Statistical Modelling Work

As an accomplished statistician with extensive skills in applied research, I am very interested to broaden and implement my statistical modelling knowledge. I offer over fifteen years of experience analyzing data that arise from various disciplines such as medicine, finance, criminology and environmental sciences.

• proposing and implementing new methodologies to study data;
• introducing formulations to model and understand dependence between events;
• extending models to study more complex datasets;
• programming functions in various languages to apply both well-established methodologies and new models;
• publishing various articles in international journals with impact factor;
• publishing two books on statistical modelling.

Although in my published work most ideas are my own, I have always found working with colleagues and students very refreshing and profitable. I have interacted with statisticians, sociologists, mathematicians, environmentalists, actuaries, engineers and MD’s

Most of my research is on survival analysis. Specifically, I have focused on the analysis of competing risks using Larson and Dinse’s mixture model. I have extended the mixture model in such a way that it accounts for immunes, those who will never experience any event of interest. Another extension of Larson and Dinse’s model that I have proposed is a semi-parametric formulation where the underlying conditional survival distributions follow the Cox semi-parametric proportional hazards model, which leads to a very flexible fashion to study competing risks, similar to the univariate version of Cox model. As a matter of fact, this extension has been the main topic of one of my PhD student’s research, which focuses on the properties of the estimators that includes the existence, consistency, asymptotic normality and consistent variance estimation.

Another important part of my research is that of Copulas. For me, modelling dependence with Copulas has turned out to be a very elegant and convenient fashion to create multivariate models. I have employed copulas to study competing risks and shown that the resulting multivariate survival distributions indeed solve the problem of identificability. Another application is the study of bivariate loss data where the underlying marginal distributions are heavily tailed. Also, I have proposed an extension of Raftery’s mixture model to study non-Gaussian time series for both continuous and discrete responses. Here, the conditional distribution of the current observation, given the present and past history, is a mixture of conditional distributions, each of them corresponding to the current observation, given each one of the p-lagged observations. Such conditional distributions are constructed using bivariate copula models which allow for a rich range of dependence.

I am working on a model for the regression analysis of extreme value time series. My main goal is to extend the GARMA model for the exponential family in such a way that one of the parameters of the univariate extreme value distribution is linked to a linear component which includes present and past history of both explanatory variables and responses in such a way that it includes both AR(p) and MA(q) effects. If successful, this model will represent a more parsimonious formulation than that of a conditional distribution obtained from the multivariate extreme value distribution. The main application of this model is the prediction of hazardous levels of ozone in Guadalajara City so that preventive actions are taken in order to protect the vulnerable population.

I am currently looking for PhD students to work with me on the topic “The copula based mixture model for non-Gaussian time series”.

For the modelling of serially correlated data, it is possible to effectively construct mixtures of one-step ahead transition distributions using the conditional copula model where the marginal distribution belongs to the exponential dispersion family.

• the representation of the time series defining arbitrary state spaces, univariate or multivariate, continuous, discrete or mixed, which need not be Euclidean;
• the comparison with the usual case of Gaussian time series without obvious nonstandard behaviours;
• the derivation of the stationarity and autocorrelation properties of the model;
• the proposal of an EM algorithm for estimation;
• the application of the model to several real and simulated datasets;
• the assessment on how well the model captures the features compared to the best competing autoregressive integrated moving average (ARIMA) model.

These are interesting projects not only for statisticians but also for econometricians.

If you wish to enrol in the PhD programme at UAM, please contact me by email at gabriel@escarela.com. CONACyT offers grants for international students.

I also have a basic interest in the teaching of statistics at the BSc, MSc and PhD levels. I have taught on Actuarial Mathematics, Introductory Statistics, Design of Experiments, Survival Analysis, Multivariate Methods, Extreme Value Theory, Generalized Linear Models and Statistical Modelling.

• teaching high quality statistics courses. The bar charts of my assessments have always been skewed with the bulk of the data taking the “very good” and “exemplary” categories;
• supervising five undergraduate dissertations and four MSc theses which led to the corresponding degrees;
• by the end of June 2010 my two PhD students must have graduated;
• publishing the work of four postgraduate students in international journals with impact factor, supervised and co-authored by myself;
• creating virtual classrooms for the e-learning of both statistics and statistical packages;
• writing spreadsheets and statistical packages manuals.

I am working at present on two books: one is on statistical modelling using the R language and the other is an introductory course on Mathematical Statistics.

As head of the Probability and Statistics group at the Maths Department of UAM, I managed to obtain a 25,000 USD research grant for the group from PROMEP. In addition, I could obtain from UAM an additional 1,500 USD research grant for each member of the group from UAM in two straight years.

My wife is Heike Ebelt, a virtual learning programmer and web page designer. We have a young daughter, Emily, and a beagle, Maggie. We live downtown in Mexico City. I love family holidays, dining out, music, and jogging with Maggie. A great hobby I have particularly enjoyed is doing agility with Maggie. Heike and I have handled Maggie in many trials very successfully, both in Mexico and the USA. Maggie got the prize “Agility dog of the year” awarded by the Mexican Kennel Club in the two years we had taken part.