Bayesian inference using two-stage Laplace approximation for differential equation models
We consider the problem of Bayesian inference for parameters in non-linear regression models whereby the underlying unknown response functions are formed by a set of differential equations. Bayesian methods of inference for unknown parameters rely primarily on the posterior obtained by Bayes rule. F...
| Main Authors: | Dass, S.C., Lee, J., Lee, K. |
|---|---|
| Format: | Conference or Workshop Item |
| Institution: | Universiti Teknologi Petronas |
| Record Id / ISBN-0: | utp-eprints.30660 / |
| Published: |
American Institute of Physics Inc.
2016
|
| Online Access: |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85005950985&doi=10.1063%2f1.4968163&partnerID=40&md5=cf2bb6e63722c1591f94ecc739befbbe http://eprints.utp.edu.my/30660/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| id |
utp-eprints.30660 |
|---|---|
| recordtype |
eprints |
| spelling |
utp-eprints.306602022-03-25T07:13:49Z Bayesian inference using two-stage Laplace approximation for differential equation models Dass, S.C. Lee, J. Lee, K. We consider the problem of Bayesian inference for parameters in non-linear regression models whereby the underlying unknown response functions are formed by a set of differential equations. Bayesian methods of inference for unknown parameters rely primarily on the posterior obtained by Bayes rule. For differential equation models, analytic and closed forms for the posterior are not available and one has to resort to approximations. We propose a two-stage Laplace expansion to approximate the marginal likelihood, and hence, the posterior, to obtain an approximate closed form solution. For large sample sizes, the method of inference borrows from non-linear regression theory for maximum likelihood estimates, and is therefore, consistent. Our approach is exact in the limit and does not need the specification of an additional penalty parameter. Examples in this paper include the exponential model and SIR (Susceptible-Infected-Recovered) disease spread model. © 2016 Author(s). American Institute of Physics Inc. 2016 Conference or Workshop Item NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85005950985&doi=10.1063%2f1.4968163&partnerID=40&md5=cf2bb6e63722c1591f94ecc739befbbe Dass, S.C. and Lee, J. and Lee, K. (2016) Bayesian inference using two-stage Laplace approximation for differential equation models. In: UNSPECIFIED. http://eprints.utp.edu.my/30660/ |
| institution |
Universiti Teknologi Petronas |
| collection |
UTP Institutional Repository |
| description |
We consider the problem of Bayesian inference for parameters in non-linear regression models whereby the underlying unknown response functions are formed by a set of differential equations. Bayesian methods of inference for unknown parameters rely primarily on the posterior obtained by Bayes rule. For differential equation models, analytic and closed forms for the posterior are not available and one has to resort to approximations. We propose a two-stage Laplace expansion to approximate the marginal likelihood, and hence, the posterior, to obtain an approximate closed form solution. For large sample sizes, the method of inference borrows from non-linear regression theory for maximum likelihood estimates, and is therefore, consistent. Our approach is exact in the limit and does not need the specification of an additional penalty parameter. Examples in this paper include the exponential model and SIR (Susceptible-Infected-Recovered) disease spread model. © 2016 Author(s). |
| format |
Conference or Workshop Item |
| author |
Dass, S.C. Lee, J. Lee, K. |
| spellingShingle |
Dass, S.C. Lee, J. Lee, K. Bayesian inference using two-stage Laplace approximation for differential equation models |
| author_sort |
Dass, S.C. |
| title |
Bayesian inference using two-stage Laplace approximation for differential equation models |
| title_short |
Bayesian inference using two-stage Laplace approximation for differential equation models |
| title_full |
Bayesian inference using two-stage Laplace approximation for differential equation models |
| title_fullStr |
Bayesian inference using two-stage Laplace approximation for differential equation models |
| title_full_unstemmed |
Bayesian inference using two-stage Laplace approximation for differential equation models |
| title_sort |
bayesian inference using two-stage laplace approximation for differential equation models |
| publisher |
American Institute of Physics Inc. |
| publishDate |
2016 |
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85005950985&doi=10.1063%2f1.4968163&partnerID=40&md5=cf2bb6e63722c1591f94ecc739befbbe http://eprints.utp.edu.my/30660/ |
| _version_ |
1741197445034934272 |
| score |
11.62408 |