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Statistics (Student) Seminar
TITLE: Non-stationary and non-Gaussian surrogate models
SPEAKER: Rui Tuo (visiting Dr. Jeff Wu)
ABSTRACT:
Emulators are central in the modeling of computer experiments. As the development of the computational techniques, we are able to simulate complex physical systems more accurately. Existing methods, specifically the stationary Gaussian process models, may be inadequate to meet the demands of modern computer simulations when the computer code has tunable precision or the response surface is highly fluctuated. This talk consists of two parts.
In the first part, I consider deterministic computer experiments with real-valued tuning parameters which determine the accuracy of the numerical algorithm. A prominent example is finite element analysis with its mesh density as the tuning parameter. The aim is to integrate computer outputs with different tuning parameters. Novel non-stationary Gaussian process models are proposed to establish a framework consistent with the results in numerical analysis. Numerical studies show the advantages of the proposed method over existing methods. The methodology is illustrated with a problem in casting simulation.
In the second part, I discuss the conditional inference for ?-stable processes. We introduce a new class of ?-stable processes. The finite dimensional distributions of these stochastic processes can be represented using independent stable random variables. This representation allows for Bayesian inference for the proposed statistical model. We can obtain the posterior distributions for the untried points as well as the model parameters through an MCMC algorithm. The computation for the representation requires some geometrical information given by the design points. We propose an efficient algorithm to solve this computational geometry problem. Two examples are given to illustrate the proposed method and its potential advantages.
Contact: rtuo3@mail.gatech.edu
