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Updated: April 5th, 2024 05:41

2022 article

Fitting sparse Markov models through a collapsed Gibbs sampler

Bennett, I., Martin, D. E. K., & Lahiri, S. N. (2022, December 15). *COMPUTATIONAL STATISTICS*.

author keywords: Markov chains; Model selection; Bayesian nonparametrics

TL;DR:
The GSDPMM method is applied to fit SMMs to patterns of wind speeds and DNA sequences and is found to perform as well or better than existing methods for fitting SMMs.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: January 3, 2023

2019 journal article

Computation of exact probabilities associated with overlapping pattern occurrences

*WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS*, *11*(5).

author keywords: Auxiliary Markov chain; distribution of a pattern statistic; Markovian sequences; sparse Markov models; VLMC

TL;DR:
An overview of the main methods used to compute distributions of statistics of overlapping pattern occurrences, specifically, generating functions, correlation functions, the Goulden‐Jackson cluster method, recursive equations, and Markov chain embedding are given.
(via Semantic Scholar)

Source: Web Of Science

Added: August 26, 2019

2019 journal article

Distributions of pattern statistics in sparse Markov models

*Annals of the Institute of Statistical Mathematics*, *72*(4), 895–913.

author keywords: Auxiliary Markov chain; Pattern distribution; Sparse Markov model; Variable length Markov chain

TL;DR:
Method for efficient computation of pattern distributions through Markov chains with minimal state spaces is extended to the sparse Markov framework, which gives a better handling of the trade-off between bias associated with having too few model parameters and variance from having too many.
(via Semantic Scholar)

Sources: Web Of Science, Crossref

Added: July 20, 2020

2018 journal article

Minimal auxiliary Markov chains through sequential elimination of states

*COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION*, *48*(4), 1040–1054.

author keywords: completion strings; failure states; Markov chain embedding; minimal deterministic finite automaton; spaced seed coverage; structured motifs

TL;DR:
A characterization of equivalent states is given so that extraneous states are deleted during the process of forming the state space, improving computational efficiency.
(via Semantic Scholar)

Source: Web Of Science

Added: June 24, 2019

2015 journal article

Faster exact distributions of pattern statistics through sequential elimination of states

*ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS*, *69*(1), 231–248.

author keywords: Active proper suffix; Auxiliary Markov chain; Computational efficiency; Extended seed patterns; Minimal deterministic finite automaton; Overlapping pattern occurrences; Seeded alignments; Spaced seed coverage

TL;DR:
This work develops a method to obtain a small set of states during the state generation process without forming a DFA, and shows that a huge reduction in the size of the AMC can be attained.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Multiple window discrete scan statistic for higher-order Markovian sequences

*JOURNAL OF APPLIED STATISTICS*, *42*(8), 1690–1705.

author keywords: variable windows; p-values; one-dimensional scan statistics; 60E05; 60J22

TL;DR:
This work gives an efficient method to compute the exact distribution of multiple window discrete scan statistics for higher-order, multi-state Markovian sequences and defines a Markov chain to efficiently keep track of probabilities needed to compute p-values for the statistic.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2014 journal article

A Coverage Criterion for Spaced Seeds and Its Applications to Support Vector Machine String Kernels and k-Mer Distances

*JOURNAL OF COMPUTATIONAL BIOLOGY*, *21*(12), 947–963.

author keywords: spaced seeds; support vector machine; coverage; alignment-free distance

MeSH headings : Algorithms; Humans; Pattern Recognition, Automated; Sequence Alignment; Sequence Analysis, Protein; Sequence Homology, Amino Acid; Software; Support Vector Machine

TL;DR:
This article shows how this coverage criterion can be directly measured by a full automaton-based approach, and illustrates how this criterion performs when compared with two other criteria frequently used, namely the single-hit and multiple-hit criteria, through correlation coefficients with the correct classification/the true distance.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 article

p-values for the Discrete Scan Statistic through Slack Variables

*COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION*, Vol. 44, pp. 2223–2239.

author keywords: Clustering of patterns; Higher order Markovian trials; Multi-state trials; One-dimensional scan statistic

TL;DR:
An algorithm is given to obtain probabilities for the discrete scan statistic over multi-state trials that are Markovian of a general order of dependence, and the algorithm's usefulness is explored.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

Distribution of Statistics of Hidden State Sequences Through the Sum-Product Algorithm

*METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY*, *15*(4), 897–918.

author keywords: Automata theory; Classification; Conditional random field; Distribution of pattern statistics; Factor graph; Sum-product algorithm

TL;DR:
The methods discussed are relevant for graphs with a sparseness of edges that allows exact computation of the normalization constant for graphs that are represented using conditional random fields and factor graphs.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2011 journal article

Distribution of Clump Statistics for a Collection of Words

*Journal of Applied Probability*, *48*(04), 1049–1059.

Source: Crossref

Added: August 14, 2021

2011 journal article

Distribution of clump statistics for a collection of words

*Journal of Applied Probability*, *48*(4), 1049–1059.

Source: NC State University Libraries

Added: August 6, 2018

2011 journal article

Implied distributions in multiple change point problems

*STATISTICS AND COMPUTING*, *22*(4), 981–993.

author keywords: Finite Markov chain imbedding; Hidden Markov models; Change point probability; Run length distributions; Generalised change points; Waiting time distributions

TL;DR:
A method for efficiently calculating exact marginal, conditional and joint distributions for change points defined by general finite state Hidden Markov Models is proposed, showing that, in contrast to sampling methods, very little computation is needed.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2008 journal article

Application of auxiliary Markov chains to start-up demonstration tests

*European Journal of Operational Research*, *184*(2), 574–583.

author keywords: higher-order Markovian sequence; runs; start-up reliability; supplementary variables

TL;DR:
This work uses auxiliary Markov chains to derive probabilistic results for five types of start-up demonstration tests, with start-ups that are Markovian of a general order.
(via Semantic Scholar)

Source: Crossref

Added: August 14, 2021

2008 journal article

Waiting time distribution of generalized later patterns

*COMPUTATIONAL STATISTICS & DATA ANALYSIS*, *52*(11), 4879–4890.

Source: Web Of Science

Added: August 6, 2018

2007 journal article

DISTRIBUTIONS ASSOCIATED WITH GENERAL RUNS AND PATTERNS IN HIDDEN MARKOV MODELS

*ANNALS OF APPLIED STATISTICS*, *1*(2), 585–611.

author keywords: Competing patterns; CpG islands; finite Markov chain imbedding; generalized later patterns; higher-order hidden Markov models; sooner/later waiting time distributions

TL;DR:
A method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence, and shows that the methods can be adapted to include restrictions related to biological knowledge.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2006 journal article

A recursive algorithm for computing the distribution of the number of successes in higher-order Markovian trials

*Computational Statistics & Data Analysis*, *50*(3), 604–610.

author keywords: binary trials; Markovian sequences; probability

TL;DR:
This paper presents a recursive method of computing the distribution of the number of successes in a sequence of binary trials that are Markovian of a general order, and recurrence relations among probabilities of partitioned events are used to compute the desired probabilities.
(via Semantic Scholar)

Source: Crossref

Added: August 14, 2021

2006 journal article

Hot-hand effects in sports and a recursive method of computing probabilities for streaks

*Computers & Operations Research*, *33*(7), 1983–2001.

author keywords: binary trials; higher-order Markovian sequences; dependence; run probabilities; waiting-time distributions; hot hand; streaks; longest run

TL;DR:
A criterion based on the longest success run for choosing the order of Markovian dependence that gives the best fit to the streakiness characteristics of an individual bowler's data is suggested.
(via Semantic Scholar)

Source: Crossref

Added: August 14, 2021

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