Recent advances on Bayesian inference for P(X min Y )

We address the statistical problem of evaluating R = P(X < Y ), where X and Y are two independent random variables. Bayesian parametric inference about R, based on the marginal posterior density of R, has been widely discussed under various distributional assumptions on X and Y . This classical approach requires both elicitation of a prior on the complete parameter and numerical integration in order to derive the marginal distribution of R. In this paper, we discuss and apply recent advances in Bayesian inference based on higher-order asymptotics and on pseudo-likelihoods, and related matching priors, which allow to perform accurate inference on the parameter of interest only. The proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals. The accuracy of the proposed methodology is illustrated both by numerical studies and by real-life data concerning clinical studie

On interval and point estimators based on a penalization of the modified profile likelihood

Various modifications of the profile likelihood have been proposed in the literature. Despite modified profile likelihood methods have better properties than those based on the profile likelihood, the signed likelihood ratio statistic based on the modified profile likelihood has a standard normal distribution only to first order, and it can be inaccurate in particular in models with many nuisance parameters. In this paper we propose an adjustment of the profile likelihood from a new perspective. The idea is to resort to suitable default priors on the parameter of interest only to be used as non-negative weight functions in order to modify the modified profile likelihood. In particular, we focus on matching priors, i.e. priors on the parameter of interest only for which there is an agreement between frequentist and Bayesian inference, derived from modified profile likelihoods. The proposed modified profile likelihood has desiderable inferential properties: the corresponding signed likelihood ratio statistic is standard normal to second order and the correponding maximizer is a refinement of the maximum likelihood estimator, which improves its small sample properties. Examples illustrate the proposed modified profile likelihood and outline its improvement over its counterparts

Performance evaluation of the inverse dynamics method for optimal spacecraft reorientation

The article of record may be found at http://dx.doi.org/10.1016/j.actaastro.2014.11.041This paper investigates the application of the inverse dynamics in the virtual domain method to Euler angles, quaternions, and modified Rodrigues parameters for rapid optimal attitude trajectory generation for spacecraft reorientation maneuvers. The impact of the virtual domain and attitude representation is numerically investigated for both minimum time and minimum energy problems. Owing to the nature of the inverse dynamics method, it yields sub-optimal solutions for minimum time problems. Further- more, the virtual domain improves the optimality of the solution, but at the cost of more computational time. The attitude representation also affects solution quality and compu- tational speed. For minimum energy problems, the optimal solution can be obtained without the virtual domain with any considered attitude representation

Objective Bayesian higher-order asymptotics in models with nuisance parameters

We discuss higher-order approximations to the marginal posterior distribution for a scalar parameter of interest in the presence of nuisance parameters. These higher-order approximations are obtained using a suitable matching prior. The proposed procedure has several advantages since it does not require the elicitation on the nuisance parameter, neither numerical integration or MCMC simulation, and it enables us to perform accurate Bayesian inference even for very small sample sizes. Numerical illustrations are given for models of practical interest, such as linear non-normal models and logistic regression. We also illustrate how the proposed accurate approximation can routinely be applied in practice using results from likelihood asymptotics and the R package bundle ho

On the use of pseudo-likelihoods in Bayesian variable selection.

In the presence of nuisance parameters, we discuss a one-parameter Bayesian analysis based on a pseudo-likelihood assuming a default prior distribution for the parameter of interest only. Although this way to proceed cannot always be considered as orthodox in the Bayesian perspective, it is of interest to evaluate whether the use of suitable pseudo-likelihoods may be proposed for Bayesian inference. Attention is focused in the context of regression models, in particular on inference about a scalar regression coefficient in various multiple regression models, i.e. scale and regression models with non-normal errors, non-linear normal heteroscedastic regression models, and log-linear models for count data with overdispersion. Some interesting conclusions emerge

A note on approximate Bayesian credible sets based on modified loglikelihood ratios

Asymptotic arguments are widely used in Bayesian inference, and in recent years there has been considerable developments of the so-called higher-order asymptotics. This theory provides very accurate approximations to posterior distributions, and to related quantities, in a variety of parametric statistical problems, even for small sample sizes. The aim of this contribution is to discuss recent advances in approximate Bayesian computations based on the asymptotic theory of modified loglikelihood ratios, both from theoretical and practical point of views. Results on third-order approximations for univariate posterior distributions, also in the presence of nuisance parameters, are reviewed and a new formula for a vector parameter of interest is presented. All these approximations may routinely be applied in practice for Bayesian inference, since they require little more than standard likelihood quantities for their implementation, and hence they may be available at little additional computational cost over simple first-order approximations. Moreover, these approximations give rise to a simple simulation scheme, alternative to MCMC, for Bayesian computation of marginal posterior distributions for a scalar parameter of interest. In addition, they can be used for testing precise null hypothesis and to define accurate Bayesian credible sets. Some illustrative examples are discussed, with particular attention to the use of matching priors

Default prior distributions from quasi- and quasi-profile likelihoods.

In some problems of practical interest, a standard Bayesian analysis can be difficult to perform. This is true, for example, when the class of sampling parametric models is unknown or if robustness with respect to data or to model misspecifications is required. These situations can be usefully handled by using a posterior distribution for the parameter of interest which is based on a pseudo-likelihood function derived from estimating equations, i.e. on a quasi-likelihood, and on a suitable prior distribution. The aim of this paper is to propose and discuss the construction of a default prior distribution for a scalar parameter of interest to be used together with a quasi-likelihood function. We show that the proposed default prior can be interpreted as a Jeffreys-type prior, since it is proportional to the square-root of the expected information derived from the quasi-likelihood. The frequentist coverage of the credible regions, based on the proposed procedure, is studied through Monte Carlo simulations in the context of robustness theory and of generalized linear models with overdispersion

Misgav Ladach versus Kerr cesarean section: Comparative study

Introducción: La técnica de cesárea conocida como Misgav Ladach es una técnica minimalista y está siendo usada cada vez más en diferentes partes del mundo. Objetivos: Determinar los beneficios de la técnica Misgav Ladach, comparados con los de la cesárea clásica de Kerr. Diseño: Estudio retrospectivo, comparativo. Lugar: Hospital II EsSalud, Huamanga, Ayacucho. Participantes: Gestantes a término con feto único vivo, con indicación de cesárea. Intervenciones: Cesárea. Principales medidas de resultados: Tiempo operatorio, tiempo de extracción fetal, sangrado operatorio, uso de analgésico en el postoperatorio. Resultados: Los tiempos operatorios promedio fueron 25 vs. 38 minutos, según el empleo de la técnica Misgav-Ladach y Kerr, respectivamente. Los tiempos de extracción fetal fueron 79 vs. 139 segundos, con diferencia significativa. La media de hemoglobina fue de 1,2 g/dL en el grupo de casos y 1,47 g/dL en el grupo control, mostrando diferencia significativa. El grupo Misgav-Ladach requirió menor analgesia postoperatoria. No se alcanzó diferencia significativa en la morbilidad febril y en la necesidad de antibiótico terapia poscirugía. Conclusiones: La cesárea Misgav- Ladach parece mostrar mejores beneficios con respecto a la cesárea clásica, lo cual debe ser confirmado mediante estudios prospectivos aleatorios.Introduction: There are reports from several countries on good outcomes with Misgav Ladach’s cesarean section technique use. Objetives: To determine results obtained with Misgav Ladach’s cesarean technique and to compare them with the traditional Kerr’s cesarean section. Design: Retrospective, comparative study. Setting: Hospital II, EsSalud, Huamanga, Ayacucho. Participants: Full term pregnant women with a single fetus and medical indication for cesarean section. Interventions: Cesarean section. Main outcome measures: Surgical time, time to fetal birth, blood loss, use of post operative analgesia. Results: Mean surgical time was 25 and 38 minutes with respectively Misgav Ladach’s and Kerr’s techniques. Time to fetal birth was 79 seconds in cases vs. 139 seconds in the control group with significant difference. Mean hemoglobin was 1,2 g/dL significantly less in cases than 1,47 in the control group. Furthermore, the cases group needed less analgesia than the control group. Fever and need of antibiotics following surgery did not show significant differences. Conclusions: Misgav Ladach’s cesarean section seems to be more beneficial than traditional cesarean section, to be confirmed in future studies

A new Bayesian discrepancy measure

A Bayesian Discrepancy Test (BDT) is proposed to evaluate the distance of a given hypothesis with respect to the available information (prior law and data). The proposed measure of evidence has properties of consistency and invariance. After having presented the similarities and differences between the BDT and other Bayesian tests, we proceed with the analysis of some multiparametric case studies, showing the properties of the BDT. Among them conceptual and interpretative simplicity, possibility of dealing with complex case studies.Comment: 20 pages 9 figure

Digitalize Work in Health Organization during pandemic Covid-19

Covid-19 has impacted many aspects of daily life. The behaviors of organizations had to adopt this evolution. The Covid-19 emergency has put Smart Working at the center of attention. Working remotely made it possible to cope with the limitations due to the current health emergency while guaranteeing business continuity. This new intelligent mode is increasingly leading to the spread of autonomous, subjective and decentralized forms of work. Technological progress offers rapid access to information and reduces space-time constraints. Modern technologies put at the service of a new way of working, as experienced during the pandemic, allow the worker to manage the organization of space and the execution time of his employment in complete autonomy. On this basis, the work in progress study seeks to provide useful information to improve practices in the field of smart work, to better investigate the phenomenon in the healthcare sector, a field that has not been explored and debated in the literature