Consistency of objective Bayes factors as the model dimension grows

In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist. Assoc. 104 (2009) 1261--1271]. However, in models where the number of parameters increases as the sample size increases, properties of the Bayes factor are not totally understood. Here we study consistency of the Bayes factors for nested normal linear models when the number of regressors increases with the sample size. We pay attention to two successful tools for model selection [Schwarz Ann. Statist. 6 (1978) 461--464] approximation to the Bayes factor, and the Bayes factor for intrinsic priors [Berger and Pericchi J. Amer. Statist. Assoc. 91 (1996) 109--122, Moreno, Bertolino and Racugno J. Amer. Statist. Assoc. 93 (1998) 1451--1460]. We find that the the Schwarz approximation and the Bayes factor for intrinsic priors are consistent when the rate of growth of the dimension of the bigger model is $O(n^b)$ for $b<1$. When $b=1$ the Schwarz approximation is always inconsistent under the alternative while the Bayes factor for intrinsic priors is consistent except for a small set of alternative models which is characterized.Comment: Published in at http://dx.doi.org/10.1214/09-AOS754 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the frequentist and Bayesian approaches to hypothesis testing

Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper we briefly revise the basic aspects of hypothesis testing for both the frequentist and Bayesian procedures and discuss the variable selection problem in normal linear regression for which the discrepancies are more apparent. Illustrations on simulated and real data are given

Consistency of Bayesian procedures for variable selection

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that the asymptotics of the Bayes factors for intrinsic priors are equivalent to those of the Schwarz (BIC) criterion. Also, recall that the Jeffreys--Lindley paradox refers to the well-known fact that a point null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity. This implies that some limiting forms of proper prior distributions are not necessarily suitable for testing problems. Intrinsic priors are limits of proper prior distributions, and for finite sample sizes they have been proved to behave extremely well for variable selection in regression; a consequence of our results is that for intrinsic priors Lindley's paradox does not arise.Comment: Published in at http://dx.doi.org/10.1214/08-AOS606 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A bayesian approach for one-way ANOVA under unequal variances

In this report a Bayesian solution to the problem of testing the equality of the means of k independent normal populations with unknown and arbitrary variances is provided. An important issue in the solution of this problem is the determination of groups with equal means, often solved by multiple comparisons, which can lead to results that are difficult to interpret. In order to avoid this drawback, we propose to treat all possible alternatives existing in the alternative hypothesis by considering the set of all possible configurations of the set of k means. This idea is closely related to the statistical pro-blem of cluster analysis. This allows us to reformulate the testing problem in terms of model selection. A hierarchical model is proposed to compute the Bayes factor of all models, as well as the posterior probability of all the possible configurations. Some illustrative examples of the goodness of the proposed solution are presented.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A Bayesian Solution to the Behrens-Fisher problem

A simple solution to the Behrens–Fisher problem based on Bayes factors is presented, and its relation with the Behrens–Fisher distribution is explored. The construction of the Bayes factor is based on a simple hierarchical model, and has a closed form based on the densities of general Behrens–Fisher distributions. Simple asymptotic approximations of the Bayes factor, which are functions of the Kullback–Leibler divergence between normal distributions, are given, and it is also proved to be consistent. Some examples and comparisons are also presented.Open access funding provided by Universidad de Málaga/CBUA

Nutritional Characteristics of the Seed Protein in 23 Mediterranean Legumes

The search for new sources of plant protein for food and animal feed is driven by an increasing demand in developing countries and the interest in healthy alternatives to animal protein. Seeds from 23 different wild legumes belonging to tribes Gallegeae, Trifolieae, and Loteae were collected in southern Spain and their total amino acid composition was analyzed, by reverse phase-high performance liquid chromatography (RP-HPLC), in order to explore their nutritional value. Protein content in the seeds ranged from 15.5% in Tripodium tetraphyllum to 37.9% and 41.3% in Medicago minima and Medicago polymorpha, respectively. Species belonging to tribe Trifolieae, such as Melilotus elegans and Trifolium spp., showed the most equilibrated amino acid composition and the best theoretical nutritional values, although all species were deficient in sulfur amino acids. The amino acid composition of the seeds from some of these legumes was characterized by high levels of the anticancer non-proteic amino acid canavanine This amino acid was found free in the seeds from some of the species belonging to each of the three tribes included in the present work. Astragalus pelecinus in tribe Gallegea, Trifolium angustifolium in tribe Trifolieae, and Anthyllis vulneraria in tribe Loteae have 3.2%, 3.7%, and 7.2% canavanine, respectively. Seeds from Anthyllis vulneraria, Hymenocarpus lotoides, and Hymenocarpos cornicina have the highest contents in canavanine overall. In conclusion, the seeds from some of these legumes could be used for human consumption and for feeding animals because they contain protein of good nutritional quality. These plants could be useful in domestication and breeding programs for production of new varieties with improved nutritional and functional properties. In addition, some of these species may be of interest as a source of the bioactive compound canavanineinfo:eu-repo/semantics/publishedVersio

Plitidepsin has a positive therapeutic index in adult patients with COVID-19 requiring hospitalization

Plitidepsin is a marine-derived cyclic-peptide that inhibits SARS-CoV-2 replication at low nanomolar concentrations by the targeting of host protein eEF1A (eukaryotic translation-elongation-factor-1A). We evaluated a model of intervention with plitidepsin in hospitalized COVID-19 adult patients where three doses were assessed (1.5, 2 and 2.5 mg/day for 3 days, as a 90-minute intravenous infusion) in 45 patients (15 per dose-cohort). Treatment was well tolerated, with only two Grade 3 treatment-related adverse events observed (hypersensitivity and diarrhea). The discharge rates by Days 8 and 15 were 56.8% and 81.8%, respectively, with data sustaining dose-effect. A mean 4.2 log10 viral load reduction was attained by Day 15. Improvement in inflammation markers was also noted in a seemingly dose-dependent manner. These results suggest that plitidepsin impacts the outcome of patients with COVID-19.This study has been funded by Pharmamar, S.A. (Madrid, Spain). This work was supported by grants from the Government of Spain (PIE_INTRAMURAL_ LINEA 1 - 202020E079; PIE_INTRAMURAL_CSIC-202020E043). The research of CBIG consortium (constituted by IRTA-CReSA, BSC, & IrsiCaixa) is supported by Grifols pharmaceutical. We also acknowledge the crowdfunding initiative #Yomecorono (https://www.yomecorono.com). N.I.U. has non-restrictive funding from PharmaMar to study the antiviral effect of Plitidepsin. N.J.K. was funded by grants from the National Institutes of Health (P50AI150476, U19AI135990, U19AI135972, R01AI143292, R01AI120694, and P01AI063302); by the Excellence in Research Award (ERA) from the Laboratory for Genomics Research (LGR), a collaboration between UCSF, UCB, and GSK (#133122P); by the Roddenberry Foundation, and gifts from QCRG philanthropic donors. This work was supported by the Defense Advanced Research Projects Agency (DARPA) under Cooperative Agreement #HR0011-19-2-0020. The views, opinions, and/or findings contained in this material are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. This research was partly funded by CRIP (Center for Research for Influenza Pathogenesis), a NIAID supported Center of Excellence for Influenza Research and Surveillance (CEIRS, contract # HHSN272201400008C), by DARPA grant HR0011-19-2-0020, by supplements to NIAID grants U19AI142733, U19AI135972 and DoD grant W81XWH-20-1-0270, and by the generous support of the JPB Foundation, the Open Philanthropy Project (research grant 2020-215611 (5384)), and anonymous donors to AG-S. S.Y. received funding from a Swiss National Foundation (SNF) Early Postdoc Mobility fellowship (P2GEP3_184202).N

Preclinical and randomized phase I studies of plitidepsin in adults hospitalized with COVID-19

Plitidepsin, a marine-derived cyclic-peptide, inhibits SARS-CoV-2 replication at nanomolar concentrations by targeting the host protein eukaryotic translation elongation factor 1A. Here, we show that plitidepsin distributes preferentially to lung over plasma, with similar potency against across several SARS-CoV-2 variants in preclinical studies. Simultaneously, in this randomized, parallel, open-label, proof-of-concept study (NCT04382066) conducted in 10 Spanish hospitals between May and November 2020, 46 adult hospitalized patients with confirmed SARS-CoV-2 infection received either 1.5 mg (n = 15), 2.0 mg (n = 16), or 2.5 mg (n = 15) plitidepsin once daily for 3 d. The primary objective was safety; viral load kinetics, mortality, need for increased respiratory support, and dose selection were secondary end points. One patient withdrew consent before starting procedures; 45 initiated treatment; one withdrew because of hypersensitivity. Two Grade 3 treatment-related adverse events were observed (hypersensitivity and diarrhea). Treatment-related adverse events affecting more than 5% of patients were nausea (42.2%), vomiting (15.6%), and diarrhea (6.7%). Mean viral load reductions from baseline were 1.35, 2.35, 3.25, and 3.85 log10 at days 4, 7, 15, and 31. Nonmechanical invasive ventilation was required in 8 of 44 evaluable patients (16.0%); six patients required intensive care support (13.6%), and three patients (6.7%) died (COVID-19-related). Plitidepsin has a favorable safety profile in patients with COVID-19.This work was supported by grants from the Government of Spain (PIE_INTRAMURAL_ LINEA 1 - 202020E079; PIE_INTRAMURAL_CSIC-202020E043). The research of CBIG consortium (constituted by IRTA-CReSA, BSC, & IrsiCaixa) is supported by Grifols pharmaceutical. We also acknowledge the crowdfunding initiative #Yomecorono (https://www.yomecorono.com). N Izquierdo-Useros has nonrestrictive funding from PharmaMar to study the antiviral effect of Plitidepsin. NJ Krogan was funded by grants from the National Institutes of Health (P50AI150476, U19AI135990, U19AI135972, R01AI143292, R01AI120694, and P01AI063302); by the Excellence in Research Award (ERA) from the Laboratory for Genomics Research (LGR), a collaboration between the University of California, San Francisco (UCSF), University of California, Berkley (UCB), and GlaxoSmithKline (GSK) (#133122P); by the Roddenberry Foundation, and gifts from QCRG philanthropic donors. This work was supported by the Defense Advanced Research Projects Agency (DARPA) under Cooperative Agreement #HR0011-19-2-0020. The views, opinions, and/or findings contained in this material are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. This research was partly funded by Center for Research for Influenza Pathogenesis and Transmission (CRIPT), a National Institute of Allergy and Infectious Diseases (NIAID) supported Center of Excellence for Influenza Research and Response (CEIRS, contract # 75N93021C00014), by DARPA grant HR0011-19-2-0020, by supplements to NIAID grants U19AI142733, U19AI135972, and DoD grant W81XWH-20-1-0270, and by the generous support of the JPB Foundation, the Open Philanthropy Project (research grant 2020-215611 (5384)), and anonymous donors to A García-Sastre. S Yildiz received funding from a Swiss National Foundation Early Postdoc Mobility fellowship (P2GEP3_184202).Peer reviewe

Idescat. SORT. On the frequentist and Bayesian approaches to hypothesis testing. Volume 30 (1)

Abstract Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper we briefly revise the basic aspects of hypothesis testing for both the frequentist and Bayesian procedures and discuss the variable selection problem in normal linear regression for which the discrepancies are more apparent. Illustrations on simulated and real data are given. MSC: 62A01; 62F03; 62F1