Distributions associated with general runs and patterns in hidden Markov models

DOI10.1214/07-AOAS125zbMath1126.62008arXiv0706.3985OpenAlexW3105867654MaRDI QIDQ2466479

John A. D. Aston, Donald E. K. Martin

Publication date: 15 January 2008

Published in: The Annals of Applied Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.3985

zbMATH Keywords

finite Markov chain imbeddingcompeting patternscpg islandsgeneralized later patternshigher-order hidden Markov modelssooner/later waiting time distributions

Mathematics Subject Classification ID

Applications of statistics to biology and medical sciences; meta analysis (62P10) Exact distribution theory in statistics (62E15) Numerical analysis or methods applied to Markov chains (65C40)

Related Items (10)

Duality between the local score of one sequence and constrained hidden Markov model ⋮ Faster exact distributions of pattern statistics through sequential elimination of states ⋮ Minimal auxiliary Markov chains through sequential elimination of states ⋮ Quantifying the uncertainty in change points ⋮ ESTIMATOR FOR THE DISTRIBUTION OF THE NUMBERS OF RUNS IN A RANDOM SEQUENCE CONTROLLED BY STATIONARY MARKOV CHAIN ⋮ Implied distributions in multiple change point problems ⋮ Moments of the count of a regular expression in a heterogeneous random sequence ⋮ Distribution of statistics of hidden state sequences through the sum-product algorithm ⋮ Flexible Latent-State Modelling of Old Faithful's Eruption Inter-Arrival Times in 2009 ⋮ Distributions of pattern statistics in sparse Markov models

Uses Software

• Sarment
• CpG island searcher

Cites Work

• Waiting time distribution of generalized later patterns
• Stochastic models for heterogeneous DNA sequences
• Runs, scans and urn model distributions: A unified Markov chain approach
• Inference in hidden Markov models.
• Hidden Markov Models for Microarray Time Course Data in Multiple Biological Conditions
• A Look at Some Data on the Old Faithful Geyser
• Approximations for Distributions of Scan Statistics
• A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle
• Biological Sequence Analysis
• Distribution Theory of Runs: A Markov Chain Approach
• On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials
• The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1
• Waiting time distributions of competing patterns in higher-order Markovian sequences
• Error bounds for convolutional codes and an asymptotically optimum decoding algorithm
• An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology
• Hidden Markov models for bioinformatics
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