### Abstract

In this paper we develop an approach to estimate the rates of occurrence of events assuming correlations exist between the rates. The approach developed uses the Method of Moments to find Empirical Bayes estimates of the model parameters. These estimates are adjusted to give individual estimates for each event using Bayes linear methods, a linear fitting procedure which uses a similar subjective basis for inference as a full Bayesian analysis. We compare the accuracy of the estimates obtained with our proposed methods relative to exact inference for a full Bayesian model based on a Homogeneous Poisson Process (HPP) with a multivariate gamma prior distribution.

Language | English |
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Number of pages | 10 |

Publication status | Published - Jun 2012 |

Event | PSAM11 & ESREL 2012 - Helsinki, Finland Duration: 25 Jun 2012 → 29 Jun 2012 |

### Conference

Conference | PSAM11 & ESREL 2012 |
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Country | Finland |

City | Helsinki |

Period | 25/06/12 → 29/06/12 |

### Fingerprint

### Keywords

- correlated event rates
- homogeneous poisson process
- bayes linear
- empirical bayes inference
- linear adjustments

### Cite this

*Bayes linear adjustments to improve empirical bayes inference for correlated event rates*. Paper presented at PSAM11 & ESREL 2012, Helsinki, Finland.

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**Bayes linear adjustments to improve empirical bayes inference for correlated event rates.** / Quigley, John; Wilson, Kevin; Bedford, Tim; Walls, Lesley.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Bayes linear adjustments to improve empirical bayes inference for correlated event rates

AU - Quigley, John

AU - Wilson, Kevin

AU - Bedford, Tim

AU - Walls, Lesley

PY - 2012/6

Y1 - 2012/6

N2 - Empirical Bayes offers a means of obtaining robust inference by pooling data on processes that have similar, although not identical, rates of occurrence and then adjusting the pooled estimate through Bayes Theorem to adjust the estimate to the experience of each individual process. The accuracy of Empirical Bayes estimates depends on the degree of homogeneity of the processes within the pool. To date, Empirical Bayes inference methods have been developed assuming that rates are statistically independent of one another. While a useful starting assumption, it may not be realistic in practice.In this paper we develop an approach to estimate the rates of occurrence of events assuming correlations exist between the rates. The approach developed uses the Method of Moments to find Empirical Bayes estimates of the model parameters. These estimates are adjusted to give individual estimates for each event using Bayes linear methods, a linear fitting procedure which uses a similar subjective basis for inference as a full Bayesian analysis. We compare the accuracy of the estimates obtained with our proposed methods relative to exact inference for a full Bayesian model based on a Homogeneous Poisson Process (HPP) with a multivariate gamma prior distribution.

AB - Empirical Bayes offers a means of obtaining robust inference by pooling data on processes that have similar, although not identical, rates of occurrence and then adjusting the pooled estimate through Bayes Theorem to adjust the estimate to the experience of each individual process. The accuracy of Empirical Bayes estimates depends on the degree of homogeneity of the processes within the pool. To date, Empirical Bayes inference methods have been developed assuming that rates are statistically independent of one another. While a useful starting assumption, it may not be realistic in practice.In this paper we develop an approach to estimate the rates of occurrence of events assuming correlations exist between the rates. The approach developed uses the Method of Moments to find Empirical Bayes estimates of the model parameters. These estimates are adjusted to give individual estimates for each event using Bayes linear methods, a linear fitting procedure which uses a similar subjective basis for inference as a full Bayesian analysis. We compare the accuracy of the estimates obtained with our proposed methods relative to exact inference for a full Bayesian model based on a Homogeneous Poisson Process (HPP) with a multivariate gamma prior distribution.

KW - correlated event rates

KW - homogeneous poisson process

KW - bayes linear

KW - empirical bayes inference

KW - linear adjustments

UR - https://www.psam11.org/www/fi/index.php

M3 - Paper

ER -