Sparsity information and regularization in the horseshoe and other shrinkage priors

Piironen, Juho; Vehtari, Aki

doi:10.1214/17-ejs1337si

Cited by 338 publications

(455 citation statements)

References 27 publications

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“…The second shrinkage-based analysis (and third applied method) used a regularized horseshoe prior (Piironen & Vehtari, 2017) and was implemented in Stan (Carpenter et al, 2017;Supporting Information S.6). The advantage of the regularized horseshoe is to have explicit control on the prior for the number of non-null predictor variables, which was set to 10 (based on the outputs of the two previous investigations).…”

Section: Statistical Assessment Of Potential Common Causes Of Mortamentioning

confidence: 99%

High mortality rates in a juvenile free‐ranging marine predator and links to dive and forage ability

Cox

Authier

Orgeret

et al. 2019

Ecology and Evolution

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1. High juvenile mortality rates are typical of many long-lived marine vertebrate predators. Insufficient development in dive and forage ability is considered a key driver of this. However, direct links to survival outcome are sparse, particularly in free-ranging marine animals that may not return to land.2. In this study, we conduct exploratory investigations toward early mortality in juvenile southern elephant seals Mirounga leonina. Twenty postweaning pups were equipped with (a) a new-generation satellite relay data tag, capable of remotely transmitting fine-scale behavioral movements from accelerometers, and (b) a location transmitting only tag (so that mortality events could be distinguished from device failures). Individuals were followed during their first trip at sea (until mortality or return to land). Two analyses were conducted. First, the behavioral movements and encountered environmental conditions of nonsurviving pups were individually compared to temporally concurrent observations from grouped survivors. Second, common causes of mortality were investigated using Cox's proportional hazard regression and penalized shrinkage techniques.3. Nine individuals died (two females and seven males) and 11 survived (eight females and three males). All but one individual died before the return phase of their first trip at sea, and all but one were negatively buoyant. Causes of death were variable, although common factors included increased horizontal travel speeds and distances, decreased development in dive and forage ability, and habitat type visited (lower sea surface temperatures and decreased total [eddy] kinetic energy).4. For long-lived marine vertebrate predators, such as the southern elephant seal, the first few months of life following independence represent a critical period, when small deviations in behavior from the norm appear sufficient to increase mortality risk. Survival rates may subsequently be particularly vulnerable to changes in climate and environment, which will have concomitant consequences on the demography and dynamics of populations. | 411COX et al.

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Section: Statistical Assessment Of Potential Common Causes Of Mortamentioning

confidence: 99%

High mortality rates in a juvenile free‐ranging marine predator and links to dive and forage ability

Cox

Authier

Orgeret

et al. 2019

Ecology and Evolution

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“…We further set a half Cauchy prior in ρ with mean 0 and standard deviation 1 as recommended (11). Note that this prior can be adapted according to the expected number of non-zero parameters (41).…”

Section: Methodsmentioning

confidence: 99%

dSreg: A bayesian model to integrate changes in splicing and RNA binding protein activity

Martí-Gómez

Lara‐Pezzi

Sánchez-Cabo

2019

Preprint

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Alternative splicing (AS) is an important mechanism in the generation of transcript diversity across mammals. AS patterns are dynamically regulated during development and in response to environmental changes. Defects or perturbations in its regulation may lead to cancer or neurological disorders, among other pathological conditions. The regulatory mechanisms controlling AS in a given biological context are typically inferred using a two step-framework: differential AS analysis followed by enrichment methods. These strategies require setting rather arbitrary thresholds and are prone to error propagation along the analysis. To overcome these limitations, we propose dSreg, a Bayesian model that integrates RNAseq with data from regulatory features, e.g. binding sites of RNA binding proteins (RBPs). dSreg identifies the key underlying regulators controlling AS changes and quantifies their activity while simultaneously estimating the changes in exon inclusion rates. dSreg increased both the sensitivity and the specificity of the identified alternative splicing changes in simulated data, even at low read coverage. dSreg also showed improved performance when analyzing a collection of knock-down RBPs experiments from ENCODE, as opposed to traditional enrichment methods such as Over-representation Analysis (ORA) and Gene Set Enrichment Analysis (GSEA). dSreg opens the possibility to integrate a large amount of readily available RNAseq datasets at low coverage for AS analysis and allows more cost-effective RNA-seq experiments. dSreg was implemented in python using stan and is freely available to the community at https://bitbucket.org/cmartiga/dsreg. Bayesian models | Alternative splicing | RNA binding proteins | Splicing regulationCorrespondence: *elara@cnic.es, fscabo@cnic.es

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“…A popular alternative is the horseshoe prior of Carvalho, Polson, & Scott, 2010, which is known to mimic variable selection priors, without their computational overhead. In a recent paper, Piironen and Vehtari (2017) provided an excellent discussion, where the properties of the horseshoe prior were compared and contrasted with spike and slab priors. In doing so, the authors pointed out two shortcomings of the horseshoe prior.…”

Section: Horseshoe Priormentioning

confidence: 99%

“…We chose to omit the mathematical details of the different horseshoe priors for brevity. Interested readers will find the relevant information in Carvalho et al (2010), Piironen and Vehtari (2017), and the references therein. Recently, Boonstra, Barbaro, and Sen (2019) have proposed alternative informative choices for the prior for the intercept parameter.…”

Section: Regularized Horseshoe Priormentioning

confidence: 99%

“…We set the prior guess for relevant variables at p/2, to be consistent with the variable selection prior value of p j = 0.5. Other hyperparameter values are chosen to be the same as in section 4.2 of Piironen & Vehtari, 2017. The proportion of correct classifications for the regularized horseshoe prior is 0.76, which is comparable with other priors.…”

Section: Spect Data With Spike and Slab Priorsmentioning

confidence: 99%

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Cauchy and other shrinkage priors for logistic regression in the presence of separation

Ghosh

2019

WIREs Computational Stats

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In recent years, the choice of prior distributions for Bayesian logistic regression has received considerable interest. It is widely acknowledged that noninformative, improper priors have to be used with caution because posterior propriety may not always hold. As an alternative, heavy‐tailed priors such as Cauchy prior distributions have been proposed by Gelman et al. (2008). The motivation for using Cauchy prior distributions is that they are proper, and thus, unlike noninformative priors, they are guaranteed to yield proper posterior distributions. The heavy tails of the Cauchy distribution allow the posterior distribution to adapt to the data. Thus Gelman et al. (2008) suggested the use of these prior distributions as a default weakly informative choice, in the absence of prior knowledge about the regression coefficients. While these prior distributions are guaranteed to have proper posterior distributions, Ghosh, Li, and Mitra (2018), showed that the posterior means may not exist, or can be unreasonably large, when they exist, for datasets with separation. In this paper, we provide a short review of the concept of separation, and we discuss how common prior distributions like the Cauchy and normal prior perform in data with separation. Theoretical and empirical results suggest that lighter tailed prior distributions such as normal prior distributions can be a good default choice when there is separation. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical Models

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Sparsity information and regularization in the horseshoe and other shrinkage priors

Cited by 338 publications

References 27 publications

High mortality rates in a juvenile free‐ranging marine predator and links to dive and forage ability

High mortality rates in a juvenile free‐ranging marine predator and links to dive and forage ability

dSreg: A bayesian model to integrate changes in splicing and RNA binding protein activity

Cauchy and other shrinkage priors for logistic regression in the presence of separation

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