Research Environment: (1) Bayesian Methods Group (UCM, UC3M); (2) Interdisciplinary Mathematics Institute (IMI); (3) MatGen Group

The "Bayesian Methods" group with number 910395, started on 22/12/2004, an is a consolidated research group since 2005, when the Complutense University of Madrid (UCM) submited the researching calls at first time. It is currently made up of researchers from the Complutense University of Madrid and Carlos III University of Madrid. The main objective of Statistics is to analyze data, to discover unknown mechanisms and to make decisions in an uncertainty environment, using probability and assumes that a probability can always be defined over any unknown quantity. The "Bayesian Methods" group is devoted to the study of some aspects within Bayesian statistical inference, more specifically, to the fundamentals of Bayesian inference, Bayesian networks and specific multivariate distributions, such as exponential potential distribution.<br />The Interdisciplinary Mathematics Institute (IMI) is one of the Scientific Institutes of the Faculty of Mathematical Science at Complutense University of Madrid (UCM), with a national and international Scientific Committee, oriented to promote research in different scientific fields.<br />The "MatGen" is a group registered in the Mathematical Action against the Coronavirus of the CEMat (Spanish Committee of Mathematics). The CEMat was founded on January 13th, 2004, as a re-estructuration and extension of the Spanish IMU Committee (International Mathematical Union (IMU)).

1. Microarrays with biological data: the problem of testing simultaneously several hypotheses in biological experiments is considered and a Bayesian procedure of multiple hypotheses testing under dependence is developed. Assuming prior distributions for the model parameters, we are interested in estimating the posterior probability that each null hypothesis is true. The dependence is modeled by copula function. The posterior distribution obtained does not present an analytical expression. Hence, Bayesian inference may be performed using Markov Chain Monte Carlo (MCMC) methods, specifically, we use the Metropolis-Hastings-within-Gibbs algorithm.<br />2. Transport problems: Transport planning requires tools to model current and future situations for infrastructure networks, with macroscopic and microscopic scales. In this way, advances in algorithms and processing of large amounts of information (big data and machine learning) are facilitating new techniques, such as BN approaches, for acknowledged alternatives, with promising results. These findings open a new line of BN applications: energy, data information, autonomous vehicles (AV) and RPAs.<br />3. SOM maps: SOMs were developed by Kohonen (1980) as a tool to represent structures such as cortical layers in the brain as two or three dimensional maps. The final purpose is to carry out implementations with parallel processing in distributed data generated from different data sources, performing the integration and debugging of necessary data. Finally, apply and adapt frequentist statistical techniques to the Bayesian methodology under the big data paradigm simulating cases and practical examples developed in Spark as a big data framework.<br /><br />These points are being used to the analysis & evolution of the Covid-19, the last study case

-Personal statement.<br />-Detailed CV.<br />-Motivation letter.<br />-Academic / professional references. (University, Department, Directors and colleagues)<br />-Copies of your degree certificate and academic transcripts.<br />-Research proposal (if app