Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model
| Autor: | Anthony N. Pettitt, Geoff K. Nicholls, Matthew T. Moores, Kerrie Mengersen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Computer science exchange algorithm Applied Mathematics Posterior probability Indirect Inference indirect inference Bayesian inference hidden Markov random field Statistics - Computation approximate Bayesian computation 62-04 Surrogate model image analysis State space 62M40 62F15 Approximate Bayesian computation Algorithm Computation (stat.CO) intractable likelihood Parametric statistics Potts model |
| Zdroj: | Bayesian Anal. 15, no. 1 (2020), 1-27 |
| ISSN: | 1936-0975 |
| DOI: | 10.1214/18-ba1130 |
| Popis: | The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There are a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open source implementation of our algorithm is available in the R package "bayesImageS." |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|