)
14:13	Estimation of Bayes Factors (13)
14:32	Estimation of Bayes Factors (14)
14:51	Estimation of Bayes Factors (15)
15:01	Estimation of Bayes Factors (16)
15:08	Estimation of Bayes Factors (17)
15:36	Estimation of Bayes Factors (18)
16:17	The Thermodynamic Integral (1)
17:04	The Thermodynamic Integral (2)
18:28	The Thermodynamic Integral (3)
18:33	The Thermodynamic Integral (4)
19:18	The Thermodynamic Integral (5)
19:37	The Thermodynamic Integral (6)
19:46	The Thermodynamic Integral (7)
20:25	Path Sampling (1)
20:34	Path Sampling (2)
20:39	Path Sampling (3)
20:45	Path Sampling (4)
20:55	Path Sampling (5)
21:00	Path Sampling (6)
21:10	Path Sampling (7)
21:17	Path Sampling (8)
22:04	Path Sampling (9)
22:59	Stratified Path Sampling (1)
23:17	Stratified Path Sampling (2)
23:21	Path Sampling (4)
23:22	Stratified Path Sampling (1)
23:35	Stratified Path Sampling (2)
24:21	Stratified Path Sampling (3)
24:46	Stratified Path Sampling (4)
25:31	Stratified Path Sampling (5)
25:44	Stratified Path Sampling (6)
25:47	Stratified Path Sampling (7)
25:49	Stratified Path Sampling (8)
27:46	Stratified Path Sampling (9)
28:27	Stratified Path Sampling (10)
28:44	Stratified Path Sampling (11)
30:28	Optimal Path Partition (1)
30:51	Optimal Path Partition (2)
31:04	Optimal Path Partition (3)
31:05	Optimal Path Partition (4)
31:57	Stratified Path Sampling (11)
32:10	Optimal Path Partition (4)
32:30	Illustrative Performance - Linear Regression Examples (1)
33:32	Illustrative Performance - Linear Regression Examples (2)
33:54	Illustrative Performance - Linear Regression Examples (3)
34:44	Illustrative Performance - Linear Regression Examples (4)
35:27	Nonlinear ODE Oscillator Model (1)
35:37	Nonlinear ODE Oscillator Model (2)
36:27	Non-Uniqueness of Solutions
37:39	Parameter Posteriors from Metropolis
38:15	Population Markov Chain Monte Carlo Promising Solution (1)
38:44	Nonlinear ODE Oscillator Model (2)
38:52	Parameter Posteriors from Metropolis
39:07	Population Markov Chain Monte Carlo Promising Solution (1)
39:09	Population Markov Chain Monte Carlo Promising Solution (2)
40:28	Population Markov Chain Monte Carlo Promising Solution (1)
40:53	Population Markov Chain Monte Carlo Promising Solution (2)
41:31	Parameter Posteriors from Population MCMC
41:46	Two Possible Goodwin Oscillator Models
42:30	Population Markov Chain Monte Carlo Promising Solution
43:38	Now Can Tackle a Major Large Scale Study: The ERK Signalling Pathway
44:40	Crosstalk with the cAMP Pathway
44:41	Models
45:43	Experimental Data (1)
46:00	Experimental Data (2)
46:05	Experimental Data (3)
46:07	Experimental Data (4)
46:08	Experimental Data (5)
46:11	Experimental Data (6)
46:13	Experimental Data (7)
46:15	Experimental Data (8)
46:17	Experimental Data (9)
46:18	Experimental Data (10)
46:20	Experimental Data (11)
46:36	Hypotheses Testing: Result
47:56	Hypotheses Testing: Implications
48:20	Hot of the Press - Very Recent Results from siRNA Knock Down Experiments (2)
49:02	Hot of the Press - Very Recent Results from siRNA Knock Down Experiments (1)
49:03	Hypotheses Testing: Implications
49:29	Hot of the Press - Very Recent Results from siRNA Knock Down Experiments (1)
49:31	Hot of the Press - Very Recent Results from siRNA Knock Down Experiments (2)
49:35	Conclusions & Discussion (1)
49:53	Conclusions & Discussion (2)
50:01	Conclusions & Discussion (3)
50:09	Conclusions & Discussion (4)
50:21	Conclusions & Discussion (5)
50:23	Acknowledgements
50:26	Funding Acknowledgements

Lecture rating

People found this lecture:
Worth seeing
because it is:
Valuable and informative
Well presented
Easily understandable
Acceptably recorded
You need to login to cast your vote.

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.