- Programmes

**Brief description:**

The group of Bayesian Methods is devoted to the study of some aspects within the Bayesian statistical inference, more specifically, to the fundamentals of Bayesian inference, Bayesian networks and specific multivariate distributions, such as exponential potential distribution.

Bayesian methods have proved effective to fit a probability model to a set of data and summarize the result by a probability distribution over the model parameters and unobserved quantities, such as new observations to be predicted. The main practical advantages of the Bayesian approach appear in hierarchical models, which allow to study problems with complicated structures. An important aspect is the use of initial probability distributions that allow the data speak: they are objective probability distributions.

**Aims of the program:**

1. The null hypothesis timely raises, from the Bayesian point of view, a specific problem. The determination of the initial distribution of this hypothesis requires using a distribution of mixed type, i.e. with discrete and continuous part. It is in this type of problem where the discrepancy appears between the p-value and the final probability. One line of research is to delve into the explanation of this phenomenon. Specifically, this group has introduced a way to construct the mixed distribution that explains this phenomenon better.

2. A particularly helpful tool in decision making processes is Bayesian Networks that can be roughly described as a set of techniques that help in ascertaining causality relations among large set of experimental data. Particular fields where such tools are currently wanted are designing and processing of microarray fields and selecting optimal therapy protocols among all drug treatments available.

3. In the development of robust methods, from the Bayesian viewpoint, elliptical distributions have been used, and especially the extension potential multivariate exponential distribution, which has been introduced by this group. We have studied its expression in terms of mixtures of normal distributions and its application focuses on dynamic linear models as well as methods of classification and discrimination.

**Website: ** http://www.ucm.es/info/bayesianos

** ** http://www.mat.ucm.es/imi/Metodosbayesianos14/

**Researchers:** **Miguel Ángel Gómez Villegas (Full Professor, Fac. ****Math. UCM)**

Beatriz González Pérez (Associate Professor, Fac. Math. UCM)

Paloma Main Yaque (Associate Professor, Fac. Math. UCM)

Juan Miguel Marin Diazaraque (UC3M)

Hilario Navarro Veguillas (UNED)

Isabel Salazar Mendoza (Fac. Math. UCM)

Luis Sanz San Miguel (Fac. Math. UCM)

Rosario Susi García (Associate Professor, Fac. Statistics UCM)

** External collaborators: **

Christian P. Robert (Université Paris Dauphine)

José M. Bernardo (Universidad de Valencia)

Manuel Mendoza (Instituto Tecnológico Autónomo de México)

Luis R. Pericchi (Universidad Rio Piedras de Puerto Rico)

**Future events: **Organization of the Workshop Bayesian Methods 2014 (November) in Madrid.

- RedIUMIMI is a member of RedIUM, Red de Institutos Universitarios de Matemáticas. See List of members. See official website.
- Ph.D. programsIMI researchers are currently involved in the following Ph.D. programs in Mathematics: