scholarly journals The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models

2014 ◽  
Vol 7 (1) ◽  
pp. 1-117 ◽  
Author(s):  
Chandra R. Bhat
Keyword(s):  
Marginal Likelihood

scholarly journals Markov-Modulated Continuous-Time Markov Chains to Identify Site- and Branch-Specific Evolutionary Variation in BEAST

2020 ◽  
Vol 70 (1) ◽  
pp. 181-189
Author(s):  
Guy Baele ◽  
Mandev S Gill ◽  
Paul Bastide ◽  
Philippe Lemey ◽  
Marc A Suchard
Keyword(s):  
High Performance ◽  
Markov Models ◽  
Marginal Likelihood ◽  
Likelihood Estimation ◽  
Phylogenetic Inference ◽  
Time Variability ◽  
Substitution Process ◽  
Wide Range ◽  
Markov Modulated ◽  
Over Time

Abstract Markov models of character substitution on phylogenies form the foundation of phylogenetic inference frameworks. Early models made the simplifying assumption that the substitution process is homogeneous over time and across sites in the molecular sequence alignment. While standard practice adopts extensions that accommodate heterogeneity of substitution rates across sites, heterogeneity in the process over time in a site-specific manner remains frequently overlooked. This is problematic, as evolutionary processes that act at the molecular level are highly variable, subjecting different sites to different selective constraints over time, impacting their substitution behavior. We propose incorporating time variability through Markov-modulated models (MMMs), which extend covarion-like models and allow the substitution process (including relative character exchange rates as well as the overall substitution rate) at individual sites to vary across lineages. We implement a general MMM framework in BEAST, a popular Bayesian phylogenetic inference software package, allowing researchers to compose a wide range of MMMs through flexible XML specification. Using examples from bacterial, viral, and plastid genome evolution, we show that MMMs impact phylogenetic tree estimation and can substantially improve model fit compared to standard substitution models. Through simulations, we show that marginal likelihood estimation accurately identifies the generative model and does not systematically prefer the more parameter-rich MMMs. To mitigate the increased computational demands associated with MMMs, our implementation exploits recent developments in BEAGLE, a high-performance computational library for phylogenetic inference. [Bayesian inference; BEAGLE; BEAST; covarion, heterotachy; Markov-modulated models; phylogenetics.]

Hyperparameter Estimation Based on Gaussian Process and its Application in Injection Molding

2011 ◽  
Vol 328-330 ◽  
pp. 524-529
Author(s):  
Jun Yan Ma ◽  
Xiao Ping Liao ◽  
Wei Xia ◽  
Xue Lian Yan
Keyword(s):  
Injection Molding ◽  
Gaussian Process ◽  
Process Model ◽  
Marginal Likelihood ◽  
Best Value ◽  
Highly Nonlinear ◽  
General Scientific ◽  
Wolfe Line Search ◽  
Search Approach ◽  
Hyperparameter Estimation

As a powerful modeling tool, Gaussian process (GP) employs a Bayesian statistics approach and adopts a highly nonlinear regression technique for general scientific and engineering tasks. In the first step of constructing Gaussian process model is to estimate the best value of the hyperparameter which turned to be used in the second step where a satisfactory nonlinear model was fitted. In this paper, a modified Wolfe line search approach for hyperparameters estimation by maximizing the marginal likelihood based on conjugate gradient method is proposed. And then we analyze parameter correlation according to the value of hyperparameters to control the warpage which is a main defect for a thin shell structure part in injection molding.

Marginal likelihood, conditional likelihood and empirical likelihood: Connections and applications

Biometrika ◽  
2005 ◽  
Vol 92 (2) ◽  
pp. 251-270 ◽  
Author(s):  
Jing Qin ◽  
Biao Zhang
Keyword(s):  
Empirical Likelihood ◽  
Marginal Likelihood ◽  
Conditional Likelihood

Pitfalls of Estimating the Marginal Likelihood Using the Modified Harmonic Mean

2015 ◽  
Author(s):  
Joshua C. C. Chan ◽  
Angelia Grant
Keyword(s):  
Marginal Likelihood ◽  
Harmonic Mean

The Estimation of Heteroscedasticity from a Marginal Likelihood Function

1973 ◽  
Vol 68 (342) ◽  
pp. 436-439 ◽  
Author(s):  
Hans Levenbach
Keyword(s):  
Likelihood Function ◽  
Marginal Likelihood

scholarly journals Quantifying the closeness to a set of random curves via the mean marginal likelihood

2020 ◽  
Author(s):  
Cédric Rommel ◽  
Joseph Frédéric Bonnans ◽  
Baptiste Gregorutti ◽  
Pierre Martinon
Keyword(s):  
Marginal Likelihood ◽  
Marginal Density ◽  
Random Curves ◽  
Practical Applications ◽  
Random Functions ◽  
Practical Usefulness ◽  
Class Of Estimators ◽  
The Mean ◽  
Multivariate Density ◽  
Aircraft Trajectories

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

scholarly journals Closed-Form Estimation of Multiple Change-Point Models

2013 ◽  
Author(s):  
Greg Jensen
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Change Point ◽  
Marginal Likelihood ◽  
Stationary Time Series ◽  
Change Points ◽  
Model Complexity ◽  
Marginal Model ◽  
General Strategy ◽  
Change Point Models

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

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