Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models
We develop a mixture model and diagnostic for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both extend the mixture transition distribution, which constructs a transition probability tensor by aggregating probabilities from a set of single-lag transition matrices, th...
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ftsmithonian:oai:figshare.com:article/16624595 2023-05-15T17:59:39+02:00 Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models Matthew Heiner (837351) Athanasios Kottas (2919086) 2021-09-15T21:20:07Z https://doi.org/10.6084/m9.figshare.16624595.v2 unknown https://figshare.com/articles/dataset/Estimation_and_Selection_for_High-Order_Markov_Chains_with_Bayesian_Mixture_Transition_Distribution_Models/16624595 doi:10.6084/m9.figshare.16624595.v2 CC BY 4.0 CC-BY Genetics Inorganic Chemistry Infectious Diseases Computational Biology Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Information Systems not elsewhere classified Categorical time series Dimension reduction Model selection Shrinkage prior Tensor decomposition Dataset 2021 ftsmithonian https://doi.org/10.6084/m9.figshare.16624595.v2 2021-12-19T21:41:44Z We develop a mixture model and diagnostic for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both extend the mixture transition distribution, which constructs a transition probability tensor by aggregating probabilities from a set of single-lag transition matrices, through inclusion of mixture components dependent on multiple lags. We demonstrate two uses for the proposed model: identification of relevant lags through over-specification and shrinkage via priors for sparse probability vectors, and parsimonious approximation of multi-lag dynamics by mixing low-order transition models. The diagnostic yields a general and interpretable mixture decomposition for transition probability tensors estimated by any means. We demonstrate the utility of the model and diagnostic with simulation studies, and further apply the methodology to a data analysis from the high-order Markov chain literature, and to a time series of pink salmon abundance in Alaska, United States. Supplemental files for this article are available online. Dataset Pink salmon Alaska Unknown |
institution |
Open Polar |
collection |
Unknown |
op_collection_id |
ftsmithonian |
language |
unknown |
topic |
Genetics Inorganic Chemistry Infectious Diseases Computational Biology Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Information Systems not elsewhere classified Categorical time series Dimension reduction Model selection Shrinkage prior Tensor decomposition |
spellingShingle |
Genetics Inorganic Chemistry Infectious Diseases Computational Biology Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Information Systems not elsewhere classified Categorical time series Dimension reduction Model selection Shrinkage prior Tensor decomposition Matthew Heiner (837351) Athanasios Kottas (2919086) Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models |
topic_facet |
Genetics Inorganic Chemistry Infectious Diseases Computational Biology Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Information Systems not elsewhere classified Categorical time series Dimension reduction Model selection Shrinkage prior Tensor decomposition |
description |
We develop a mixture model and diagnostic for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both extend the mixture transition distribution, which constructs a transition probability tensor by aggregating probabilities from a set of single-lag transition matrices, through inclusion of mixture components dependent on multiple lags. We demonstrate two uses for the proposed model: identification of relevant lags through over-specification and shrinkage via priors for sparse probability vectors, and parsimonious approximation of multi-lag dynamics by mixing low-order transition models. The diagnostic yields a general and interpretable mixture decomposition for transition probability tensors estimated by any means. We demonstrate the utility of the model and diagnostic with simulation studies, and further apply the methodology to a data analysis from the high-order Markov chain literature, and to a time series of pink salmon abundance in Alaska, United States. Supplemental files for this article are available online. |
format |
Dataset |
author |
Matthew Heiner (837351) Athanasios Kottas (2919086) |
author_facet |
Matthew Heiner (837351) Athanasios Kottas (2919086) |
author_sort |
Matthew Heiner (837351) |
title |
Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models |
title_short |
Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models |
title_full |
Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models |
title_fullStr |
Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models |
title_full_unstemmed |
Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models |
title_sort |
estimation and selection for high-order markov chains with bayesian mixture transition distribution models |
publishDate |
2021 |
url |
https://doi.org/10.6084/m9.figshare.16624595.v2 |
genre |
Pink salmon Alaska |
genre_facet |
Pink salmon Alaska |
op_relation |
https://figshare.com/articles/dataset/Estimation_and_Selection_for_High-Order_Markov_Chains_with_Bayesian_Mixture_Transition_Distribution_Models/16624595 doi:10.6084/m9.figshare.16624595.v2 |
op_rights |
CC BY 4.0 |
op_rightsnorm |
CC-BY |
op_doi |
https://doi.org/10.6084/m9.figshare.16624595.v2 |
_version_ |
1766168510343413760 |