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6 results on '"Austad, Haakon Michael"'

1. Approximations and bounds for binary Markov random fields

Author

Austad, Haakon Michael and Tjelmeland, Håkon

Subjects
Statistics - Computation
Abstract

Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and a fully Bayesian treatment of discrete Markov random fields difficult. We apply approximation theory for pseudo-Boolean functions to binary Markov random fields and construct approximations and upper and lower bounds for the associated computationally intractable normalising constant. As a by-product of this process we also get a partially ordered Markov model approximation of the binary Markov random field. We present numerical examples with both the pairwise interaction Ising model and with higher-order interaction models, showing the quality of our approximations and bounds. We also present simulation examples and one real data example demonstrating how the approximations and bounds can be applied for parameter estimation and to handle a fully-Bayesian model computationally., Comment: 33 pages, 17 figures

Published
2015

5. Approximations of Binary Markov Random Fields

Author

Austad, Haakon Michael and Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag

Abstract

PhD i matematikk PhD in Mathematics

Published
2011

6. Parallel Multiple Proposal MCMC Algorithms

Author

Austad, Haakon Michael, Tjelmeland, Håkon, and Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag

Subjects
3425 [ntnudaim], ntnudaim:3425, Industriell matematikk, SIF3 fysikk og matematikk
Abstract

We explore the variance reduction achievable through parallel implementation of multi-proposal MCMC algorithms and use of control variates. Implemented sequentially multi-proposal MCMC algorithms are of limited value, but they are very well suited for parallelization. Further, discarding the rejected states in an MCMC sampler can intuitively be interpreted as a waste of information. This becomes even more true for a multi-proposal algorithm where we discard several states in each iteration. By creating an alternative estimator consisting of a linear combination of the traditional sample mean and zero mean random variables called control variates we can improve on the traditional estimator. We present a setting for the multi-proposal MCMC algorithm and study it in two examples. The first example considers sampling from a simple Gaussian distribution, while for the second we design the framework for a multi-proposal mode jumping algorithm for sampling from a distribution with several separated modes. We find that the variance reduction achieved from our control variate estimator in general increases as the number of proposals in our sampler increase. For our Gaussian example we find that the benefit from parallelization is small, and that little is gained from increasing the number of proposals. The mode jumping example however is very well suited for parallelization and we get a relative variance reduction pr time of roughly 80% with 16 proposals in each iteration.

Published
2007

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