Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck in some applications. There is also no consensus as to how to best assess the performance of such methods without knowing the true posterior. We show how a nonparametric conditional density estimation (CDE) framework, which we refer to as ABC-CDE, help address three nontrivial challenges in ABC: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss. We provide theoretical and empirical evidence that justify ABC-CDE procedures that directly estimate and assess the posterior based on an initial ABC sample, and we describe settings where standard ABC and regression-based approaches are inadequate.

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided.

Este estudo objetiva apresentar as etapas relacionadas à utilização de algoritmos de machine learning para análises preditivas em saúde. Para isso, foi realizada uma aplicação com base em dados de idosos residentes no Município de São Paulo, Brasil, participantes do estudo Saúde Bem-estar e Envelhecimento (SABE) (n = 2.808). A variável resposta foi representada pela ocorrência de óbito em até cinco anos após o ingresso do idoso no estudo (n = 423), e os preditores, por 37 variáveis relacionadas ao perfil demográfico, socioeconômico e de saúde do idoso. A aplicação foi organizada de acordo com as seguintes etapas: divisão dos dados em treinamento (70%) e teste (30%), pré-processamento dos preditores, aprendizado e avaliação de modelos. Na etapa de aprendizado, foram utilizados cinco algoritmos para o ajuste de modelos: regressão logística com e sem penalização, redes neurais, gradient boosted trees e random forest. Os hiperparâmetros dos algoritmos foram otimizados por validação cruzada 10-fold, para selecionar aqueles correspondentes aos melhores modelos. Para cada algoritmo, o melhor modelo foi avaliado em dados de teste por meio da área abaixo da curva (AUC) ROC e medidas relacionadas. Todos os modelos apresentaram AUC ROC superior a 0,70. Para os três modelos com maior AUC ROC (redes neurais e regressão logística com penalização de lasso e sem penalização, respectivamente), foram também avaliadas medidas de qualidade da probabilidade predita. Espera-se que, com o aumento da disponibilidade de dados e de capital humano capacitado, seja possível desenvolver modelos preditivos de machine learning com potencial para auxiliar profissionais de saúde na tomada de melhores decisões.

The evaluation of associations between genotypes and diseases in a case-control framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under Hardy-Weinberg equilibrium, a property that may not hold in practice.

This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results that are easy to communicate to practitioners of statistical methods. For instance, if hypothesis A implies hypothesis B, is it possible to create optimal testing procedures that reject A whenever they reject B? Unfortunately, several standard testing procedures fail in having such logical consistency. Although this has been deeply investigated under a frequentist perspective, the literature lacks analyses under a Bayesian paradigm. In this work, we contribute to the discussion by investigating three rational relationships under a Bayesian decision-theoretic standpoint: coherence, invertibility and union consonance. We characterize and illustrate through simple examples optimal Bayes tests that fulfill each of these requisites separately. We also explore how far one can go by putting these requirements together. We show that although fairly intuitive tests satisfy both coherence and invertibility, no Bayesian testing scheme meets the desiderata as a whole, strengthening the understanding that logical consistency cannot be combined with statistical optimality in general. Finally, we associate Bayesian hypothesis testing with Bayes point estimation procedures. We prove the performance of logically-consistent hypothesis testing by means of a Bayes point estimator to be optimal only under very restrictive conditions.