Slice Sampling with Multivariate Steps
Markov chain Monte Carlo (MCMC) allows statisticians to sample from a wide variety of multidimensional probability distributions. Unfortunately, MCMC is often difficult to use when components of the target distribution are highly correlated or have disparate variances. This thesis presents three res...
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ndltd-TORONTO-oai-tspace.library.utoronto.ca-1807-319552013-04-19T19:56:42ZSlice Sampling with Multivariate StepsThompson, Madeleineadaptive Markov chain Monte Carloadaptive MCMCslice samplingcrumb framework0463Markov chain Monte Carlo (MCMC) allows statisticians to sample from a wide variety of multidimensional probability distributions. Unfortunately, MCMC is often difficult to use when components of the target distribution are highly correlated or have disparate variances. This thesis presents three results that attempt to address this problem. First, it demonstrates a means for graphical comparison of MCMC methods, which allows researchers to compare the behavior of a variety of samplers on a variety of distributions. Second, it presents a collection of new slice-sampling MCMC methods. These methods either adapt globally or use the adaptive crumb framework for sampling with multivariate steps. They perform well with minimal tuning on distributions when popular methods do not. Methods in the first group learn an approximation to the covariance of the target distribution and use its eigendecomposition to take non-axis-aligned steps. Methods in the second group use the gradients at rejected proposed moves to approximate the local shape of the target distribution so that subsequent proposals move more efficiently through the state space. Finally, this thesis explores the scaling of slice sampling with multivariate steps with respect to dimension, resulting in a formula for optimally choosing scale tuning parameters. It shows that the scaling of untransformed methods can sometimes be improved by alternating steps from those methods with radial steps based on those of the polar slice sampler.Neal, Radford2011-112012-01-11T21:35:19ZNO_RESTRICTION2012-01-11T21:35:19Z2012-01-11Thesishttp://hdl.handle.net/1807/31955en_ca |
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adaptive Markov chain Monte Carlo adaptive MCMC slice sampling crumb framework 0463 |
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adaptive Markov chain Monte Carlo adaptive MCMC slice sampling crumb framework 0463 Thompson, Madeleine Slice Sampling with Multivariate Steps |
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Markov chain Monte Carlo (MCMC) allows statisticians to sample from a wide variety of multidimensional probability distributions. Unfortunately, MCMC is often difficult to use when components of the target distribution are highly correlated or have disparate variances. This thesis presents three results that attempt to address this problem. First, it demonstrates a means for graphical comparison of MCMC methods, which allows researchers to compare the behavior of a variety of samplers on a variety of distributions. Second, it presents a collection of new slice-sampling MCMC methods. These methods either adapt globally or use the adaptive crumb framework for sampling with multivariate steps. They perform well with minimal tuning on distributions when popular methods do not. Methods in the first group learn an approximation to the covariance of the target distribution and use its eigendecomposition to take non-axis-aligned steps. Methods in the second group use the gradients at rejected proposed moves to approximate the local shape of the target distribution so that subsequent proposals move more efficiently through the state space. Finally, this thesis explores the scaling of slice sampling with multivariate steps with respect to dimension, resulting in a formula for optimally choosing scale tuning parameters. It shows that the scaling of untransformed methods can sometimes be improved by alternating steps from those methods with radial steps based on those of the polar slice sampler. |
author2 |
Neal, Radford |
author_facet |
Neal, Radford Thompson, Madeleine |
author |
Thompson, Madeleine |
author_sort |
Thompson, Madeleine |
title |
Slice Sampling with Multivariate Steps |
title_short |
Slice Sampling with Multivariate Steps |
title_full |
Slice Sampling with Multivariate Steps |
title_fullStr |
Slice Sampling with Multivariate Steps |
title_full_unstemmed |
Slice Sampling with Multivariate Steps |
title_sort |
slice sampling with multivariate steps |
publishDate |
2011 |
url |
http://hdl.handle.net/1807/31955 |
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AT thompsonmadeleine slicesamplingwithmultivariatesteps |
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1716582154042867712 |