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

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.

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An Integrated Framework for the Inference of Viral Population History From Reconstructed Genealogies

Genetics ◽

10.1093/genetics/155.3.1429 ◽

2000 ◽

Vol 155 (3) ◽

pp. 1429-1437

Author(s):

Oliver G Pybus ◽

Andrew Rambaut ◽

Paul H Harvey

Keyword(s):

Maximum Likelihood ◽

Sequence Data ◽

Demographic History ◽

Population History ◽

Maximum Likelihood Estimates ◽

Viral Population ◽

True Parameter ◽

Subtype B ◽

Exponential Growth Model ◽

Parameter Values

Abstract We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.

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

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595908002061 ◽

2008 ◽

Vol 25 (06) ◽

pp. 847-864 ◽

Cited By ~ 1

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.

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ON MOMENT CONDITIONS FOR QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE ARCH MODELS

Econometric Theory ◽

10.1017/s0266466612000473 ◽

2012 ◽

Vol 29 (3) ◽

pp. 545-566 ◽

Cited By ~ 11

Author(s):

Marco Avarucci ◽

Eric Beutner ◽

Paolo Zaffaroni

Keyword(s):

Maximum Likelihood ◽

Asymptotic Normality ◽

Likelihood Function ◽

Likelihood Estimation ◽

Multivariate Garch ◽

Moment Condition ◽

Arch Models ◽

Moment Conditions ◽

True Parameter ◽

Quasi Maximum Likelihood

This paper questions whether it is possible to derive consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator (QMLE) for possibly the simplest multivariate GARCH model, namely, the multivariate ARCH(1) model of the Baba, Engle, Kraft, and Kroner form, under weak moment conditions similar to the univariate case. In contrast to the univariate specification, we show that the expectation of the log-likelihood function is unbounded, away from the true parameter value, if (and only if) the observable has unbounded second moment. Despite this nonstandard feature, consistency of the Gaussian QMLE is still warranted. The same moment condition proves to be necessary and sufficient for the stationarity of the score when evaluated at the true parameter value. This explains why high moment conditions, typically bounded sixth moment and above, have been used hitherto in the literature to establish the asymptotic normality of the QMLE in the multivariate framework.

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Maximum Likelihood Estimation and Testing of a Poisson Regression Model

Methods of Information in Medicine ◽

10.1055/s-0038-1634875 ◽

1992 ◽

Vol 31 (03) ◽

pp. 215-218

Author(s):

J. Y. Wan ◽

A. T. Galecki

Keyword(s):

Maximum Likelihood ◽

Regression Model ◽

Poisson Regression ◽

Likelihood Function ◽

Likelihood Estimation ◽

Incidence Rates ◽

Maximum Likelihood Estimates ◽

Categorical Variables ◽

Poisson Regression Model ◽

Regression Parameters

Abstract:A Poisson regression model is proposed for the analysis of incidence rates presented in a two-way table classified by two categorical variables. It is shown that the likelihood function is the same as that using Glasser’s exponential covariate model. An algorithm is given to solve the maximum likelihood estimates of the regression parameters. The model is evaluated via deviance and the method is illustrated with an example. Some extensions of the model are discussed.

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Directional Selection and the Site-Frequency Spectrum

Genetics ◽

10.1093/genetics/159.4.1779 ◽

2001 ◽

Vol 159 (4) ◽

pp. 1779-1788 ◽

Cited By ~ 2

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.

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

New Mathematics and Natural Computation ◽

10.1142/s1793005705000160 ◽

2005 ◽

Vol 01 (02) ◽

pp. 295-303 ◽

Cited By ~ 2

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.

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On Bayesian procedure for maximum earthquake magnitude estimation

Research in Geophysics ◽

10.4081/rg.2012.e7 ◽

2012 ◽

Vol 2 (1) ◽

pp. 7 ◽

Cited By ~ 5

Author(s):

Andrzej Kijko

Keyword(s):

Maximum Likelihood ◽

Posterior Distribution ◽

Ad Hoc ◽

Likelihood Function ◽

Fundamental Problem ◽

Likelihood Estimation ◽

Earthquake Magnitude ◽

Bayesian Estimator ◽

Bayesian Procedure ◽

Posterior Estimate

This work is focused on the Bayesian procedure for the estimation of the regional maximum possible earthquake magnitude mmax. The paper briefly discusses the currently used Bayesian procedure for mmax, as developed by Cornell, and a statistically justifiable alternative approach is suggested. The fundamental problem in the application of the current Bayesian formalism for mmax estimation is that one of the components of the posterior distribution is the sample likelihood function, for which the range of observations (earthquake magnitudes) depends on the unknown parameter mmax. This dependence violates the property of regularity of the maximum likelihood function. The resulting likelihood function, therefore, reaches its maximum at the maximum observed earthquake magnitude mobsmax and not at the required maximum possible magnitude mmax. Since the sample likelihood function is a key component of the posterior distribution, the posterior estimate of m^max is biased. The degree of the bias and its sign depend on the applied Bayesian estimator, the quantity of information provided by the prior distribution, and the sample likelihood function. It has been shown that if the maximum posterior estimate is used, the bias is negative and the resulting underestimation of mmax can be as big as 0.5 units of magnitude. This study explores only the maximum posterior estimate of mmax, which is conceptionally close to the classic maximum likelihood estimation. However, conclusions regarding the shortfall of the current Bayesian procedure are applicable to all Bayesian estimators, e.g. posterior mean and posterior median. A simple, ad hoc solution of this non-regular maximum likelihood problem is also presented.

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The Weibull Birnbaum-Saunders Distribution And Its Applications

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-887 ◽

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.

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Maximum-likelihood estimation in non-standard conditions

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100050088 ◽

1971 ◽

Vol 70 (3) ◽

pp. 441-450 ◽

Cited By ~ 93

Author(s):

P. A. P. Moran

Keyword(s):

Maximum Likelihood ◽

Parameter Space ◽

Null Hypothesis ◽

Maximum Likelihood Estimators ◽

Likelihood Estimation ◽

Standard Theory ◽

True Parameter ◽

Open Set ◽

Estimation Problems ◽

Parameter Point

The origin of the present paper is the desire to study the asymptotic behaviour of certain tests of significance which can be based on maximum-likelihood estimators. The standard theory of such problems (e.g. Wald(4)) assumes, sometimes tacitly, that the parameter point corresponding to the null hypothesis lies inside an open set in the parameter space. Here we wish to study what happens when the true parameter point, in estimation problems, lies on the boundary of the parameter space.

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

Statistical Applications in Genetics and Molecular Biology ◽

10.1515/sagmb-2018-0031 ◽

2019 ◽

Vol 18 (1) ◽

Cited By ~ 2

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.

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