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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de la Cruz, R., Salinas, H. S., & Meza, C. (2022). Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution. Symmetry, 14(4), 837.
Abstract: Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stress-strength reliability in the case of two independent unit-half-normal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets.
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Marquez, M., Meza, C., Lee, D. J., & De la Cruz, R. (2023). Classification of longitudinal profiles using semi-parametric nonlinear mixed models with P-Splines and the SAEM algorithm. Stat. Med., Early Access.
Abstract: In this work, we propose an extension of a semiparametric nonlinear mixed-effects model for longitudinal data that incorporates more flexibility with penalized splines (P-splines) as smooth terms. The novelty of the proposed approach consists of the formulation of the model within the stochastic approximation version of the EM algorithm for maximum likelihood, the so-called SAEM algorithm. The proposed approach takes advantage of the formulation of a P-spline as a mixed-effects model and the use of the computational advantages of the existing software for the SAEM algorithm for the estimation of the random effects and the variance components. Additionally, we developed a supervised classification method for these non-linear mixed models using an adaptive importance sampling scheme. To illustrate our proposal, we consider two studies on pregnant women where two biomarkers are used as indicators of changes during pregnancy. In both studies, information about the women's pregnancy outcomes is known. Our proposal provides a unified framework for the classification of longitudinal profiles that may have important implications for the early detection and monitoring of pregnancy-related changes and contribute to improved maternal and fetal health outcomes. We show that the proposed models improve the analysis of this type of data compared to previous studies. These improvements are reflected both in the fit of the models and in the classification of the groups.
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Vicuna, L., Barrientos, E., Norambuena, T., Alvares, D., Gana, J. C., Leiva-Yamaguchi, V., et al. (2023). New insights from GWAS on BMI-related growth traits in a longitudinal cohort of admixed children with Native American and European ancestry. iScience, 26(2), 106091.
Abstract: Body-mass index (BMI) is a hallmark of adiposity. In contrast with adulthood, the genetic architecture of BMI during childhood is poorly understood. The few genome-wide association studies (GWAS) on children have been performed almost exclusively in Europeans and at single ages. We performed cross-sectional and longitudinal GWAS for BMI-related traits on 904 admixed children with mostly Mapuche Native American and European ancestries. We found regulatory variants of the immune gene HLA-DQB3 strongly associated with BMI at 1.5 – 2.5 years old. A variant in the sex-determining gene DMRT1 was associated with the age at adiposity rebound (Age-AR) in girls (P = 9.8 x 10(-9)). BMI was significantly higher in Mapuche than in Europeans between 5.5 and 16.5 years old. Finally, Ag
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