A New Calibrated Bayesian Internal Goodness-of-Fit Method: Sampled Posterior p-Values as Simple and General p-Values That Allow Double Use of the Data

Background: Recent approaches mixing frequentist principles with Bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of Bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function. Methodology/Principal Findings: We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution. Conclusions/Significance: These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values

Bayesian astrostatistics: a backward look to the future

This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects that do not pass traditional detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in "Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed., Springer, New York, forthcoming in 2012), the inaugural volume for the Springer Series in Astrostatistics. Version 2 has minor clarifications and an additional referenc

Photoperiodic Modulation of Circadian Clock and Reproductive Axis Gene Expression in the Pre-Pubertal European Sea Bass Brain

The acquisition of reproductive competence requires the activation of the brain-pituitary-gonad (BPG) axis, which in most vertebrates, including fishes, is initiated by changes in photoperiod. In the European sea bass long-term exposure to continuous light (LL) alters the rhythm of reproductive hormones, delays spermatogenesis and reduces the incidence of precocious males. In contrast, an early shift from long to short photoperiod (AP) accelerates spermatogenesis. However, how photoperiod affects key genes in the brain to trigger the onset of puberty is still largely unknown. Here, we investigated if the integration of the light stimulus by clock proteins is sufficient to activate key genes that trigger the BPG axis in the European sea bass. We found that the clock genes clock, npas2, bmal1 and the BPG genes gnrh, kiss and kissr share conserved transcription factor frameworks in their promoters, suggesting co-regulation. Other gene promoters of the BGP axis were also predicted to be co-regulated by the same frameworks. Co-regulation was confirmed through gene expression analysis of brains from males exposed to LL or AP photoperiod compared to natural conditions: LL fish had suppressed gnrh1, kiss2, galr1b and esr1, while AP fish had stimulated npas2, gnrh1, gnrh2, kiss2, kiss1rb and galr1b compared to NP. It is concluded that fish exposed to different photoperiods present significant expression differences in some clock and reproductive axis related genes well before the first detectable endocrine and morphological responses of the BPG axis.European Community [222719 - LIFECYCLE]; Foundation for Science and Technology of Portugal (FCT) [SFRH/BPD/66742/2009, PEst-C/MAR/LA0015/2011]; Valencian Regional Goverment [Prometeo II/2014/051]; Spanish Ministry of Science and Innovation (MICINN) [CSD 2007-0002]info:eu-repo/semantics/publishedVersio

A Bayesian Outlier Criterion to Detect SNPs under Selection in Large Data Sets

Background: The recent advent of high-throughput SNP genotyping technologies has opened new avenues of research for population genetics. In particular, a growing interest in the identification of footprints of selection, based on genome scans for adaptive differentiation, has emerged.[br/] Methodology/Principal Findings: The purpose of this study is to develop an efficient model-based approach to perform Bayesian exploratory analyses for adaptive differentiation in very large SNP data sets. The basic idea is to start with a very simple model for neutral loci that is easy to implement under a Bayesian framework and to identify selected loci as outliers via Posterior Predictive P-values (PPP-values). Applications of this strategy are considered using two different statistical models. The first one was initially interpreted in the context of populations evolving respectively under pure genetic drift from a common ancestral population while the second one relies on populations under migration-drift equilibrium. Robustness and power of the two resulting Bayesian model-based approaches to detect SNP under selection are further evaluated through extensive simulations. An application to a cattle data set is also provided.[br/] Conclusions/Significance: The procedure described turns out to be much faster than former Bayesian approaches and also reasonably efficient especially to detect loci under positive selection

Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial

In this work we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example we calibrate the model against experimental data that is subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model

Melatonin Induces Follicle Maturation in Danio rerio

Most organisms modulate their reproductive activity responding to day length by the nocturnal release of melatonin by the pineal gland. This hormone is also responsible for synchronizing reproduction with specific external environment stimuli in order to optimize reproductive success

Neural computations underpinning the strategic management of influence in advice giving

Research on social influence has focused mainly on the target of influence (e.g., consumer and voter); thus, the cognitive and neurobiological underpinnings of the source of the influence (e.g., politicians and salesmen) remain unknown. Here, in a three-sided advice-giving game, two advisers competed to influence a client by modulating their own confidence in their advice about which lottery the client should choose. We report that advisers’ strategy depends on their level of influence on the client and their merit relative to one another. Moreover, blood-oxygenation-level-dependent (BOLD) signal in the temporo-parietal junction is modulated by adviser’s current level of influence on the client, and relative merit prediction error affects activity in medial-prefrontal cortex. Both types of social information modulate ventral striatum response. By demonstrating what happens in our mind and brain when we try to influence others, these results begin to explain the biological mechanisms that shape inter-individual differences in social conduct