Comparing and calibrating discrepancy measures for Bayesian model selection

Different approaches have been considered in the literatur e for the problem of Bayesian model selection. Recently, a new method was introduced and analys ed in De la Horra (2008) by minimizing the posterior expected discrepancy between the set of data and the Bayesian model, where the chi-square discrepancy was used. In this article, several discrepancy measures are considered and compared by simulation, and it is obtained th at the chi-square discrepancy is reasonable to use. Then, an easy method for calibrating disc repancies is proposed, and the behaviour of this approach is studied on simulated data. Fin ally, a set of real data is analysedPeer Reviewe

Comparing and calibrating discrepancy measures for Bayesian model selection

Abstract Different approaches have been considered in the literature for the problem of Bayesian model selection. Recently, a new method was introduced and analysed in De la Horra MSC: 62F1

Comparing and calibrating discrepancy measures for Bayesian model selection

Different approaches have been considered in the literature for the problem of Bayesian model selection. Recently, a new method was introduced and analysed in De la Horra (2008) by minimizing the posterior expected discrepancy between the set of data and the Bayesian model, where the chi-square discrepancy was used. In this article, several discrepancy measures are considered and compared by simulation, and it is obtained that the chi-square discrepancy is reasonable to use. Then, an easy method for calibrating discrepancies is proposed, and the behaviour of this approach is studied on simulated data. Finally, a set of real data is analysed

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality

Comparing Bayesian and frequentist estimators in the exchangeable case

Consider a sample of observations (X1,...Xn) with density fQ(X1,...,Xn)= [integral operator][Theta]Pi=1nf[Theta](Xi)dQ([Theta]), where f[theta](x) is a known model, [theta] [set membership, variant] [Theta], a finite-dimensional space, and Q is an unknown distribution ranging over a suitable set of probability distributions over [Theta]. This is the most interesting case of exchangeable observations. The problem of estimating h(Q), a real-valued function of Q of interest, is considered, both from a Bayesian and a frequentist perspective. In particular, it is proved that the uniformly minimum variance unbiased estimator (UMVUE) for h([theta]) is the UMVUE for h(Q) = EQ[h([theta])]. Finally, following the idea in the paper by Samaniego and Reneau (1994), Bayesian and frequentist estimators of h(Q) are compared.Exchangeable observations Bayesian estimators Uniformly minimum variance unbiased estimators Mean squared error

Invariance and R-e criterion

The R-e criterion is considered as a generalization of the minimax criterion, in a decision problem with T = {?1, ..., ?n}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule d, there exists an invariant rule d' which is either preferred or equivalent to d. The question raised in this paper is: given that the minimax ordering is a particular case of R-e ordering, is it possible to extend this property to the R-e criterion? And, if the answer is negative, is it possible to give a sufficient and necessary condition for R-e orderings with this property? A complete answer is given to this problem; it is proved that the property does not hold true for any R-e ordering that does not coincide with the minimax orderin

Existencia de reglas de decisión con mínimo riesgo R-e

R-e criterion is considered in a decision problem (T, D*, R). Some considerations are made for the case in which the parameter space T is finite. Finally the existence of a decision rule with the minimum R-e risk is examined, when the risk set is closed from below and bounde

Convergencia del vector de probabilidad a posteriori bajo una distribución predictiva

La convergencia casi segura de una sucesión de variables aleatorias, con respecto a PX,Q (distribución predictiva), se estudia en relación con la convergencia casi segura, con respecto a PX,? (para todo ? Î T), donde {PX,?}? Î T es una familia de modelos de probabilidad sobre el espacio muestral ?. Como consecuencia, se estudia la convergencia casi segura del vector de probabilidad a posteriori con respecto a PX,

Sobre la caracterización del criterio R-e en ambiente de incertidumbre

Se considera el criterio R-e en ambiente de incertidumbre y se consigue una caracterización de dicho criterio en las regiones {(a1, ..., an) Î Rn / ai(1) = ... = ai(n)}, (siendo n el número de elementos del espacio paramétrico T) utilizando los axiomas de Milnor que verifica el R-e y un axioma adicional de invariancia por transformaciones monótonas. Se comprueba además que el criterio queda caracterizado, por esos axiomas, en todo Rn, para n = 2 y n = 3, quedando abierto el problema en el caso genera