A Bayesian Model for Markov Chains via Jeffrey's Prior

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

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Empirical Markov chains as models of dynamic processes

PsycEXTRA Dataset ◽

10.1037/e484502008-001 ◽

2008 ◽

Author(s):

Stephen Merrill

Keyword(s):

Markov Chains ◽

Dynamic Processes

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Markov models—Markov chains

Nature Methods ◽

10.1038/s41592-019-0476-x ◽

2019 ◽

Vol 16 (8) ◽

pp. 663-664 ◽

Cited By ~ 1

Author(s):

Jasleen K. Grewal ◽

Martin Krzywinski ◽

Naomi Altman

Keyword(s):

Markov Chains ◽

Markov Models

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Evaluating the Validity of a Bayesian Program for Predicting Stage in Hodgkin’s Disease

Methods of Information in Medicine ◽

10.1055/s-0038-1635305 ◽

1981 ◽

Vol 20 (03) ◽

pp. 174-178 ◽

Cited By ~ 2

Author(s):

A. I. Barnett ◽

J. Cynthia ◽

F. Jane ◽

Nancy Gutensohn ◽

B. Davies

Keyword(s):

New England ◽

Hodgkin's Disease ◽

Bayesian Model ◽

Medical Center ◽

Hodgkin’S Disease ◽

Test Procedure ◽

Disease Patient ◽

Probabilistic Information ◽

Probabilistic Forecasts ◽

England Medical

A Bayesian model that provides probabilistic information about the spread of malignancy in a Hodgkin’s disease patient has been developed at the Tufts New England Medical Center. In assessing the model’s reliability, it seemed important to use it to make predictions about patients other than those relevant to its construction. The accuracy of these predictions could then be tested statistically. This paper describes such a test, based on 243 Hodgkin’s disease patients of known pathologic stage. The results obtained were supportive of the model, and the test procedure might interest those wishing to determine whether the imperfections that attend any attempt to make probabilistic forecasts have gravely damaged their accuracy.

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Machine Learning of Motor Vehicle Accident Categories from Narrative Data

Methods of Information in Medicine ◽

10.1055/s-0038-1634680 ◽

1996 ◽

Vol 35 (04/05) ◽

pp. 309-316 ◽

Cited By ~ 4

Author(s):

M. R. Lehto ◽

G. S. Sorock

Keyword(s):

Machine Learning ◽

Bayesian Model ◽

Keyword Search ◽

Motor Vehicle ◽

Motor Vehicle Accident ◽

Computer Search ◽

Vehicle Accident ◽

Learning Technique ◽

Expert Ratings ◽

Keyword Searches

Abstract:Bayesian inferencing as a machine learning technique was evaluated for identifying pre-crash activity and crash type from accident narratives describing 3,686 motor vehicle crashes. It was hypothesized that a Bayesian model could learn from a computer search for 63 keywords related to accident categories. Learning was described in terms of the ability to accurately classify previously unclassifiable narratives not containing the original keywords. When narratives contained keywords, the results obtained using both the Bayesian model and keyword search corresponded closely to expert ratings (P(detection)≥0.9, and P(false positive)≤0.05). For narratives not containing keywords, when the threshold used by the Bayesian model was varied between p>0.5 and p>0.9, the overall probability of detecting a category assigned by the expert varied between 67% and 12%. False positives correspondingly varied between 32% and 3%. These latter results demonstrated that the Bayesian system learned from the results of the keyword searches.

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