More for less: predicting and maximizing genomic variant discovery via Bayesian nonparametrics

Masoero, Lorenzo; Camerlenghi, Federico; Favaro, Stefano; Broderick, Tamara

doi:10.1093/biomet/asab012

Cited by 9 publications

(26 citation statements)

References 52 publications

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“…The use of MAP estimates for hyperparameters is becoming increasingly popular in Bayesian nonparametrics, see e.g. Masoero et al (2019) and Di Benedetto et al (2017), where the number of hyperparameters is usually small and wellinformed by the data. This contrasts with flexible Bayesian nonparametric regression approaches which model the logarithm of the survival time using a dependent Dirichlet process.…”

Section: Discussionmentioning

confidence: 99%

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Riva-Palacio

Leisen

Griffin

2021

Journal of the American Statistical Association

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We present a novel Bayesian nonparametric model for regression in survival analysis. Our model builds on the classical neutral to the right model of Doksum (1974) and on the Cox proportional hazards model of Kim and Lee (2003). The use of a vector of dependent Bayesian nonparametric priors allows us to efficiently * Fabrizio Leisen was supported by the European Community's Seventh Framework Programme [FP7/2007[FP7/ -2013 under grant agreement no: 630677. model the hazard as a function of covariates whilst allowing nonproportionality. The model can be seen as having competing latent risks. We characterize the posterior of the underlying dependent vector of completely random measures and study the asymptotic behavior of the model. We show how an MCMC scheme can provide Bayesian inference for posterior means and credible intervals. The method is illustrated using simulated and real data.

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Section: Discussionmentioning

confidence: 99%

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Riva-Palacio

Leisen

Griffin

2021

Journal of the American Statistical Association

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“…where c > 0, σ ∈ (0, 1), and α > 0 (James [28], Masoero et al [30]). Now, we describe the predictive distribution for an arbitrary CRM μ.…”

Section: Priors Based On Crmsmentioning

confidence: 99%

On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

Camerlenghi

Favaro

2021

Mathematics

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In the 1920s, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson’s “sufficientness” postulate, and it has been the subject of many contributions in Bayesian statistics, leading to predictive characterization for infinite-dimensional generalizations of the Dirichlet distribution, i.e., species-sampling models. In this paper, we review “sufficientness” postulates for species-sampling models, and then investigate analogous predictive characterizations for the more general feature-sampling models. In particular, we present a “sufficientness” postulate for a class of feature-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of feature-sampling models.

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“…BNP estimation of U relies on the specification of a prior distribution on the unknown feature proportions p i 's, and completely random measures (CRM) [Kingman, 1967] provide a natural framework to define such a prior [James, 2017, Broderick et al, 2018, the most common being the beta process and the stable-Beta process priors Gorur, 2009, Griffiths andGhahramani, 2011]. In a recent work, Masoero et al [2021] applied the stable-Beta process to develop the first BNP approach to the unseen-features problem, bringing out the upside and the downside of the use of CRMs as prior models: i) the downside lies in the use of the sampling information, that is the posterior distribution of U , given Z 1:N , depends on Z 1:N only through the sample size N ; ii) the upside lies in the analytical tractability and the interpretability, that is the posterior distribution of U , given Z 1:N , is a Poisson distribution whose parameter depends on N and the prior's parameters. While analytically appealing, CRMs lead to a questionable oversimplification of the BNP approach, in the sense that the posterior distribution of U does not depend on the sampling information except through the sample size.…”

Section: Our Contributionsmentioning

confidence: 99%

“…Our empirical analysis shows that the proposed methodology outperforms parametric and nonparametric competitors, both classical (frequentist) and Bayesian, in terms of estimation accuracy of U . Moreover, the proposed methodology also provides improved coverage for the estimation with respect to the recent BNP approach of Masoero et al [2021].…”

Section: Our Contributionsmentioning

confidence: 99%

“…In biology we may think of individuals as organisms and of features as groups to which organisms belong to, with each group being defined by any difference in the genome relative to a reference genome, namely a (genetic) variant. A wide range of approaches have been developed to estimate the unseen genetic variation, including Bayesian methods [Ionita-Laza et al, 2009, Masoero et al, 2021, jackknife [Gravel, 2014], linear programming [Gravel, 2014, Zou et al, 2016, and Good-Toulmin estimators [Orlitsky et al, 2016, Chakraborty et al, 2019.…”

Section: Introductionmentioning

confidence: 99%

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Scaled process priors for Bayesian nonparametric estimation of the unseen genetic variation

Camerlenghi¹,

Favaro²,

Masoero³

et al. 2021

Preprint

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There is a growing interest in the estimation of the number of unseen features, mostly driven by applications in biological sciences. A recent work brought out the upside and the downside of the popular stable-Beta process prior, and generalizations thereof, in Bayesian nonparametric inference for the unseen-features problem: i) the downside lies in the limited use of the sampling information in the posterior distributions, which depend on the observable sample only through the sample size; ii) the upside lies in the analytical tractability and interpretability of the posterior distributions, which are simple Poisson distributions whose parameters are simple to compute, and depend on the sample size and the prior's parameter. In this paper, we introduce and investigate an alternative nonparametric prior, referred to as the stable-Beta scaled process prior, which is the first prior that allows to enrich the posterior distribution of the number of unseen features, through the inclusion of the sampling information on the number of distinct features in the observable sample, while maintaining the same analytical tractability and interpretability as the stable-Beta process prior. Our prior leads to a negative Binomial posterior distribution, whose parameters depends on the sample size, the observed number of distinct features and the prior's parameter, providing estimates that are simple, linear in the sampling information and computationally efficient. We apply our approach to synthetic and real genetic data, showing that it outperforms parametric and nonparametric competitors in terms of estimation accuracy.

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More for less: predicting and maximizing genomic variant discovery via Bayesian nonparametrics

Cited by 9 publications

References 52 publications

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Survival Regression Models With Dependent Bayesian Nonparametric Priors

On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

Scaled process priors for Bayesian nonparametric estimation of the unseen genetic variation

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