Speeding Up MCMC by Delayed Acceptance and Data Subsampling

The complexity of the Metropolis-Hastings (MH) algorithm arises from the requirement of a likelihood evaluation for the full data set in each iteration. Payne and Mallick (2015) propose to speed up the algorithm by a delayed acceptance approach where the acceptance decision proceeds in two stages. In the first stage, an estimate of the likelihood based on a random subsample determines if it is likely that the draw will be accepted and, if so, the second stage uses the full data likelihood to decide upon final acceptance. Evaluating the full data likelihood is thus avoided for draws that are unlikely to be accepted. We propose a more precise likelihood estimator which incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data. We prove that the resulting delayed acceptance MH is more efficient compared to that of Payne and Mallick (2015). The caveat of this approach is that the full data set needs to be evaluated in the second stage. We therefore propose to substitute this evaluation by an estimate and construct a state-dependent approximation thereof to use in the first stage. This results in an algorithm that (i) can use a smaller subsample m by leveraging on recent advances in Pseudo-Marginal MH (PMMH) and (ii) is provably within $O(m^{-2})$ of the true posterior.Comment: Accepted for publication in Journal of Computational and Graphical Statistic

Speeding up MCMC by Efficient Data Subsampling

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a general and highly efficient unbiased estimator of the log-likelihood based on control variates obtained from clustering the data. The cost of computing the log-likelihood estimator is much smaller than that of the full log-likelihood used by standard MCMC. The likelihood estimate is bias-corrected and used in two correlated pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. A practical estimator of the error is proposed and we show that the error is negligible even for a very small m in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature

Aplicación del estudio del trabajo para mejorar la productividad en la fabricación de ruedas dentadas, en la empresa Servitec Go&Cia S.R.L., Comas, 2019

El actual trabajo de investigación que lleva por título “Aplicación del Estudio del Trabajo para mejorar la productividad en la fabricación de ruedas dentadas, en la empresa SERVITEC GO&CIA S.R.L., Comas, 2019.”, tiene como principal objetivo general, resolver de qué manera la aplicación del Estudio de Trabajo mejora la productividad en la fabricación de ruedas dentadas en la empresa SERVITEC GO&CIA S.R.L., Comas, 2019. El trabajo de investigación es de tipo aplicada y tiene un diseño cuasi-experimental. La población de este proyecto está conformada por el mes de abril del 2019; sin embargo, se obtuvo datos del área de producción desde el mes de noviembre 2018, los cuales fueron analizados antes y después de la aplicación del Estudio del Trabajo. La muestra analizada es igual a la población, se empleó como técnica, la observación y los instrumentos utilizados fueron: hojas de verificación de toma de tiempos, formato de Cálculo de Número de Muestras, medición de Tiempo Estándar, ficha de registro de Diagrama de Actividades de Proceso, ficha de control de producción, la ficha de estimación de eficiencia, eficacia y productividad y el cronómetro. Los instrumentos de recolección de datos fueron validados por tres jueces expertos en el tema

Parental Burnout Around the Globe: a 42-Country Study

High levels of stress in the parenting domain can lead to parental burnout, a condition that has severe consequences for both parents and children. It is not yet clear, however, whether parental burnout varies by culture, and if so, why it might do so. In this study, we examined the prevalence of parental burnout in 42 countries (17,409 parents; 71% mothers; M_{age} = 39.20) and showed that the prevalence of parental burnout varies dramatically across countries. Analyses of cultural values revealed that individualistic cultures, in particular, displayed a noticeably higher prevalence and mean level of parental burnout. Indeed, individualism plays a larger role in parental burnout than either economic inequalities across countries, or any other individual and family characteristic examined so far, including the number and age of children and the number of hours spent with them. These results suggest that cultural values in Western countries may put parents under heightened levels of stress

A Survey of Bayesian Statistical Approaches for Big Data

The modern era is characterised as an era of information or Big Data. This has motivated a huge literature on new methods for extracting information and insights from these data. A natural question is how these approaches differ from those that were available prior to the advent of Big Data. We present a review of published studies that present Bayesian statistical approaches specifically for Big Data and discuss the reported and perceived benefits of these approaches. We conclude by addressing the question of whether focusing only on improving computational algorithms and infrastructure will be enough to face the challenges of Big Data