With Bayesian Estimation One Can Get All That Bayes Factors Offer, and More

Null Hypothesis Bayesian Testing (NHBT) has been proposed as an alternative to Null Hypothesis Significance Testing (NHST). Whereas NHST has a close link to parameter estimation via confidence intervals, such a link of NHBT with Bayesian estimation via a posterior distribution is less straightforward, but does exist, and has recently been reiterated by Rouder, Haaf, and Vandekerckhove (2018). It hinges on a combination of a point mass probability and a probability density function as prior (denoted as the spike-and-slab prior). In the present paper it is first carefully explained how the spike-and-slab prior is defined, and how results can be derived for which proofs were not given in Rouder et al. (2018). Next, it is shown that this spike-and-slab prior can be approximated by a pure probability density function with a rectangular peak around the center towering highly above the remainder of the density function. Finally, we will indicate how this ‘hill-and-chimney’ prior may in turn be approximated by fully continuous priors. In this way it is shown that NHBT results can be approximated well by results from estimation using a strongly peaked prior, and it is noted that the estimation itself offers more than merely the posterior odds ratio on which NHBT is based. Thus, it complies with the strong APA requirement of not just mentioning testing results but also offering effect size information. It also offers a transparent perspective on the NHBT approach employing a prior with a strong peak around the chosen point null hypothesis value.

Salud oral y déficit nutricional en adultos mayores no institucionalizados en Londrina, Paraná, Brasil

OBJETIVO: Examinar la asociación entre el déficit nutricional y problemas de salud oral en adultos mayores no institucionalizados de una comunidad en Brasil. MÉTODOS: En este estudio transversal fueron obtenidos datos de 267 adultos mayores (160 mujeres y 107 hombres) con edad entre los 60 y 74 años provenientes del censo del área de cobertura de un Equipo del Programa Salud de la Familia de Londrina, Brasil. El déficit nutricional fue identificado con la Mini Evaluación Nutricional (< 24 puntos). La valoración odontológica incluyó exploración bucodental, medición del flujo salivar estimulado y aplicación del Geriatric Oral Health Assessment Index para la percepción oral. Los análisis multivariantes fueron ajustados por variables sociodemográficas, depresión y consumo de medicamentos. RESULTADOS: El déficit nutricional fue detectado en 58 ancianos (21,7%). Entre las variables odontológicas, la ausencia de oclusión posterior (Odds Ratio, OR: 2,18; Intervalo de Confianza, IC95%: 1,06 - 4,45), el flujo salivar estimulado < 0,7 ml/minuto (OR: 2,18, IC95%: 1,06 - 4,50), la enfermedad periodontal avanzada (OR: 6,54; IC95%: 2,03 -21,00) y la percepción negativa de la salud oral (OR: 3,41; IC95%: 1,59 - 7,33) se asociaron al déficit nutricional de modo independiente del sexo, edad, clase económica, escolaridad, consumo de tabaco, depresión y uso de medicamentos. CONCLUSIONES: El deterioro de la salud oral se asoció al déficit nutricional, y por lo tanto se requiere mayor integración entre odontología y nutrición en la promoción de salud en adultos mayores, especialmente en la prevención de la pérdida dental y en la rehabilitación oclusal posterior, evitándose obstáculos para una dieta adecuada.

Priors for Macroeconomic Time Series and Their Application

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter that can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odd ratios by using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson–Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and they indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.

A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model

In this paper we extend some of Phillips's [4] results to nonlinear unobserved components models and develop a posterior odds ratio test of the unit root hypothesis based on flat and Jeffreys priors. In contrast to the analysis presented by Schotman and van Dijk [9], we utilize a nondegenerate structural representation of the components model that allows us to determine well-behaved Jeffreys priors, posterior densities under flat priors and Jeffreys priors, and posterior odds ratios for the unit root hypothesis without a proper prior for the level parameter. The analysis highlights the importance of the treatment of initial values for inference concerning stationarity and unit roots.