Approximate Bayesian Estimation of Varying Binomial Process
Summary :
Bayesian methods are often applied for estimating the event rate from a series of event occurrences. However, the Bayesian posterior distribution requires the computation of the marginal likelihood which generally involves an analytically intractable integration. As an event rate is defined in a very high dimensional space, it is computationally demanding to obtain the Bayesian posterior distribution for the rate. We estimate the rate underlying a sequence of event counts by deriving an approximate Bayesian inference algorithm for the time-varying binomial process. This enables us to calculate the posterior distribution analytically. We also provide a method for estimating the prior hyperparameter, which determines the smoothness of the estimated event rate. Moreover, we provide an efficient method to compute the upper and lower bounds of the marginal likelihood, which evaluate the approximation accuracy. Numerical experiments demonstrate the effectiveness of the proposed method in terms of the estimation accuracy.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.12 pp.2879-2885
- Publication Date
- 2011/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E94.A.2879
- Type of Manuscript
- PAPER
- Category
- General Fundamentals and Boundaries
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Kazuho WATANABE, Masato OKADA, "Approximate Bayesian Estimation of Varying Binomial Process" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 12, pp. 2879-2885, December 2011, doi: 10.1587/transfun.E94.A.2879.
Abstract: Bayesian methods are often applied for estimating the event rate from a series of event occurrences. However, the Bayesian posterior distribution requires the computation of the marginal likelihood which generally involves an analytically intractable integration. As an event rate is defined in a very high dimensional space, it is computationally demanding to obtain the Bayesian posterior distribution for the rate. We estimate the rate underlying a sequence of event counts by deriving an approximate Bayesian inference algorithm for the time-varying binomial process. This enables us to calculate the posterior distribution analytically. We also provide a method for estimating the prior hyperparameter, which determines the smoothness of the estimated event rate. Moreover, we provide an efficient method to compute the upper and lower bounds of the marginal likelihood, which evaluate the approximation accuracy. Numerical experiments demonstrate the effectiveness of the proposed method in terms of the estimation accuracy.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.2879/_p
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@ARTICLE{e94-a_12_2879,
author={Kazuho WATANABE, Masato OKADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Approximate Bayesian Estimation of Varying Binomial Process},
year={2011},
volume={E94-A},
number={12},
pages={2879-2885},
abstract={Bayesian methods are often applied for estimating the event rate from a series of event occurrences. However, the Bayesian posterior distribution requires the computation of the marginal likelihood which generally involves an analytically intractable integration. As an event rate is defined in a very high dimensional space, it is computationally demanding to obtain the Bayesian posterior distribution for the rate. We estimate the rate underlying a sequence of event counts by deriving an approximate Bayesian inference algorithm for the time-varying binomial process. This enables us to calculate the posterior distribution analytically. We also provide a method for estimating the prior hyperparameter, which determines the smoothness of the estimated event rate. Moreover, we provide an efficient method to compute the upper and lower bounds of the marginal likelihood, which evaluate the approximation accuracy. Numerical experiments demonstrate the effectiveness of the proposed method in terms of the estimation accuracy.},
keywords={},
doi={10.1587/transfun.E94.A.2879},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Approximate Bayesian Estimation of Varying Binomial Process
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2879
EP - 2885
AU - Kazuho WATANABE
AU - Masato OKADA
PY - 2011
DO - 10.1587/transfun.E94.A.2879
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2011
AB - Bayesian methods are often applied for estimating the event rate from a series of event occurrences. However, the Bayesian posterior distribution requires the computation of the marginal likelihood which generally involves an analytically intractable integration. As an event rate is defined in a very high dimensional space, it is computationally demanding to obtain the Bayesian posterior distribution for the rate. We estimate the rate underlying a sequence of event counts by deriving an approximate Bayesian inference algorithm for the time-varying binomial process. This enables us to calculate the posterior distribution analytically. We also provide a method for estimating the prior hyperparameter, which determines the smoothness of the estimated event rate. Moreover, we provide an efficient method to compute the upper and lower bounds of the marginal likelihood, which evaluate the approximation accuracy. Numerical experiments demonstrate the effectiveness of the proposed method in terms of the estimation accuracy.
ER -
English
