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Bayesian modeling and estimation for complex multiparameter problems with real applications
(2021) Koki, Constandina; Κοκή, Κωνσταντίνα; Athens University of Economics and Business, Department of Statistics; Meligkotsidou, Loukia; Karlis, Dimitrios; Dellaportas, Petros; Kypraios, Theodore; Fouskakis, Dimitris; Kalogeropoulos, Kostas; Vrontos, Ioannis
In the big data era, the study of complex multiparameter problems is more than necessary. The development of Machine Learning techniques enhanced the inferentialability of statistical models. In this direction, by leveraging Machine Learning techniques, we propose a new predictive Hidden Markov model with exogenous variables, within a Bayesian framework, for joint inference and variable selection. Wepropose a computational Markov Chain Monte Carlo algorithm that offers improved forecasting and variable selection performance, compared to existing benchmarkmodels. Our methodology is applied in various simulated and real datasets, such as realized volatility data and cryptocurrency return series. Furthermore, we exploit the Bayesian methodology in implementing the X-ray luminosity function of the ActiveGalactic Nuclei under the assumption of Poisson errors in the determination of X-ray fluxes and estimation uncertainties.