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Celis, P., de la Cruz, R., Fuentes, C., & Gomez, H. W. (2021). Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications. Symmetry, 13(5), 908.
Abstract: We introduce a new class of distributions called the epsilon-positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon-positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log-normal, log-logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon-positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM-type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.
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de la Cruz, R., Meza, C., Narria, N., & Fuentes, C. (2022). A Bayesian Change Point Analysis of the USD/CLP Series in Chile from 2018 to 2020: Understanding the Impact of Social Protests and the COVID-19 Pandemic. Mathematics, 10(18), 3380.
Abstract: Exchange rates are determined by factors such as interest rates, political stability, confidence, the current account on balance of payments, government intervention, economic growth and relative inflation rates, among other variables. In October 2019, an increased climate of citizen discontent with current social policies resulted in a series of massive protests that ignited important political changes in Chile. This event along with the global COVID-19 pandemic were two major factors that affected the value of the US dollar and produced sudden changes in the typically stable USD/CLP (Chilean Peso) exchange rate. In this paper, we use a Bayesian approach to detect and locate change points in the currency exchange rate process in order to identify and relate these points with the important dates related to the events described above. The implemented method can successfully detect the onset of the social protests, the beginning of the COVID-19 pandemic in Chile and the economic reactivation in the US and Europe. In addition, we evaluate the performance of the proposed MCMC algorithms using a simulation study implemented in Python and R.
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Gaskins, J. T., Fuentes, C., & De la Cruz, R. (2022). A Bayesian nonparametric model for classification of longitudinal profiles. Biostatistics, Early Access.
Abstract: Across several medical fields, developing an approach for disease classification is an important challenge. The usual procedure is to fit a model for the longitudinal response in the healthy population, a different model for the longitudinal response in the diseased population, and then apply Bayes' theorem to obtain disease probabilities given the responses. Unfortunately, when substantial heterogeneity exists within each population, this type of Bayes classification may perform poorly. In this article, we develop a new approach by fitting a Bayesian nonparametric model for the joint outcome of disease status and longitudinal response, and then we perform classification through the clustering induced by the Dirichlet process. This approach is highly flexible and allows for multiple subpopulations of healthy, diseased, and possibly mixed membership. In addition, we introduce an Markov chain Monte Carlo sampling scheme that facilitates the assessment of the inference and prediction capabilities of our model. Finally, we demonstrate the method by predicting pregnancy outcomes using longitudinal profiles on the human chorionic gonadotropin beta subunit hormone levels in a sample of Chilean women being treated with assisted reproductive therapy.
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