Adaptive Priors Based on Splines with Random Knots

Belitser, Eduard; Serra, Paulo

doi:10.1214/14-ba879

Cited by 13 publications

(6 citation statements)

References 16 publications

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“…The B-spline prior in Section 3.3.1 depends on the smoothness p of the true function, which is not known in practice. In this section, we show that we can obtain the (almost) optimal convergence rate and Bayes factor consistency even when p is unknown by putting a certain prior on p: Similar adaptive priors have been considered by Belitser & Serra (2014) and Shen & Ghosal (2015) for linear regression models.…”

Section: Adaptive Priorsmentioning

confidence: 92%

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: Adaptive Priorsmentioning

confidence: 92%

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

Kim

Choi

2017

Scandinavian J Statistics

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“…Alternatively, RLM could be extended to estimate the shape of the weight function using Bayesian adaptive priors for the splines, 39 , 40 with the advantage of not having to perform model selection.…”

Section: Discussionmentioning

confidence: 99%

A Bayesian approach to investigate life course hypotheses involving continuous exposures

Madathil

Joseph

Hardy

et al. 2018

International Journal of Epidemiology

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BackgroundDifferent hypotheses have been proposed in life course epidemiology on how a time-varying exposure can affect health or disease later in life. Researchers are often interested in investigating the probability of these hypotheses based on observed life course data. However, current techniques based on model/variable selection do not provide a direct estimate of this probability. We propose an alternative technique for a continuous exposure, using a Bayesian approach that has specific advantages, to investigate which life course hypotheses are supported by the observed data.MethodsWe demonstrate the technique, the relevant life course exposure model (RLM), using simulations. We also analyse data from a case-control study on risk factors of oral cancer, with repeated measurements of betel quid chewing across life. We investigate the relative importance of chewing one quid of betel per day, at three life periods: ≤20 years, 21–40 years and above 40 years of age, on the risk of developing oral cancer.ResultsRLM was able to correctly identify the life course hypothesis under which the data were simulated. Results from the case-control study showed that there was 74.3% probability that betel quid exposure earlier in life, compared with later, results in higher odds of developing oral cancer later in life.ConclusionsRLM is a useful option to identify the life course hypothesis supported by the observed data prior to the estimation of a causal effect.

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“…The theory of random series prior distributions suggests that a prior on |δ j\0 | should decay to zero to ensure optimal posterior contraction (Belitser and Serra, 2014;Shen and Ghosal, 2015). Although we use a different basis, with this in mind, we set a geometric prior distribution on |δ j\0 |, renormalized so that 1 ≤ |δ j\0 | ≤ L j , and assume that all values of δ j\0 resulting in the same value of |δ j\0 | are equally likely.…”

Section: 31mentioning

confidence: 99%

Bayesian model selection in additive partial linear models via locally adaptive splines

Jeong¹,

Park²,

Dyk³

2020

Preprint

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We consider a model selection problem for additive partial linear models that provide a flexible framework allowing both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model and simultaneously determine whether nonzero nonlinear components can be further simplified to linear components in the final model. In this paper, we propose a new Bayesian framework for data-driven model selection by conducting careful model specification, including the choice of prior distribution and of nonparametric model for the nonlinear additive components, and propose new sophisticated computational strategies. Our models, methods, and algorithms are deployed on a suite of numerical studies and applied to a nutritional epidemiology study. The numerical results show that the proposed methodology outperforms previously available methodologies in terms of effective sample sizes of the Markov chain samplers and the overall misclassification rates, especially in high-dimensional and large-sample cases.

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Adaptive Priors Based on Splines with Random Knots

Cited by 13 publications

References 16 publications

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

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

A Bayesian approach to investigate life course hypotheses involving continuous exposures

Bayesian model selection in additive partial linear models via locally adaptive splines

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