Estimating the Marginal Likelihood Using the Arithmetic Mean Identity
By Anna Pajor. 2017
50 citations recorded by the source corpus.
In this paper we propose a conceptually straightforward method to estimate the marginal data density value (also called the marginal likelihood). We show that the marginal likelihood is equal to the prior mean of the conditional density of the data given the vector of parameters restricted to a certain subset of the parameter space, A, times the reciprocal of the posterior probability of the subset A. This identity motivates one to use Arithmetic Mean estimator based on simulation from the prior distribution restricted to any (but reasonable) subset of the space of parameters. By trimming this space, regions of relatively low likelihood are removed, and thereby the efficiency of the Arithmetic Mean estimator is improved. We show that the adjusted Arithmetic Mean estimator is unbiased and consistent.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a049873399b9dcbedacb1d203970f1d1c3bd17c8
How researchers see this paper
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In Artificial Intelligence
- H. Steingroever
- Ruud Wetzels
- Annette Horstmann
- Jane Neumann
- Eric-Jan Wagenmakers
- Joachim Vandekerckhove
In Statistics and Probability
- Ruud Wetzels
- H. Steingroever
- Jane Neumann
- Annette Horstmann
- Eric-Jan Wagenmakers
- John K. Kruschke
- Zoltan Dienes
- M. Masson
Citations in the corpus
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