Our research group works on prediction and optimisation techniques. Prediction of future observations and optimisation in order to build automatic decision support tools in an uncertain environment. This has already led to interesting results, especially in the fields of medicine and public health, but also in industry and finance. Consequently, our purpose is twofold: to deepen the study of prediction models that can incorporate temporal and/or spatial relationships, as well as covariates, and to continue advancing in the development of methodologies that incorporate uncertainty in optimisation, which will allow us to build new tools to support decision-making in different areas of planning and management. In particular, we will investigate the analysis of scenarios with the presence of uncertainty for which there is information given by a series of historical data, for which we will use time series models, and those in which in addition to the temporal relationship there is a neighbourhood relationship between contemporaneous observations, for which we will use spatio-temporal models. Previous work have considered prediction models based on dynamic state-space models with innovations, and have advanced theoretically in the incorporation of multistationarity, covariates and autocorrelated errors, with the aim that they can be used in the automatic prediction of banks of time series. Recently, we have introduced fuzzy time series methods to obtain as a prediction a fuzzy number that can be incorporated into optimisation models using fuzzy logic to incorporate uncertainty. Our aim is to extend the field of application of these methodologies by means of simulation-optimisation models that make it possible to analyse the quality of the solutions and the optimisation of the objectives. We are also working on compositional time series, which allow us to contextualise mixed models for multivariate longitudinal compositional data in a microbiome setting.
Recently, we have been working on the combination of forecasts, using weighted averages of forecasts obtained with different methods, with the aim of designing a decision support system that allows the adjustment of weights and the optimal selection of prediction models to obtain more reliable forecasts. The study of the geographical and temporal variability of health phenomena is currently very popular in the world of epidemiology. Numerous risk smoothing models that simultaneously incorporate the spatial dependence of risks between nearby regions and the temporal dependence of risks for each of the regions have been proposed in recent years. Classical models have been designed for retrospective analysis of incidence time series and therefore do not address fundamental issues from the point of view of planning preventive and control actions such as predicting the onset of outbreaks, predicting epidemic peaks and ending epidemics. We want to analyse some problems related to the prediction of the spread of epidemics, focusing simultaneously on the spatial and temporal components of the problem. Along the same lines, simultaneous incorporation of temporal and spatial components in the models studied, we are working on various scenarios: Bayesian hierarchical model extension, recently proposed by members of our team, which allows estimating risks and detecting clusters simultaneously where it is considered that the spatial dependence between relative risks does not necessarily conform to neighbourhood criteria; spatio-temporal extension of Bayesian stochastic compartment models; proposal of a spatio-temporal model for the treatment of epidemiological data in the compositional scenario, and proposal of a spatio-temporal model for the analysis of associations between environmental exposures and health. All these prediction results will be used in the construction of decision support systems based on optimisation models under uncertainty for different domains. Among them, in addition to the areas mentioned above, we will work on financial management problems, in particular the problem of portfolio selection. The portfolio selection problem is about determining an optimal portfolio that satisfies the decision-maker's preferences, in terms of risk and return on investment. We have introduced the approximation of portfolio performance by credibility distributions and alternative measures of investment risk. We will address the portfolio selection problem by introducing a loss function that can be visualised by the investor as a measure of his preferences and develop evolutionary multi-objective optimisation strategies to determine efficient portfolios for different investor risk profiles.
Development of methodologies to incorporate uncertainty in optimisation in different areas of process planning and management.
- Investment portfolio selection models
Development of portfolio selection models, in which uncertainty about performance is described by possibility and credibility distributions. Multi-objective analysis of the selection problem, seeking approximations to the Pareto front using evolutionary algorithms.
- Bayesian Multivariate Time Series Analysis
Development of multivariate dynamic models and their analysis by Bayesian mehtodology, using MCMC simulation methods. Incorporation of spatial dependencies into the temporal structure of the models. Design and implementation in R of algorithms for their analysis, estimation and prediction.
- Compositional data modelling
Development of models with compositional data. In environments such as biology, economics or geology, it is common to work with data vectors whose components reflect the relative contribution of different parts in relation to a total, obtaining compositional samples. Work will be done on the progress of statistical modelling of compositional data, its application and its mathematical foundations.
- Disease mapping
Development of Bayesian hierarchical models for the study of the geographical variability of diseases and their temporal evolution with the aim of aiding decision-making and the development of surveillance programmes.
- IFTIMI -, ADINA ALEXANDRA
- PDI-Titular d'Universitat
- Coordinador/a Curs
- Coordinador/a Curs
- SANTONJA GOMEZ, FRANCISCO JOSE
- PDI-Titular d'Universitat
Contributors
- José Vicente Segura Heras - Miguel Hernández University of Elche.
- ExpandirIFTIMI -, ADINA ALEXANDRAPDI-Titular d'UniversitatCoordinador/a CursCoordinador/a Curs
Burjassot/Paterna Campus
C/ Dr. Moliner, 50
46100 Burjassot (Valencia)
