Luis Pericchi

We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (app...

We put forward a novel calibration of p values, the "Adaptive Robust Lower Bound" (ARLB) which maps p values into approximations of posterior probabilities taking into account the effect of sample sizes. We build on the Robust Lower Bound proposed by Sellke, Bayarri and Berger (2001), but we incorporate a simple power of the sample size to make it...

We propose to change the default P-value threshold for statistical significance for claims of new discoveries from 0.05 to 0.005.

"We propose to change the default P-value threshold forstatistical significance for claims of new discoveries from 0.05 to 0.005."

Objective: Although contemporary mortality data are important for health assessment and planning purposes, their availability lag several years. Statistical projection techniques can be employed to obtain current estimates. This study aimed to assess annual trends of mortality in Puerto Rico due to cancer and Ischemic Heart Disease (IHD), and to p...

Stroke is the fifth leading cause of death and the first cause of long-term disability in Puerto Rico. Trained staff reviewed and independently validated the medical records of patients who had been hospitalized with possible stroke at any of the 20 largest hospitals located in Puerto Rico during 2007, 2009, and 2011. The mean age of the 5005 newly...

In this paper, we propose a new wide class of hypergeometric heavy tailed priors that is given as the convolution of a Student-t density for the location parameter and a Scaled Beta 2 prior for the squared scale parameter. These priors may have heavier tails than Student-t priors, and the variances have a sensible behaviour both at the origin and a...

We review a substantial literature, spanning 50 years, concerning the resolution of conflicts using Bayesian heavy-tailed models. Conflicts arise when different sources of information about the model parameters (e.g., prior information, or the information in individual observations) suggest quite different plausible regions for those parameters. Tr...

Modelling outliers and structural breaks in dynamic linear models with a novel use of a heavy tailed prior for the variances: An alternative to the Inverted Gamma

Genetic distances between mtDNA sequences of diverse human groups. Differences between median distances were significant for each of the human groups (Kruskal-Wallis test p<2.2×10−15; Wilcoxon with Bonferroni adjustment p<10−14). Permutation tests with 5,000 permutations confirmed human group differences (p = 0). Distances decreased in the order: m...

Genetic distances of human mtDNA sequences within Africans, Spanish, Koreans and groups of Amerindians and Mestizos. South American Amerindians studied have a degree of admixture as indicated by their higher genetic diversity than the Inuit. The Mestizos with African or Amerindian haplotypes have increased diversity in relation to Mestizos with Eur...

Intrapopulation genetic distance of H. pylori strains hpAfrica1 and hpEurope, by host source. hpAfrica1 strains from Mestizos were much more diverse than those from Africans (Kruskal-Wallis p<10−14). In contrast, neither Mestizos nor Amerindians increased the already high variability hpEurope strains from Spain. Medians are represented as the waist...

The hoatzin is unique among known avian species because of the fermentative function of its enlarged crop. A small-bodied flying foregut fermenter is a paradox, and this bird provides an interesting model to examine how diet selection and the gut microbiota contribute to maximizing digestive efficiency. Therefore, we characterized the bacterial pop...

We studied the diversity of bacteria and host in the H. pylori-human model. The human indigenous bacterium H. pylori diverged along with humans, into African, European, Asian and Amerindian groups. Of these, Amerindians have the least genetic diversity. Since niche diversity widens the sets of resources for colonizing species, we predicted that the...

Gastrointestinal parasites have evolved with humans and colonize many asymptomatic subjects. We investigated the influence of microbial gastrointestinal colonization on the nutritional status of rural Amerindians (40 males and 61 females). Helicobacter pylori was detected by 13C-breath test, and intestinal parasites were detected in fecal specimens...

Background:Gastric atrophy and intestinal metaplasia are pre-malignant lesions of intestinal type gastric cancer (GC). Certain H. pylori and human genotypes have been associated with increased risk for GC. The aim of this study was to assess H. pylori strains and human cytokine genotypes in patients with and without GC precursor lesions. Methods:Cl...

Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal tr...

When catastrophes strike it is easy to be wise after the event. It is also often argued that such catastrophic events are unforeseeable, or at least so implausible as to be negligible for planning purposes. We consider these issues in the context of daily rainfall measurements recorded in Venezuela. Before 1999 simple extreme value techniques were...

Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal tr...

Infection by Helicobacter pylori is recognized as a risk factor for gastric cancer and peptic ulcer disease. Venezuela has regions with different gastric cancer risks; the Andean region has the highest gastric cancer mortality in the country. We performed a cross-sectional study on 357 patients who underwent endoscopy attending 2 private (n = 76) a...

In Rodriguez and Pericchi (2000), Local Bayes Factors are defined and developed for Dynamic Linear Models (DLM), West and Harrison (1997). Local Intrinsic Bayes Factors are based on simulated replicas of the initial set of observations. This generates well calibrated Intrinsic Priors, leaving the whole set of observations for model determination. W...

The basics of the Bayesian approach to model selection are first presented, as well as the motivations for the Bayesian approach. We then review four methods of developing default Bayesian procedures that have undergone considerable recent development, the Conventional Prior approach, the Bayes Information Criterion, the Intrinsic Bayes Factor, and...

This paper explores the usefulness of robust Bayesian analysis in the context of an applied problem, finding priors to model judicial neutrality in an age discrimination case. We seek large classes of prior distributions without trivial bounds on the posterior probability of a key set, that is, without bounds that are independent of the data. Such...

We analyze the pioneering work on the theory of precise measurement of Edwards, Lindman and Savage (1963) in light of some recent developments in the theory of robust Bayesian analysis. The key points of the former are the concept of “actual” prior and bounds for the errors when replacing the actual prior by a uniform prior. The class of “actual” p...

In Bayesian analysis with a "minimal" data set and common noninformative priors, the (formal) marginal density of the data is surprisingly often independent of the error distribution. This results in great simplifications in certain model selection methodologies; for instance, the Intrinsic Bayes Factor for models with this property reduces simply...

About half the world population is infected with Helicobacter pylori. Most live in developing countries where clinical studies face the constraints of high costs of imported rapid diagnostic tests. In this work, we describe and validate a simple local urease test (LUT) to determine the presence of the bacterium in gastric biopsies, and report the i...

In Bayesian model selection or hypothesis testing, it is difficult to develop default Bayes factors, since (improper) noninformative priors cannot typically be used. In developing such default Bayes factors, we feel that it is important to keep several principles in mind. The first is that the default Bayes factor should correspond, in some sense,...

Summary Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis.

In the robust Bayesian literature in order to investigate robustness with respect to the functional form of a base prior distribution π0 (in particular with respect to the shape of the prior tails) the ε-contamination model of prior distributions Γ={π: π=(1−ε)π0(θ|λ)+εq,q∈Q}, has been proposed. Here π0(θ|λ) is the base elicited prior, λ is a vector...

In this work we examine the e-contamination model of prior densities γ={π:π=(1-ε)π0(θ)+εq: qεG}, where π0(θ) is the base elicited prior, q is a contamination belonging to some suitable class G and ε reflects the amount of error in π0(θ). Various classes with shape and/or quantile constraints are analysed, and a posterior robust analysis is carried...

. We outline a brief review of the different approaches which use sets of probability measures as models for prior imprecise knowledge. This is a L A T E X version of a page at the web site of the Imprecise Probabilities Project : http://eepkibm2.rug.ac.be/~ipp. c fl 1998 by Luis Raul Pericchi and the Imprecise Probabilities Project 1. Justificatio...

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