Maximum likelihood estimates for Markov networks using inhomogeneous Markov chains

1995 ◽  
pp. 207-210 ◽  
Author(s):  
Hermann von Hasseln
Keyword(s):  
Maximum Likelihood ◽  
Markov Chains ◽  
Maximum Likelihood Estimates ◽  
Markov Networks

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.

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

Genetics ◽  
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.

Metric for Disassembly and Reuse Decisions: Formulation and Validation

2008 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Deborah Thurston
Keyword(s):  
Maximum Likelihood ◽  
Value Function ◽  
Choice Theory ◽  
Decision Makers ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Maximum Value ◽  
Long Range Planning ◽  
The Relationship ◽  
The Value Function

Design for disassembly and reuse focuses on developing methods to minimize difficulty in disassembly for maintenance or reuse. These methods can gain substantially if the relationship between component attributes (material mix, ease of disassembly etc.) and their likelihood of reuse or disposal is understood. For products already in the marketplace, a feedback approach that evaluates willingness of manufacturers or customers (decision makers) to reuse a component can reveal how attributes of a component affect reuse decisions. This paper introduces some metrics and combines them with ones proposed in literature into a measure that captures the overall value of a decision made by the decision makers. The premise is that the decision makers would choose a decision that has the maximum value. Four decisions are considered regarding a component’s fate after recovery ranging from direct reuse to disposal. A method on the lines of discrete choice theory is utilized that uses maximum likelihood estimates to determine the parameters that define the value function. The maximum likelihood method can take inputs from actual decisions made by the decision makers to assess the value function. This function can be used to determine the likelihood that the component takes a certain path (one of the four decisions), taking as input its attributes, which can facilitate long range planning and also help determine ways reuse decisions can be influenced.

On Updating Algorithms and Inference for Stochastic Point Processes

1975 ◽  
Vol 12 (S1) ◽  
pp. 239-259 ◽  
Author(s):  
D. Vere-Jones
Keyword(s):  
Stochastic Process ◽  
Maximum Likelihood ◽  
Stochastic Approximation ◽  
Approximation Theory ◽  
Point Processes ◽  
Maximum Likelihood Estimates ◽  
Doubly Stochastic ◽  
Stochastic Point Processes ◽  
Asymptotically Efficient ◽  
Estimation And Filtering

This paper is an attempt to interpret and extend, in a more statistical setting, techniques developed by D. L. Snyder and others for estimation and filtering for doubly stochastic point processes. The approach is similar to the Kalman-Bucy approach in that the updating algorithms can be derived from a Bayesian argument, and lead ultimately to equations which are similar to those occurring in stochastic approximation theory. In this paper the estimates are derived from a general updating formula valid for any point process. It is shown that almost identical formulae arise from updating the maximum likelihood estimates, and on this basis it is suggested that in practical situations the sequence of estimates will be consistent and asymptotically efficient. Specific algorithms are derived for estimating the parameters in a doubly stochastic process in which the rate alternates between two levels.

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.

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