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Inference for Trans-dimensional Bayesian Models with Diffusive Nested Sampling | | Brendon J. Brewer
; | | Date: |
14 Nov 2014 | | Abstract: | Many inference problems involve inferring the number $N$ of objects in some
region, along with their properties ${mathbf{x}_i}_{i=1}^N$, from a dataset
$mathcal{D}$. A common statistical example is finite mixture modelling. In the
Bayesian framework, these problems are typically solved using one of the
following two methods: i) by executing a Monte Carlo algorithm (such as Nested
Sampling) once for each possible value of $N$, and calculating the marginal
likelihood or evidence as a function of $N$; or ii) by doing a single run that
allows the model dimension $N$ to change (such as Markov Chain Monte Carlo with
birth/death moves), and obtaining the posterior for $N$ directly. In this paper
we present a general approach to this problem that uses trans-dimensional MCMC
embedded {it within} a Nested Sampling algorithm, allowing us to explore the
posterior distribution and calculate the marginal likelihood (summed over $N$)
even if the problem contains a phase transition or other difficult features
such as multimodality. We present two example problems, finding sinusoidal
signals in noisy data, and finding and measuring galaxies in a noisy
astronomical image. Both of the examples demonstrate phase transitions in the
relationship between the likelihood and the cumulative prior mass. | | Source: | arXiv, 1411.3921 | | Services: | Forum | Review | PDF | Favorites | |
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