Estimating the frequency of the oldest allele: a bayesian approach

1991 ◽  
Vol 23 (3) ◽  
pp. 456-475 ◽  
Author(s):  
Paul Joyce
Keyword(s):  
Stationary Distribution ◽  
Bayesian Approach ◽  
Dirichlet Distribution ◽  
Allele Frequencies ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Infinite Alleles Model

In this paper we calculate posterior distributions associated with a version of the Poisson–Dirichlet distribution called the GEM. The GEM has been shown (by several authors) to be the limiting stationary distribution for allele frequencies listed in age order associated with the neutral infinite alleles model. In view of this result, we use our posterior distributions to calculate Bayes estimators for the frequency of the oldest allele given a sample.

Estimating the frequency of the oldest allele: a bayesian approach

1991 ◽  
Vol 23 (03) ◽  
pp. 456-475 ◽  
Author(s):  
Paul Joyce
Keyword(s):  
Stationary Distribution ◽  
Bayesian Approach ◽  
Dirichlet Distribution ◽  
Allele Frequencies ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Infinite Alleles Model

In this paper we calculate posterior distributions associated with a version of the Poisson–Dirichlet distribution called the GEM. The GEM has been shown (by several authors) to be the limiting stationary distribution for allele frequencies listed in age order associated with the neutral infinite alleles model. In view of this result, we use our posterior distributions to calculate Bayes estimators for the frequency of the oldest allele given a sample.

scholarly journals Methods for Estimating Gene Frequencies and Detecting Selection in Bacterial Populations

Genetics ◽  
2000 ◽  
Vol 155 (2) ◽  
pp. 499-508 ◽  
Author(s):  
Bruce Rannala ◽  
Wei-Gang Qiu ◽  
Daniel E Dykhuizen
Keyword(s):  
Ixodes Scapularis ◽  
Balancing Selection ◽  
Surface Protein ◽  
Allele Frequencies ◽  
Gene Frequencies ◽  
Bacterial Populations ◽  
Polymerase Chain ◽  
Host Infection ◽  
Infinite Alleles Model

Abstract Recent breakthroughs in molecular technology, most significantly the polymerase chain reaction (PCR) and in situ hybridization, have allowed the detection of genetic variation in bacterial communities without prior cultivation. These methods often produce data in the form of the presence or absence of alleles or genotypes, however, rather than counts of alleles. Using relative allele frequencies from presence-absence data as estimates of population allele frequencies tends to underestimate the frequencies of common alleles and overestimate those of rare ones, potentially biasing the results of a test of neutrality in favor of balancing selection. In this study, a maximum-likelihood estimator (MLE) of bacterial allele frequencies designed for use with presence-absence data is derived using an explicit stochastic model of the host infection (or bacterial sampling) process. The performance of the MLE is evaluated using computer simulation and a method is presented for evaluating the fit of estimated allele frequencies to the neutral infinite alleles model (IAM). The methods are applied to estimate allele frequencies at two outer surface protein loci (ospA and ospC) of the Lyme disease spirochete, Borrelia burgdorferi, infecting local populations of deer ticks (Ixodes scapularis) and to test the fit to a neutral IAM.

scholarly journals Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 111-120 ◽  
Author(s):  
Dewi Rahardja
Keyword(s):  
Bayesian Inference ◽  
Closed Form ◽  
Bayesian Approach ◽  
Interval Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Binomial Data ◽  
The Difference ◽  
Data Subject

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

Likelihood ratios for the infinite alleles model

1994 ◽  
Vol 31 (03) ◽  
pp. 595-605 ◽  
Author(s):  
Paul Joyce
Keyword(s):  
Likelihood Ratio ◽  
Stationary Distribution ◽  
Random Sequence ◽  
Random Variable ◽  
Single Locus ◽  
Likelihood Ratios ◽  
Gene Frequencies ◽  
Random Samples ◽  
Infinite Alleles Model

The stationary distribution for the population frequencies under an infinite alleles model is described as a random sequence (x 1, x 2, · ··) such that Σxi = 1. Likelihood ratio theory is developed for random samples drawn from such populations. As a result of the theory, it is shown that any parameter distinguishing an infinite alleles model with selection from the neutral infinite alleles model cannot be consistently estimated based on gene frequencies at a single locus. Furthermore, the likelihood ratio (neutral versus selection) converges to a non-trivial random variable under both hypotheses. This shows that if one wishes to test a completely specified infinite alleles model with selection against neutrality, the test will not obtain power 1 in the limit.

Bayesian Analysis of the Brown–Proschan Model

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Dinh Tuan Nguyen ◽  
Yann Dijoux ◽  
Mitra Fouladirad
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Failure Rate ◽  
Bayesian Approach ◽  
Real Data ◽  
Posterior Distributions ◽  
Imperfect Maintenance ◽  
Maintenance Model ◽  
Informative Prior Distributions

AbstractThe paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

scholarly journals On Bayesian Analysis of Burr Type VII Distribution under Different Censoring Schemes

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Navid Feroze ◽  
Muhammad Aslam
Keyword(s):  
Comparative Study ◽  
Bayesian Analysis ◽  
Simulation Study ◽  
Type Ii ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Type Ii Censoring ◽  
The Comparative Study ◽  
Posterior Estimation

This paper includes the Bayesian analysis of Burr type VII distribution. Three censoring schemes, namely, left censoring, singly type II censoring, and doubly type II censoring have been used for posterior estimation. The results of different censoring schemes have been compared with those under complete samples. The comparative study among the performance of different censoring schemes has also been made. Two noninformative (uniform and Jeffreys) priors have been assumed to derive the posterior distributions under each case. The performance of Bayes estimators has been compared in terms of posterior risks under a simulation study.

scholarly journals A Bayesian Analysis of Spectral ARMA Model

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Manoel I. Silvestre Bezerra ◽  
Fernando Antonio Moala ◽  
Yuzo Iano
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Interval ◽  
Bayesian Analysis ◽  
Least Squares ◽  
Bayesian Approach ◽  
Arma Model ◽  
New Method ◽  
Posterior Distributions ◽  
Numerical Illustration

Bezerra et al. (2008) proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967). The Bayesian computations, simulation via Markov Monte Carlo (MCMC) is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.

Consistent ordered sampling distributions: characterization and convergence

1991 ◽  
Vol 23 (2) ◽  
pp. 229-258 ◽  
Author(s):  
Peter Donnelly ◽  
Paul Joyce
Keyword(s):  
Weak Convergence ◽  
Population Size ◽  
Wide Class ◽  
Unsolved Problem ◽  
Dirichlet Distribution ◽  
Allele Frequencies ◽  
Sampling Distributions ◽  
Population Distributions ◽  
Alternative Characterization ◽  
Central Result

This paper is concerned with models for sampling from populations in which there exists a total order on the collection of types, but only the relative ordering of types which actually appear in the sample is known. The need for consistency between different sample sizes limits the possible models to what are here called ‘consistent ordered sampling distributions'. We give conditions under which weak convergence of population distributions implies convergence of sampling distributions and conversely those under which population convergence may be inferred from convergence of sampling distributions. A central result exhibits a collection of ‘ordered sampling functions', none of which is continuous, which separates measures in a certain class. More generally, we characterize all consistent ordered sampling distributions, proving an analogue of de Finetti's theorem in this context. These results are applied to an unsolved problem in genetics where it is shown that equilibrium age-ordered population allele frequencies for a wide class of exchangeable reproductive models converge weakly, as the population size becomes large, to the so-called GEM distribution. This provides an alternative characterization which is more informative and often more convenient than Kingman's (1977) characterization in terms of the Poisson–Dirichlet distribution.

Weak limit for the stationary distribution of the infinite-alleles model

1979 ◽  
Vol 16 (3) ◽  
pp. 459-472
Author(s):  
Haim Avni
Keyword(s):  
Laplace Transform ◽  
Order Statistics ◽  
Frequency Spectrum ◽  
Stationary Distribution ◽  
Weak Limit ◽  
Limit Behavior ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Spectrum Density ◽  
Infinite Alleles Model

The limit behavior of the stationary distribution of the infinite-alleles model is reduced to a single Laplace transform formula. Some known results, such as Ewens' sampling formula, the distribution of the order-statistics and the frequency spectrum density are shown to follow from this relation. All the results are obtained within the framework of the configuration process, without recourse to finite alleles models.In view of some recent results by Kingman (1977), the results apply wherever the Ewens' sampling formula is valid.

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