ALGORITHM OF GLOBAL EXTREMUM SEARCH AREA DEFINITION FOR SEVERAL VARIABLES FUNCTION

Abstract: The article is devoted to the problem of global extremum search for several variables function. Amodified algorithm is developed for the search of global extremum function, based on evolutionary calculations and differing by the approach of an area development to create an initial population of agents. They developed the algorithm for the function extremum search area definition, which ultimately performs the decomposition of the research area into subsets. It is suggested to take into account the knowledge of an expert, an agent and the available group agents. Based on the available knowledge, the region is divided into three subsets with different priorities. At that, the possibility of the function extremum drift is taken into account and a separate procedure of a search area definition is implemented, taking into account the retrospective information on the drift of parameters.Keywords: multicriteria optimization, multiextremal function, global extremum, extremum drift, solutionsearch area, decision support system

Thompson sampling guided stochastic searching on the line for deceptive environments with applications to root-finding problems

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Inference for SDE models via Approximate Bayesian Computation

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus is on the case where the SDE describes latent dynamics in state-space models; however the methodology is not limited to the state-space framework. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a MATLAB package implementing our ABC-MCMC algorithm is provided.Comment: Version accepted for publication in Journal of Computational & Graphical Statistic