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Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model

Journal Article


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Abstract


  • 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 is 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.

UOW Authors


  •   Moores, Matt T.
  •   Nicholls, Geoff K. (external author)
  •   Pettit, Anthony N. (external author)
  •   Mengersen, Kerrie (external author)

Publication Date


  • 2020

Citation


  • Moores, M., Nicholls, G. K., Pettit, A. N. & Mengersen, K. (2020). Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model. Bayesian Analysis, 15 (1), 1-27.

Scopus Eid


  • 2-s2.0-85081739516

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=4290&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/3269

Number Of Pages


  • 26

Start Page


  • 1

End Page


  • 27

Volume


  • 15

Issue


  • 1

Place Of Publication


  • United States

Abstract


  • 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 is 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.

UOW Authors


  •   Moores, Matt T.
  •   Nicholls, Geoff K. (external author)
  •   Pettit, Anthony N. (external author)
  •   Mengersen, Kerrie (external author)

Publication Date


  • 2020

Citation


  • Moores, M., Nicholls, G. K., Pettit, A. N. & Mengersen, K. (2020). Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model. Bayesian Analysis, 15 (1), 1-27.

Scopus Eid


  • 2-s2.0-85081739516

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=4290&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/3269

Number Of Pages


  • 26

Start Page


  • 1

End Page


  • 27

Volume


  • 15

Issue


  • 1

Place Of Publication


  • United States