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About 7,092 papers for “Marginal likelihood”
John D. Kalbfleisch · Wiley StatsRef: Statistics Reference Online · 2014
Abstract In a multivariate situation, where inference is required about a subset of the parameters, the others being nuisance parameters, it may be possible to factorize the full likelihood so that the parameters of interest are associated with one aspect of the data. This gives the marginal likelihood. Examples include the partial likelihood used in the Cox model for survival data.
Cited by 0
Milkey, Analisa · Figshare · 2022
LoRaD: Marginal Likelihood from a Single Posterior Sample
Cited by 0Open access
Springer series in statistics · 2006
Cited by 0
Lotus A. Lofgren (9253428), Brandon S. Ross (14135875), Robert A. Cramer (8844023) et al. · Figshare · 2022
<p>Marginal likelihood increased until K = 5, with the largest increase occurring between K = 1–3. The data underlying this figure can be found in DOI: <a href="https://doi.org/10.5281/zenodo.5775265" target="_blank">10.5281/zenodo.5775265</a>.</p> <p>(TIFF)</p>
Cited by 0Open access
Milkey, Analisa · Figshare · 2022
LoRaD: Marginal Likelihood from a Single Posterior Sample
Cited by 0Open access
Jing Qin, Biao Zhang · Biometrika · 2005
Marginal likelihood and conditional likelihood are often used for eliminating nuisance parameters. For a parametric model, it is well known that the full likelihood can be decomposed into the product of a conditional likelihood and a marginal likelihood. This property is less transparent in a nonparametric or semiparametric likelihood setting. In this paper we show that this nice parametric likelihood property can be carried over to the empirical likelihood world. We discuss applications in case-control studies, genetical linkage analysis, genetical quantitative traits analysis, tuberculosis infection data and unordered-paired data, all of which can be treated as semiparametric finite mixture models. We consider the estimation problem in detail in the simplest case of unordered-paired data where we can only observe the minimum and maximum values of two random variables; the identities of the minimum and maximum values are lost. The profile empirical likelihood approach is used for maximum semiparametric likelihood estimation. We present some large-sample results along with a simulation study. Copyright 2005, Oxford University Press.
Cited by 19
Peter McCullagh · Bernoulli · 2008
Suppose that k series, all having the same autocorrelation function, are observed in parallel at n points in time or space. From a single series of moderate length, the autocorrelation parameter can be estimated with limited accuracy, so we aim to increase the information by formulating a suitable model for the joint distribution of all series. Three Gaussian models of increasing complexity are considered, two of which assume that the series are independent. This paper studies the rate at which the information for accumulates as k increases, possibly even beyond n. The profile log likelihood for the model with k(k + 1)/2 covariance parameters behaves anomalously in two respects. On the one hand, it is a log likelihood, so the derivatives satisfy the Bartlett identities. On the other hand, the Fisher information for increases to a maximum at k = n/2, decreasing to zero for k n. In any parametric statistical model, one expects the Fisher information to increase with additional data; decreasing Fisher information is an anomaly demanding an explanation.
Cited by 3Open access
Peter McCullagh · 2009
A Wishart model is proposed for random distance matrices in which the components are correlated gamma random variables, all having the same degrees of freedom. The marginal likelihood is obtained in closed form. Its use is illustrated by multidimensional scaling, by rooted tree models for response covariances in social survey work, and unrooted trees for ancestral relationships in genetic applications. 1
Cited by 28
Masashi Sugiyama · Elsevier eBooks · 2016
Cited by 0
Siddhartha Chib · Journal of the American Statistical Association · 1995
Abstract In the context of Bayes estimation via Gibbs sampling, with or without data augmentation, a simple approach is developed for computing the marginal density of the sample data (marginal likelihood) given parameter draws from the posterior distribution. Consequently, Bayes factors for model comparisons can be routinely computed as a by-product of the simulation. Hitherto, this calculation has proved extremely challenging. Our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density. This simple identity holds for any parameter value. An estimate of the posterior density is shown to be available if all complete conditional densities used in the Gibbs sampler have closed-form expressions. To improve accuracy, the posterior density is estimated at a high density point, and the numerical standard error of resulting estimate is derived. The ideas are applied to probit regression and finite mixture models.
Cited by 1,815
Rutger van Haasteren · Springer theses · 2013
Cited by 6
Omiros Papaspiliopoulos, Timothée Stumpf-Fétizon, Jonathan Weare · arXiv (Cornell University) · 2026
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters. The method requires samples from the posterior distribution of the parameters for different values of the hyperparameters on a simulation grid and returns inference on the marginal likelihood defined everywhere on its domain, and on its functionals. We show how the method relates to many of the methods that have been used in this context, including sequential Monte Carlo, Gibbs sampling, Monte Carlo maximum likelihood, and umbrella sampling. We establish the consistency of the proposed estimators as the sampling effort increases, both when the simulation grid is kept fixed and when it becomes dense in the domain. We showcase the approach on Gaussian process regression and classification and crossed effect models.
Cited by 0Open access
Elisa Loza, David S. Phillips · 2013
Cited by 0
渡邊澄夫, SUMIO WATANABE · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2016
Cited by 0
Omiros Papaspiliopoulos, Timothée Stumpf-Fétizon, Jonathan Weare · arXiv (Cornell University) · 2026
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters. The method requires samples from the posterior distribution of the parameters for different values of the hyperparameters on a simulation grid and returns inference on the marginal likelihood defined everywhere on its domain, and on its functionals. We show how the method relates to many of the methods that have been used in this context, including sequential Monte Carlo, Gibbs sampling, Monte Carlo maximum likelihood, and umbrella sampling. We establish the consistency of the proposed estimators as the sampling effort increases, both when the simulation grid is kept fixed and when it becomes dense in the domain. We showcase the approach on Gaussian process regression and classification and crossed effect models.
Cited by 0Open access
Du, Chao, Chu-Lan Michael Kao, S. C. Kou · Figshare · 2015
This article studies the estimation of a stepwise signal. To determine the number and locations of change-points of the stepwise signal, we formulate a maximum marginal likelihood estimator, which can be computed with a quadratic cost using dynamic programming. We carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator. We propose to treat each possible set of change-points equally and adopt an empirical Bayes approach to specify the prior distribution of segment parameters. A detailed simulation study is performed to compare the effectiveness of this method with other existing methods. We demonstrate our method on single-molecule enzyme reaction data and on DNA array comparative genomic hybridization (CGH) data. Our study shows that this method is applicable to a wide range of models and offers appealing results in practice. Supplementary materials for this article are available online.
Cited by 0Open access
Shaowei Lin · 2010
In Bayesian statistics, marginal likelihood integrals are important for model selection. Unfortunately, they are generally difficult to compute. We present algebraic algorithms for evaluating such integrals exactly for small sample sizes, and compare them with some existing approximations. Our methods will be applied to mixtures of discrete independence models, and are available as a library in Maple.
Cited by 0
Chao Du, Chu-Lan Michael Kao, S. C. Kou · Journal of the American Statistical Association · 2015
This paper studies the estimation of stepwise signal. To determine the number and locations of change-points of the stepwise signal, we formulate a maximum marginal likelihood estimator, which can be computed with a quadratic cost using dynamic programming. We carry out extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator. We propose to treat each possible set of change-points equally and adopt an empirical Bayes approach to specify the prior distribution of segment parameters. Detailed simulation study is performed to compare the effectiveness of this method with other existing methods. We demonstrate our method on single-molecule enzyme reaction data and on DNA array CGH data. Our study shows that this method is applicable to a wide range of models and offers appealing results in practice.
Cited by 60Open access
Benedict Escoto · 2016
This paper describes a method for estimating the marginal likelihood or Bayes fac-tors of Bayesian models using non-parametric importance sampling (“arrogance sam-pling”). This method can also be used to compute the normalizing constant of probabil-ity distributions. Because the required inputs are samples from the distribution to be normalized and the scaled density at those samples, this method may be a convenient replacement for the harmonic mean estimator. The method has been implemented in the open source R package margLikArrogance. 1
Cited by 0
Du, Chao, Chu-Lan Michael Kao, S. C. Kou · Figshare · 2015
This article studies the estimation of a stepwise signal. To determine the number and locations of change-points of the stepwise signal, we formulate a maximum marginal likelihood estimator, which can be computed with a quadratic cost using dynamic programming. We carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator. We propose to treat each possible set of change-points equally and adopt an empirical Bayes approach to specify the prior distribution of segment parameters. A detailed simulation study is performed to compare the effectiveness of this method with other existing methods. We demonstrate our method on single-molecule enzyme reaction data and on DNA array comparative genomic hybridization (CGH) data. Our study shows that this method is applicable to a wide range of models and offers appealing results in practice. Supplementary materials for this article are available online.
Cited by 0Open access