Sequential Batch Design for Gaussian Processes Employing Marginalization †

Sequential Batch Design for Gaussian Processes Employing Marginalization †

Within the Bayesian framework, we utilize Gaussian processes for parametric studies of long running computer codes. Since the simulations are expensive, it is necessary to exploit the computational budget in the best possible manner. Employing the sum over variances —being indicators for the quality of the fit—as the utility function, we establish an optimized and automated sequential parameter...

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Warped Gaussian processes and derivative-based sequential design for functions with heterogeneous variations

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Bayesian Gaussian Processes for Sequential Prediction, Optimisation and Quadrature

Closure Theorem for Sequential-Design Processes

This chapter focuses on stochastic control and decision processes that occur in a variety of theoretical and applied contexts, such as statistical decision problems, stochastic dynamic programming problems, gambling processes, optimal stopping problems, stochastic adaptive control processes, and so on. It has long been recognized that these are all mathematically closely related. That being the...