10 research outputs found
Bayesian Quantile and Expectile Optimisation
Bayesian optimisation is widely used to optimise stochastic black box
functions. While most strategies are focused on optimising conditional
expectations, a large variety of applications require risk-averse decisions and
alternative criteria accounting for the distribution tails need to be
considered. In this paper, we propose new variational models for Bayesian
quantile and expectile regression that are well-suited for heteroscedastic
settings. Our models consist of two latent Gaussian processes accounting
respectively for the conditional quantile (or expectile) and variance that are
chained through asymmetric likelihood functions. Furthermore, we propose two
Bayesian optimisation strategies, either derived from a GP-UCB or Thompson
sampling, that are tailored to such models and that can accommodate large
batches of points. As illustrated in the experimental section, the proposed
approach clearly outperforms the state of the art
Importance Sampling and its Optimality for Stochastic Simulation Models
We consider the problem of estimating an expected outcome from a stochastic
simulation model. Our goal is to develop a theoretical framework on importance
sampling for such estimation. By investigating the variance of an importance
sampling estimator, we propose a two-stage procedure that involves a regression
stage and a sampling stage to construct the final estimator. We introduce a
parametric and a nonparametric regression estimator in the first stage and
study how the allocation between the two stages affects the performance of the
final estimator. We analyze the variance reduction rates and derive oracle
properties of both methods. We evaluate the empirical performances of the
methods using two numerical examples and a case study on wind turbine
reliability evaluation.Comment: 37 pages, 6 figures, 2 tables. Accepted to the Electronic Journal of
Statistic
Future proofing a building design using history matching inspired levelâset techniques
This is the final version. Available on open access from Wiley via the DOI in this record.âŻHow can one design a building that will be sufficiently protected against overheating and sufficiently energy efficient, whilst considering the expected increases in temperature due to climate change? We successfully manage to address this questionâgreatly reducing a large set of initial candidate building designs down to a small set of acceptable buildings. We do this using a complex computer model, statistical models of said computer model (emulators), and a modification to the history matching calibration technique. This modification tackles the problem of levelâset estimation (rather than calibration), where the goal is to find input settings which lead to the simulated output being below some threshold. The entire procedure allows us to present a practitioner with a set of acceptable building designs, with the final design chosen based on other requirements (subjective or otherwise).Engineering and Physical Sciences Research Council (EPSRC
Generalized Bayesian MARS: Tools for Emulating Stochastic Computer Models
The multivariate adaptive regression spline (MARS) approach of Friedman
(1991) and its Bayesian counterpart (Francom et al. 2018) are effective
approaches for the emulation of computer models. The traditional assumption of
Gaussian errors limits the usefulness of MARS, and many popular alternatives,
when dealing with stochastic computer models. We propose a generalized Bayesian
MARS (GBMARS) framework which admits the broad class of generalized hyperbolic
distributions as the induced likelihood function. This allows us to develop
tools for the emulation of stochastic simulators which are parsimonious,
scalable, interpretable and require minimal tuning, while providing powerful
predictive and uncertainty quantification capabilities. GBMARS is capable of
robust regression with t distributions, quantile regression with asymmetric
Laplace distributions and a general form of "Normal-Wald" regression in which
the shape of the error distribution and the structure of the mean function are
learned simultaneously. We demonstrate the effectiveness of GBMARS on various
stochastic computer models and we show that it compares favorably to several
popular alternatives
Replication or exploration? Sequential design for stochastic simulation experiments
We investigate the merits of replication, and provide methods for optimal
design (including replicates), with the goal of obtaining globally accurate
emulation of noisy computer simulation experiments. We first show that
replication can be beneficial from both design and computational perspectives,
in the context of Gaussian process surrogate modeling. We then develop a
lookahead based sequential design scheme that can determine if a new run should
be at an existing input location (i.e., replicate) or at a new one (explore).
When paired with a newly developed heteroskedastic Gaussian process model, our
dynamic design scheme facilitates learning of signal and noise relationships
which can vary throughout the input space. We show that it does so efficiently,
on both computational and statistical grounds. In addition to illustrative
synthetic examples, we demonstrate performance on two challenging real-data
simulation experiments, from inventory management and epidemiology.Comment: 34 pages, 9 figure