scholarly journals Maximum likelihood estimation of individual inbreeding coefficients and null allele frequencies

2012 ◽  
Vol 94 (3) ◽  
pp. 151-161 ◽  
Author(s):  
NATHAN HALL ◽  
LAINA MERCER ◽  
DAISY PHILLIPS ◽  
JONATHAN SHAW ◽  
AMY D. ANDERSON
Keyword(s):  
Maximum Likelihood ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Allele Frequencies ◽  
Maximum Likelihood Estimates ◽  
Null Alleles ◽  
Single Individual ◽  
Em Algorithms ◽  
Inbreeding Coefficients ◽  
Missing Genotypes

SummaryIn this paper, we developed and compared several expectation–maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).

scholarly journals Estimation of different types of entropies for the Kumaraswamy distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0249027
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood ◽  
Numerical Study ◽  
Beta Function ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Kumaraswamy Distribution ◽  
Random System ◽  
Entropy Measures

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

A HYBRID GENETIC ALGORITHM FOR THE MAXIMUM LIKELIHOOD ESTIMATION OF MODELS WITH MULTIPLE EQUILIBRIA: A FIRST REPORT

2005 ◽  
Vol 01 (02) ◽  
pp. 295-303 ◽  
Author(s):  
VICTOR AGUIRREGABIRIA ◽  
PEDRO MIRA
Keyword(s):  
Genetic Algorithm ◽  
Maximum Likelihood ◽  
Multiple Equilibria ◽  
Structural Parameters ◽  
Hybrid Genetic Algorithm ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Large Space ◽  
Pseudo Maximum Likelihood ◽  
Structural Econometric

This paper presents a hybrid genetic algorithm to obtain maximum likelihood estimates of parameters in structural econometric models with multiple equilibria. The algorithm combines a pseudo maximum likelihood (PML) procedure with a genetic algorithm (GA). The GA searches globally over the large space of possible combinations of multiple equilibria in the data. The PML procedure avoids the computation of all the equilibria associated with every trial value of the structural parameters.

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

MLML2R: an R package for maximum likelihood estimation of DNA methylation and hydroxymethylation proportions

2019 ◽  
Vol 18 (1) ◽  
Author(s):  
Samara F. Kiihl ◽  
Maria Jose Martinez-Garrido ◽  
Arce Domingo-Relloso ◽  
Jose Bermudez ◽  
Maria Tellez-Plaza
Keyword(s):  
Dna Methylation ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Analytical Form ◽  
R Package ◽  
Maximum Likelihood Estimates ◽  
Computational Time ◽  
Iterative Approximation ◽  
Sequencing Technologies ◽  
Combining Data

Abstract Accurately measuring epigenetic marks such as 5-methylcytosine (5-mC) and 5-hydroxymethylcytosine (5-hmC) at the single-nucleotide level, requires combining data from DNA processing methods including traditional (BS), oxidative (oxBS) or Tet-Assisted (TAB) bisulfite conversion. We introduce the R package MLML2R, which provides maximum likelihood estimates (MLE) of 5-mC and 5-hmC proportions. While all other available R packages provide 5-mC and 5-hmC MLEs only for the oxBS+BS combination, MLML2R also provides MLE for TAB combinations. For combinations of any two of the methods, we derived the pool-adjacent-violators algorithm (PAVA) exact constrained MLE in analytical form. For the three methods combination, we implemented both the iterative method by Qu et al. [Qu, J., M. Zhou, Q. Song, E. E. Hong and A. D. Smith (2013): “Mlml: consistent simultaneous estimates of dna methylation and hydroxymethylation,” Bioinformatics, 29, 2645–2646.], and also a novel non iterative approximation using Lagrange multipliers. The newly proposed non iterative solutions greatly decrease computational time, common bottlenecks when processing high-throughput data. The MLML2R package is flexible as it takes as input both, preprocessed intensities from Infinium Methylation arrays and counts from Next Generation Sequencing technologies. The MLML2R package is freely available at https://CRAN.R-project.org/package=MLML2R.

Maximum likelihood estimation in nonlinear structured fisheries models using survey and catch-at-age data

2011 ◽  
Vol 68 (10) ◽  
pp. 1717-1731 ◽  
Author(s):  
Christian N. Brinch ◽  
Anne Maria Eikeset ◽  
Nils Chr. Stenseth
Keyword(s):  
Maximum Likelihood ◽  
Gadus Morhua ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Simulated Maximum Likelihood ◽  
True Parameter ◽  
Bayesian Techniques ◽  
Age Structured ◽  
Parameter Values

Age-structured population dynamics models play an important role in fisheries assessments. Such models have traditionally been estimated using crude likelihood approximations or more recently using Bayesian techniques. We contribute to this literature with three main messages. Firstly, we demonstrate how to estimate such models efficiently by simulated maximum likelihood using Laplace importance samplers for the likelihood function. Secondly, we demonstrate how simulated maximum likelihood estimates may be validated using different importance samplers known to approach the exact likelihood function in different regions of the parameter space. Thirdly, we show that our method works in practice by Monte Carlo simulations using parameter values as estimated from data on the Northeast Arctic cod ( Gadus morhua ) stock. The simulations suggest that we are able to recover the unknown true maximum likelihood estimates using moderate importance sample sizes and show that we are able to adequately recover the true parameter values.

The Rasch Model and Multistage Testing

1988 ◽  
Vol 13 (1) ◽  
pp. 45-52 ◽  
Author(s):  
C. A. W. Glas
Keyword(s):  
Maximum Likelihood ◽  
Rasch Model ◽  
Latent Trait ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Marginal Maximum Likelihood ◽  
Marginal Maximum Likelihood Estimation ◽  
Multistage Testing ◽  
Estimation Equations ◽  
The Rasch Model

This paper concerns the problem of estimating the item parameters of latent trait models in a multistage testing design. It is shown that using the Rasch model and conditional maximum likelihood estimates does not lead to solvable estimation equations. It is also shown that marginal maximum likelihood estimation, which assumes a sample of subjects from a population with a specified distribution of ability, will lead to solvable estimation equations, both in the Rasch model and in the Birnbaum model.

AN ANALYSIS OF ACCELERATED PERFORMANCE DEGRADATION TESTS ASSUMING THE ARRHENIUS STRESS-RELATIONSHIP

2008 ◽  
Vol 25 (06) ◽  
pp. 847-864 ◽  
Author(s):  
TAE HYOUNG KANG ◽  
SANG WOOK CHUNG ◽  
WON YOUNG YUN
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Exposure Time ◽  
Failure Time ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Performance Degradation ◽  
Maximum Likelihood Estimates ◽  
Degradation Tests

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.

The Estimated Probability of Dizygotic Twins: A Comparison of Two Methods

2009 ◽  
Vol 12 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Jill Hardin ◽  
Steve Selvin ◽  
Suzan L. Carmichael ◽  
Gary M. Shaw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Data Sources ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Dizygotic Twin ◽  
Twin Data ◽  
Dizygotic Twins ◽  
The Relationship

AbstractThis study presents a general model of two binary variables and applies it to twin sex pairing data from 21 twin data sources to estimate the frequency of dizygotic twins. The purpose of this study is to clarify the relationship between maximum likelihood and Weinberg's differential rule zygosity estimation methods. We explore the accuracy of these zygosity estimation measures in relation to twin ascertainment methods and the probability of a male. Twin sex pairing data from 21 twin data sources representing 15 countries was collected for use in this study. Maximum likelihood estimation of the probability of dizygotic twins is applied to describe the variation in the frequency of dizygotic twin births. The differences between maximum likelihood and Weinberg's differential rule zygosity estimation methods are presented as a function of twin data ascertainment method and the probability of a male. Maximum likelihood estimation of the probability of dizygotic twins ranges from 0.083 (95% approximate CI: 0.082, 0.085) to 0.750 (95% approximate CI: 0.749, 0.752) for voluntary ascertainment data sources and from 0.374 (95% approximate CI: 0.373, 0.375) to 0.987 (95% approximate CI: 0.959, 1.016) for active ascertainment data sources. In 17 of the 21 twin data sources differences of 0.01 or less occur between maximum likelihood and Weinberg zygosity estimation methods. The Weinberg and maximum likelihood estimates are negligibly different in most applications. Using the above general maximum likelihood estimate, the probability of a dizygotic twin is subject to substantial variation that is largely a function of twin data ascertainment method.

Sign in / Sign up

Export Citation Format

Share Document