Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence

Belief revision characterizes the process of revising an agent’s beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation
is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster
rule of combination, just like revision in the sense of Alchourron, Gardenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey’s rule of updating, Dempster rule of conditioning and a form of AGM revision.

Flexible paleoclimate age-depth models using an autoregressive gamma process

Radiocarbon dating is routinely used in paleoecology to build chronolo- gies of lake and peat sediments, aiming at inferring a model that would relate the sediment depth with its age. We present a new approach for chronology building (called “Bacon”) that has received enthusiastic attention by paleoecologists. Our methodology is based on controlling core accumulation rates using a gamma autoregressive semiparametric model with an arbitrary number of subdivisions along the sediment. Using prior knowledge about accumulation rates is crucial and informative priors are routinely used. Since many sediment cores are currently analyzed, using different data sets and prior distributions, a robust (adaptive) MCMC is very useful. We use the t-walk (Christen and Fox, 2010), a self adjusting, robust MCMC sampling algorithm, that works acceptably well in many situations. Outliers are also addressed using a recent approach that considers a Student-t model for radiocarbon data. Two examples are presented here, that of a peat core and a core from a lake, and our results are compared with other approaches.

WASP-23b: a transiting hot Jupiter around a K dwarf and its Rossiter-McLaughlin effect

We report the discovery of a new transiting planet in the southern hemisphere. It was found by the WASP-south transit survey and confirmed photometrically and spectroscopically by the 1.2 m Swiss Euler telescope, LCOGT 2m Faulkes South Telescope, the 60 cm TRAPPIST telescope, and the ESO 3.6 m telescope. The orbital period of the planet is 2.94 days. We find that it is a gas giant with a mass of 0.88 ± 0.10 MJ and an estimated radius of 0.96 ± 0.05 RJ. We obtained spectra during transit with the HARPS spectrograph and detect the Rossiter-McLaughlin effect despite its small amplitude. Because of the low signal-to-noise ratio of the effect and a small impact parameter, we cannot place a strong constraint on the projected spin-orbit angle. We find two conflicting values for the stellar rotation. We find, via spectral line broadening, that v sin I = 2.2 ± 0.3 km s-1, while applying another method, based on the activity level using the index log R'_HK, gives an equatorial rotation velocity of only v = 1.35 ± 0.20 km s-1. Using these as priors in our analysis, the planet might be either misaligned or aligned. This result raises doubts about the use of such priors. There is evidence of neither eccentricity nor any radial velocity drift with time. Using WASP-South photometric observations confirmed with LCOGT Faulkes South Telescope, the 60 cm TRAPPIST telescope, the CORALIE spectrograph and the camera from the Swiss 1.2 m Euler Telescope placed at La Silla, Chile, as well as with the HARPS spectrograph, mounted on the ESO 3.6 m, also at La Silla, under proposal 084.C-0185. The data is publicly available at the CDS Strasbourg and on demand to the main author.RV data is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/531/A24Appendix is available in electronic form at http://www.aanda.org

Bagging statistical network inference from large-scale gene expression data.

Modern biology and medicine aim at hunting molecular and cellular causes of biological functions and diseases. Gene regulatory networks (GRN) inferred from gene expression data are considered an important aid for this research by providing a map of molecular interactions. Hence, GRNs have the potential enabling and enhancing basic as well as applied research in the life sciences. In this paper, we introduce a new method called BC3NET for inferring causal gene regulatory networks from large-scale gene expression data. BC3NET is an ensemble method that is based on bagging the C3NET algorithm, which means it corresponds to a Bayesian approach with noninformative priors. In this study we demonstrate for a variety of simulated and biological gene expression data from S. cerevisiae that BC3NET is an important enhancement over other inference methods that is capable of capturing biochemical interactions from transcription regulation and protein-protein interaction sensibly. An implementation of BC3NET is freely available as an R package from the CRAN repository. © 2012 de Matos Simoes, Emmert-Streib.

Type Ia supernova bolometric light curves and ejected mass estimates from the nearby supernova factory

We present a sample of normal Type Ia supernovae (SNe Ia) from the Nearby Supernova Factory data set with spectrophotometry at sufficiently late phases to estimate the ejected mass using the bolometric light curve.Wemeasure Ni masses from the peak bolometric luminosity, then compare the luminosity in the Co-decay tail to the expected rate of radioactive energy release from ejecta of a given mass. We infer the ejected mass in a Bayesian context using a semi-analytic model of the ejecta, incorporating constraints from contemporary numerical models as priors on the density structure and distribution of Ni throughout the ejecta. We find a strong correlation between ejected mass and light-curve decline rate, and consequently Ni mass, with ejected masses in our data ranging from 0.9 to 1.4 M. Most fast-declining (SALT2 x <-1) normal SNe Ia have significantly sub-Chandrasekhar ejected masses in our fiducial analysis.

Sediment accumulation rates in subarctic lakes: insights into age-depth modeling from 22 dated lake records from the Northwest Territories, Canada

Age-depth modeling using Bayesian statistics requires well-informed prior information about the behavior of sediment accumulation. Here we present average sediment accumulation rates (represented as deposition times, DT, in yr/cm) for lakes in an Arctic setting, and we examine the variability across space (intra- and inter-lake) and time (late Holocene). The dataset includes over 100 radiocarbon dates, primarily on bulk sediment, from 22 sediment cores obtained from 18 lakes spanning the boreal to tundra ecotone gradients in subarctic Canada. There are four to twenty-five radiocarbon dates per core, depending on the length and character of the sediment records. Deposition times were calculated at 100-year intervals from age-depth models constructed using the ‘classical’ age-depth modeling software Clam. Lakes in boreal settings have the most rapid accumulation (mean DT 20 ± 10 years), whereas lakes in tundra settings accumulate at moderate (mean DT 70 ± 10 years) to very slow rates, (>100 yr/cm). Many of the age-depth models demonstrate fluctuations in accumulation that coincide with lake evolution and post-glacial climate change. Ten of our sediment cores yielded sediments as old as c. 9,000 cal BP (BP = years before AD 1950). From between c. 9,000 cal BP and c. 6,000 cal BP, sediment accumulation was relatively rapid (DT of 20 to 60 yr/cm). Accumulation slowed between c. 5,500 and c. 4,000 cal BP as vegetation expanded northward in response to warming. A short period of rapid accumulation occurred near 1,200 cal BP at three lakes. Our research will help inform priors in Bayesian age modeling.

Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

This work presents two new score functions based on the Bayesian Dirichlet equivalent uniform (BDeu) score for learning Bayesian network structures. They consider the sensitivity of BDeu to varying parameters of the Dirichlet prior. The scores take on the most adversary and the most beneficial priors among those within a contamination set around the symmetric one. We build these scores in such way that they are decomposable and can be computed efficiently. Because of that, they can be integrated into any state-of-the-art structure learning method that explores the space of directed acyclic graphs and allows decomposable scores. Empirical results suggest that our scores outperform the standard BDeu score in terms of the likelihood of unseen data and in terms of edge discovery with respect to the true network, at least when the training sample size is small. We discuss the relation between these new scores and the accuracy of inferred models. Moreover, our new criteria can be used to identify the amount of data after which learning is saturated, that is, additional data are of little help to improve the resulting model.