Optimal predictive model selection

Barbieri, Maria Maddalena; Berger, James O.

doi:10.1214/009053604000000238

Cited by 807 publications

(712 citation statements)

References 24 publications

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“…For each sample group, we then select the set of edges that appear with marginal posterior probability (PPI) > 0.5. Although this rule was proposed by Barbieri and Berger (2004) in the context of prediction rather than structure discovery, we found that it resulted in a reasonable expected false discovery rate (FDR). Following Newton et al (2004), we let ξ k,ij represent 1 - the marginal posterior probability of inclusion for edge ( i, j ) in graph k .…”

Section: Posterior Inferencementioning

confidence: 82%

Bayesian Inference of Multiple Gaussian Graphical Models

Peterson

Stingo

Vannucci

2015

Journal of the American Statistical Association

159

207

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In this paper, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab prior on the parameters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of relative network similarity across groups. Our modeling framework incorporates relevant prior knowledge through an edge-specific informative prior and can encourage similarity to an established network. Through simulations, we demonstrate the utility of our method in summarizing relative network similarity and compare its performance against related methods. We find improved accuracy of network estimation, particularly when the sample sizes within each subgroup are moderate. We also illustrate the application of our model to infer protein networks for various cancer subtypes and under different experimental conditions.

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Section: Posterior Inferencementioning

confidence: 82%

Bayesian Inference of Multiple Gaussian Graphical Models

Peterson

Stingo

Vannucci

2015

Journal of the American Statistical Association

159

207

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“…It is often of interest additionally to select the important variables affecting the response y. In the context of variable selection in a normal linear model, Barbieri and Berger (2004) advocated using the median probability model consisting of the variables with posterior marginal inclusion probability greater than or equal to half. They also proved the predictive optimality of such models.…”

Section: Resultsmentioning

confidence: 99%

Anisotropic function estimation using multi-bandwidth Gaussian processes

Bhattacharya

Pati²,

Dunson

2014

Ann. Statist.

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In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a Gaussian process prior with dimension-specific scalings, which are assigned carefully-chosen hyperpriors. We additionally show that using a homogenous Gaussian process with a single bandwidth leads to a sub-optimal rate in anisotropic cases.

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“…For prediction purpose, a Bayesian Model Averaged (BMA) approach is more consistent with fundamental Bayesian idea. As a matter of fact, Barbieri and Berger [45] have proved that the best prediction model is the median probability model (which is often not the highest probability model) for mean squared error loss function. However, in our particular case, we didn’t use the Bayesian Model Average (BMA) approach for the following reasons: (1) For targeted therapy development, it’s more important to focus on just a few biomarkers that can differentiate treatment effects.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Two-Stage Biomarker-Based Adaptive Design for Targeted Therapy Development

Chen

Wei

et al. 2014

Stat Biosci

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We propose a Bayesian two-stage biomarker-based adaptive randomization (AR) design for the development of targeted agents. The design has three main goals: (1) to test the treatment efficacy, (2) to identify prognostic and predictive markers for the targeted agents, and (3) to provide better treatment for patients enrolled in the trial. To treat patients better, both stages are guided by the Bayesian AR based on the individual patient’s biomarker profiles. The AR in the first stage is based on a known marker. A Go/No-Go decision can be made in the first stage by testing the overall treatment effects. If a Go decision is made at the end of the first stage, a two-step Bayesian lasso strategy will be implemented to select additional prognostic or predictive biomarkers to refine the AR in the second stage. We use simulations to demonstrate the good operating characteristics of the design, including the control of per-comparison type I and type II errors, high probability in selecting important markers, and treating more patients with more effective treatments. Bayesian adaptive designs allow for continuous learning. The designs are particularly suitable for the development of multiple targeted agents in the quest of personalized medicine. By estimating treatment effects and identifying relevant biomarkers, the information acquired from the interim data can be used to guide the choice of treatment for each individual patient enrolled in the trial in real time to achieve a better outcome. The design is being implemented in the BATTLE-2 trial in lung cancer at the MD Anderson Cancer Center.

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Optimal predictive model selection

Cited by 807 publications

References 24 publications

Bayesian Inference of Multiple Gaussian Graphical Models

Bayesian Inference of Multiple Gaussian Graphical Models

Anisotropic function estimation using multi-bandwidth Gaussian processes

Bayesian Two-Stage Biomarker-Based Adaptive Design for Targeted Therapy Development

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