A note on Bayes factor consistency in partial linear models

Choi, Tae-Yong; Rousseau, Judith

doi:10.1016/j.jspi.2015.03.009

Cited by 9 publications

(10 citation statements)

References 36 publications

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“…Ghosal et al (), Mcvinish et al (), and Choi & Rousseau () noted that extra conditions in addition to those for the posterior convergence rate are required for the Bayes factor consistency under the null hypothesis when a nonparametric alternative is considered as in . Simply speaking, this is because the true parameter in the null hypothesis (i.e., the constant coefficients in ) can be approximated sufficiently well using a parameter in the alternative hypothesis (i.e., time‐varying coefficients).…”

Section: Testing For the Proportional Hazards Assumptionmentioning

confidence: 99%

“…In this section, we prove the Bayes factor consistency for testing the two hypotheses (15), which implies that the Bayes factor defined as BF 10 .Data/ D .H 1 j Data/= .H 0 j Data/ converges to 0 in probability with respect to P 1 whenˇ 2 F 0 and diverges to 1 in probability with respect to P 1 whenˇ 2 F 1 ; whereˇ denotes the true value of parameter as before. Ghosal et al (2008), Mcvinish et al (2009), and Choi & Rousseau (2015) noted that extra conditions in addition to those for the posterior convergence rate are required for the Bayes factor consistency under the null hypothesis when a nonparametric alternative is considered as in (15). Simply speaking, this is because the true parameter in the null hypothesis (i.e., the constant coefficients in (15)) can be approximated sufficiently well using a parameter in the alternative hypothesis (i.e., time-varying coefficients).…”

Section: Testing For the Proportional Hazards Assumptionmentioning

confidence: 99%

“…The related work includes Ghosal et al (2000), Shen & Wasserman (2001) and Walker et al (2007) for posterior convergence rates and Dass & Lee (2004), Ghosal et al (2008), Mcvinish et al (2009) and Choi & Rousseau (2015) for Bayes factor consistency. All of these results rely on the Bayes theorem assuming the existence of a dominating -finite measure.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients

Kim

Choi

2017

Scandinavian J Statistics

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We study a Bayesian analysis of the proportional hazards model with time‐varying coefficients. We consider two priors for time‐varying coefficients – one based on B‐spline basis functions and the other based on Gamma processes – and we use a beta process prior for the baseline hazard functions. We show that the two priors provide optimal posterior convergence rates (up to the normallogn term) and that the Bayes factor is consistent for testing the assumption of the proportional hazards when the two priors are used for an alternative hypothesis. In addition, adaptive priors are considered for theoretical investigation, in which the smoothness of the true function is assumed to be unknown, and prior distributions are assigned based on B‐splines.

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Section: Testing For the Proportional Hazards Assumptionmentioning

confidence: 99%

Section: Testing For the Proportional Hazards Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients

Kim

Choi

2017

Scandinavian J Statistics

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“…One popular criterion is the Bayes factor [160], which has been shown to be asymptotically consistent for a broad range of models (e.g., [161,162]), however, for the case of general ODE models, no proofs for asymptotic efficiency and consistency are available for all the criteria presented in this section. Bayes' Theorem yields the posterior model probability…”

Section: Model Selection Criteriamentioning

confidence: 99%

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Fröhlich

Loos

Hasenauer

2018

Methods in Molecular Biology

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Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small-to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

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“…The assumptions in the former paper are similar in spirit to those in the latter, which are given above. The results discussed below regarding the independent but not identically distributed setting for comparing a linear and partially linear model (Choi & Rousseau, 2015) are also relevant here.…”

Section: Connections To Literaturementioning

confidence: 99%

Bayes factor consistency

Chib,

Kuffner

2016

Preprint

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Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent surge of attention in the literature. We thoroughly review existing results.As there exists such a wide variety of settings to be considered, e.g. parametric vs. nonparametric, nested vs. non-nested, etc., we adopt the view that a unified framework has didactic value. Using the basic marginal likelihood identity of Chib (1995), we study Bayes factor asymptotics by decomposing the natural logarithm of the ratio of marginal likelihoods into three components. These are, respectively, log ratios of likelihoods, prior densities, and posterior densities. This yields an interpretation of the log ratio of posteriors as a penalty term, and emphasizes that to understand Bayes factor consistency, the prior support conditions driving posterior consistency in each respective model under comparison should be contrasted in terms of the rates of posterior contraction they imply.

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A note on Bayes factor consistency in partial linear models

Cited by 9 publications

References 36 publications

Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients

Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Bayes factor consistency

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