Robust Bayesian inference via coarsening

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure. We introduce a simple, coherent approach to Bayesian inference that improves robustness to perturbations from the model: rather than condition on the data exactly, one conditions on a neighborhood of the empirical distribution. When using neighborhoods based on relative entropy estimates, the resulting "coarsened" posterior can be approximated by simply tempering the likelihood---that is, by raising it to a fractional power---thus, inference is often easily implemented with standard methods, and one can even obtain analytical solutions when using conjugate priors. Some theoretical properties are derived, and we illustrate the approach with real and simulated data, using mixture models, autoregressive models of unknown order, and variable selection in linear regression

The possible statistical relation of Pc1 pulsations to Earthquake occurrence at low latitudes

We examine the association between earthquakes and Pc1 pulsations observed at a low-latitude station in Parkfield, California. The period under examination is ~7.5 years in total, from February 1999 to July 2006, and we use an automatic identification algorithm to extract information on Pc1 pulsations from the magnetometer data. These pulsations are then statistically correlated to earthquakes from the USGS NEIC catalog within a radius of 200 km around the magnetometer, and <I>M</I>>3.0. Results indicate that there is an enhanced occurrence probability of Pc1 pulsations ~5–15 days in advance of the earthquakes, during the daytime. We quantify the statistical significance and show that such an enhancement is unlikely to have occurred due to chance alone. We then examine the effect of declustering our earthquake catalog, and show that even though significance decreases, there is still a statistically significant daytime enhancement prior to the earthquakes. Finally, we select only daytime Pc1 pulsations as the fiducial time of our analysis, and show that earthquakes are ~3–5 times more likely to occur in the week following these pulsations, than normal. Comparing these results to other events, it is preliminarily shown that the normal earthquake probability is unaffected by geomagnetic activity, or a random event sequence

Momentarily Excessive Construction As The Basis For Protoadaptation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137522/1/evo04677.pd

Mechanistic Hierarchical Gaussian Processes

The statistics literature on functional data analysis focuses primarily on flexible black-box approaches, which are designed to allow individual curves to have essentially any shape while characterizing variability. Such methods typically cannot incorporate mechanistic information, which is commonly expressed in terms of differential equations. Motivated by studies of muscle activation, we propose a nonparametric Bayesian approach that takes into account mechanistic understanding of muscle physiology. A novel class of hierarchical Gaussian processes is defined that favors curves consistent with differential equations defined on motor, damper, spring systems. A Gibbs sampler is proposed to sample from the posterior distribution and applied to a study of rats exposed to non-injurious muscle activation protocols. Although motivated by muscle force data, a parallel approach can be used to include mechanistic information in broad functional data analysis applications

Evidence accumulation models with R: A practical guide to hierarchical Bayesian methods

Evidence accumulation models are a useful tool to allow researchers to investigate the latent cognitive variables that underlie response time and response accuracy. However, applying evidence accumulation models can be difficult because they lack easily computable forms. Numerical methods are required to determine the parameters of evidence accumulation that best correspond to the fitted data. When applied to complex cognitive models, such numerical methods can require substantial computational power which can lead to infeasibly long compute times. In this paper, we provide efficient, practical software and a step-by-step guide to fit evidence accumulation models with Bayesian methods. The software, written in C++, is provided in an R package: 'ggdmc'. The software incorporates three important ingredients of Bayesian computation, (1) the likelihood functions of two common response time models, (2) the Markov chain Monte Carlo (MCMC) algorithm (3) a population-based MCMC sampling method. The software has gone through stringent checks to be hosted on the Comprehensive R Archive Network (CRAN) and is free to download. We illustrate its basic use and an example of fitting complex hierarchical Wiener diffusion models to four shooting-decision data sets

Prevention of Neural-Tube Defects with Periconceptional Folic Acid, Methylfolate, or Multivitamins?

Background/Aims: To review the main results of intervention trials which showed the efficacy of periconceptional folic acid-containing multivitamin and folic acid supplementation in the prevention of neural-tube defects (NTD). Methods and Results: The main findings of 5 intervention trials are known: (i) the efficacy of a multivitamin containing 0.36 mg folic acid in a UK nonrandomized controlled trial resulted in an 83-91% reduction in NTD recurrence, while the results of the Hungarian (ii) randomized controlled trial and (iii) cohort-controlled trial using a multivitamin containing 0.8 mg folic acid showed 93 and 89% reductions in the first occurrence of NTD, respectively. On the other hand, (iv) another multicenter randomized controlled trial proved a 71% efficacy of 4 mg folic acid in the reduction of recurrent NTD, while (v) a public health-oriented Chinese-US trial showed a 41-79% reduction in the first occurrence of NTD depending on the incidence of NTD. Conclusions: Translational application of these findings could result in a breakthrough in the primary prevention of NTD, but so far this is not widely applied in practice. The benefits and drawbacks of 4 main possible uses of periconceptional folic acid/multivitamin supplementation, i.e. (i) dietary intake, (ii) periconceptional supplementation, (iii) flour fortification, and (iv) the recent attempt for the use of combination of oral contraceptives with 6S-5-methytetrahydrofolate (methylfolate), are discussed. Obviously, prevention of NTD is much better than the frequent elective termination of pregnancies after prenatal diagnosis of NTD fetuses

Bayesian lasso binary quantile regression

In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantile regression is proposed. Existing approaches to variable selection in a binary classification context are sensitive to outliers, heteroskedasticity or other anomalies of the latent response. The method proposed in this study overcomes these problems in an attractive and straightforward way. A Laplace likelihood and Laplace priors for the regression parameters are proposed and estimated with Bayesian Markov Chain Monte Carlo. The resulting model is equivalent to the frequentist lasso procedure. A conceptional result is that by doing so, the binary regression model is moved from a Gaussian to a full Laplacian framework without sacrificing much computational efficiency. In addition, an efficient Gibbs sampler to estimate the model parameters is proposed that is superior to the Metropolis algorithm that is used in previous studies on Bayesian binary quantile regression. Both the simulation studies and the real data analysis indicate that the proposed method performs well in comparison to the other methods. Moreover, as the base model is binary quantile regression, a much more detailed insight in the effects of the covariates is provided by the approach. An implementation of the lasso procedure for binary quantile regression models is available in the R-package bayesQR