scholarly journals Efficient Bayesian estimation of Markov model transition matrices with given stationary distribution

2013 ◽  
Vol 138 (16) ◽  
pp. 164113 ◽  
Author(s):  
Benjamin Trendelkamp-Schroer ◽  
Frank Noé
Keyword(s):  
Markov Model ◽  
Bayesian Estimation ◽  
Stationary Distribution ◽  
Transition Matrices ◽  
Model Transition

scholarly journals Basing population genetic inferences and models of molecular evolution upon desired stationary distributions of DNA or protein sequences

2008 ◽  
Vol 363 (1512) ◽  
pp. 3931-3939 ◽  
Author(s):  
Sang Chul Choi ◽  
Benjamin D Redelings ◽  
Jeffrey L Thorne
Keyword(s):  
Molecular Evolution ◽  
Markov Model ◽  
Stationary Distribution ◽  
Population Genetic ◽  
Amino Acid Level ◽  
Protein Sequences ◽  
Relative Fitness ◽  
Evolutionary Models ◽  
Effective Population ◽  
Stationary Distributions

Models of molecular evolution tend to be overly simplistic caricatures of biology that are prone to assigning high probabilities to biologically implausible DNA or protein sequences. Here, we explore how to construct time-reversible evolutionary models that yield stationary distributions of sequences that match given target distributions. By adopting comparatively realistic target distributions, evolutionary models can be improved. Instead of focusing on estimating parameters, we concentrate on the population genetic implications of these models. Specifically, we obtain estimates of the product of effective population size and relative fitness difference of alleles. The approach is illustrated with two applications to protein-coding DNA. In the first, a codon-based evolutionary model yields a stationary distribution of sequences, which, when the sequences are translated, matches a variable-length Markov model trained on human proteins. In the second, we introduce an insertion–deletion model that describes selectively neutral evolutionary changes to DNA. We then show how to modify the neutral model so that its stationary distribution at the amino acid level can match a profile hidden Markov model, such as the one associated with the Pfam database.

Efficient Bayesian estimation of the multivariate Double Chain Markov Model

2012 ◽  
Vol 23 (4) ◽  
pp. 467-480 ◽  
Author(s):  
Matthew Fitzpatrick ◽  
Dobrin Marchev
Keyword(s):  
Markov Model ◽  
Bayesian Estimation ◽  
Double Chain

An Estimation of Thailand's Hourly Solar Radiation Using Markov Transition Matrix Method

2016 ◽  
Vol 839 ◽  
pp. 29-33
Author(s):  
Anuchit Wibun ◽  
Pipat Chaiwiwatworakul
Keyword(s):  
Solar Radiation ◽  
Markov Model ◽  
Global Radiation ◽  
Weather Forecast ◽  
Second Order ◽  
Statistical Characteristics ◽  
Transition Matrices ◽  
Radiation Data ◽  
Markov Transition ◽  
Markov Transition Matrices

To estimate global solar radiation from easy available weather forecast data (sky condition), Markov model is used for this estimation. The five-year (1996-2000) global radiation data that are taken at an hour intervals from Nakhon Pathom station, Thailand (latitude 13.81ºN and longitude 100.04ºE) are used to construct the Markov transition matrices. The global radiation sequences in 2000 will be generated by based on the characteristic probability of moving global radiation values which were observed from the obtained data during 1996-1999. The autocorrelation function is used for checking the order of probability of moving obtained data. In this study, the five first and five second-order Markov transition matrices (MTMs), which are selected from the autocorrelation functions, are constructed, each MTMs will be used for generating global radiation values in each day with different sky conditions (clear, partly cloudy, mostly cloudy, cloudy and overcast). From the results of comparison between the statistical characteristics of observed and two synthetic generated data, global radiation data behavior slightly improved by the second order Markov model.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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