arXiv subjects

Mengyang Gu

Publications and source records attributed to Mengyang Gu.

39 records · Page 3Linked to original sources

arXiv2018

Nonparametric estimation of utility functions

Inferring a decision maker's utility function typically involves an elicitation phase where the decision maker responds to a series of elicitation queries, followed by an estimation phase where the state-of-the-art is to either fit the response data to a parametric form (such as the exponential or power function) or perform linear interpolation. We introduce a Bayesian nonparametric method involving Gaussian stochastic processes for estimating a utility function. Advantages include the flexibility to fit a large class of functions, favorable theoretical properties, and a fully probabilistic view of the decision maker's preference properties including risk attitude. Using extensive simulation experiments as well as two real datasets from the literature, we demonstrate that the proposed approach yields estimates with lower mean squared errors. While our focus is primarily on single-attribute utility functions, one of the real datasets involves three attributes; the results indicate that nonparametric methods also seem promising for multi-attribute utility function estimation.

stat.AP↗

arXiv2018

Scaled Gaussian Stochastic Process for Computer Model Calibration and Prediction

We consider the problem of calibrating an imperfect computer model using experimental data. To compensate the misspecification of the computer model and make more accurate predictions, a discrepancy function is often included and modeled via a Gaussian stochastic process (GaSP). The calibrated computer model alone, however, sometimes fits the experimental data poorly, as the calibration parameters become unidentifiable. In this work, we propose the scaled Gaussian stochastic process (S-GaSP), a novel stochastic process that bridges the gap between two predominant methods, namely the $L_2$ calibration and the GaSP calibration. It is shown that our approach performs well in both calibration and prediction. A computationally feasible approach is introduced for this new model under the Bayesian paradigm. Compared with the GaSP calibration, the S-GaSP calibration enables the calibrated computer model itself to predict the reality well, based on the posterior distribution of the calibration parameters. Numerical comparisons of the simulated and real data are provided to illustrate the connections and differences between the proposed S-GaSP and other alternative approaches.

stat.ME↗

arXiv2017

Robust Gaussian Stochastic Process Emulation

We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through various generalized maximum likelihood methods, mostly involving finding posterior modes; this is because full Bayesian analysis in computer model emulation is typically prohibitively expensive. The posterior modes that are studied arise from objective priors, such as the reference prior. These priors have been studied in the literature for the situation of an isotropic covariance function or under the assumption of separability in the design of inputs for model runs used in the GaSP construction. In this paper, we consider more general designs (e.g., a Latin Hypercube Design) with a class of commonly used anisotropic correlation functions, which can be written as a product of isotropic correlation functions, each having an unknown range parameter and a fixed roughness parameter. We discuss properties of the objective priors and marginal likelihoods for the parameters of the GaSP and establish the posterior propriety of the GaSP parameters, but our main focus is to demonstrate that certain parameterizations result in more robust estimation of the GaSP parameters than others, and that some parameterizations that are in common use should clearly be avoided. These results are applicable to many frequently used covariance functions, e.g., power exponential, Mat{é}rn, rational quadratic and spherical covariance. We also generalize the results to the GaSP model with a nugget parameter. Both theoretical and numerical evidence is presented concerning the performance of the studied procedures.

math.ST↗