This area includes the modeling of data structures which arise when certain characteristics of a group of experimental units are repeatedly measured over time. The main focus is on applications to health problems, the study of correlation structures, and the analysis of categorical and univariate and multivariate continuous data.

Data mining is a broad area which involves methods from many different disciplines, such as ;machine learning;, statistics, artificial intelligence, computing, etc. for the analysis of large volumes of data. Algorithms are developed for tasks such as data grouping, classification, association analysis, etc.. One of our main interests is applying and developing methods able to extract information from large volumes of astronomical data.

This area includes the analysis of identifiability in models with random effects or latent variables, such as IRT models, latent class models, hidden Markov chain models, or structural equation models. Particular emphasis is given to the identification analysis of some semi-parametric extensions of these models (specifically, when the random effects are distributed according to some general distribution).

Models with variables that are measured with error, also known as measurement error models are models with at least one predictor that has been measured inexactly. The problem of measurement error appears frequently in various fields of expertise. Fields such as agriculture, medicine, engineering, psychology, education, and finance are some of the disciplines which have problems where the predictors are contaminated by measurement error. Univariate and multivariate statistical models are studied and developed in this area. The main topics of research are: inference (estimation and hypothesis tests) and diagnostics of influence using elliptical and skew-elliptical distributions. These models are used in the comparison of measurement methods or instruments as well as in other applications.

This area includes the study and development of Bayesian methods based on infinite-dimensional prior distributions, especially those required for spaces of probability distribution functions. Of special interest are discrete models and their connections with clustering algorithms and their applications to medicine, educational and sports data.

This area considers the modeling and analysis of data arising in educational measurement and the related problems of guessing, equating, missing values and value added. The theoretical framework comes from item response theory and multilevel models. The main applications include Chilean national tests.

In this area different techniques are studied in order to assess the sensitivity of statistics of interest (estimators and test statistics) to certain pertubations to the model assumptions and/or changes in the data. The main topics are applications of global Influence, local Influence and generalized leverage to linear and nonlinear elliptic models, with and without measurement errors, and some financial models, notably capital asset pricing model (CAPM) and models for building investment portfolios, also with elliptical distributions.

This area of research includes the development of algorithms and computer programs for the statistical modeling of complex problems. Focus is placed on implementing Bayesian models and Markov chain Monte Carlo methods.

In this area we attempt to understand the effect human genetic variation has on disease development or any other observed human characteristics such as height, eye color, etc. The main challenge in this area is the study and implementation of statistical models that help to extract relevant information from the genetic code.

In this area we analyze time to event data. In particular, we consider the development of regression models for censored data or doubly censored data in univariate and multivariate contexts. This research is generally applied to medical research.

This area considers the study of probabilistic properties of elliptical and skew-elliptical models, and the development of classical and Bayesian inferential procedures. The main applications consist of linear regression and mixed models, including error-in-variable models, and models with censored responses.

In this area we develop applied inference methods which are inspired from open dynamic systems. The theory is based on the developments of stochastic analysis and its current applications are in the fields of physics, biophysics and engineering.

The main focus in this area is the study of long-memory processes, space-state systems and econometric models for financial time series. The research also includes models for responses with exponential but not necessarily gaussian distributions, such as series of counts. Its main applications include financial and environmental data.