A generalized Gaussian process model for computer experiments with binary time series

Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which shares some common features with standard GP models. In addition, the proposed model incorporates a flexible mean function that can capture different types of time series structures. Asymptotic properties of the estimators are derived, and an optimal predictor as well as its predictive distribution are constructed. Their performance is examined via two simulation studies. The methodology is applied to study computer simulations for cell adhesion experiments. The fitted model reveals important biological information in repeated cell bindings, which is not directly observable in lab experiments.Comment: 49 pages, 4 figure

From statistical power to statistical assurance: It's time for a paradigm change in clinical trial design

A well-designed clinical trial requires an appropriate sample size with adequate statistical power to address trial objectives. The statistical power is traditionally defined as the probability of rejecting the null hypothesis with a pre-specified true clinical treatment effect. This power is a conditional probability conditioned on the true but actually unknown effect. In practice, however, this true effect is never a fixed value. Thus, we discuss a newly proposed alternative to this conventional statistical power: statistical assurance, defined as the unconditional probability of rejecting the null hypothesis. This kind of assurance can then be obtained as an expected power where the expectation is based on the prior probability distribution of the unknown treatment effect, which leads to the Bayesian paradigm. In this article, we outline the transition from conventional statistical power to the newly developed assurance and discuss the computations of assurance using Monte Carlo simulation-based approach

Prevalence of bovine viral diarrhoea virus in cattle farms in Hungary

A study was performed to survey the virological prevalence of bovine viral diarrhoea (BVD) virus (BVDV) in cattle herds in Hungary between 2008 and 2012. A total of 40,413 samples for BVDV detection and 24,547 samples for antibody testing were collected from 3,247 herds (570,524 animals), thus representing approximately 75% of the cattle population in Hungary. Retrospective Bayesian analysis demonstrated that (1) the herd-level true virus prevalence was 12.4%, (2) the mean individual (within-herd) true virus prevalence was 7.2% in the herds having at least one virus-positive animal and 0.89% for all investigated herds with a mean apparent prevalence of 1.15% for the same population. This is the first study about BVDV prevalence in Hungary

Adaptively Optimised Adaptive Importance Samplers

We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposals to improve the mean-squared error of the importance sampling estimators by parameterising the proposal and optimising the $\chi^2$-divergence between the target and the proposal. We show that a naive implementation of OAIS using stochastic gradient descent may lead to unstable estimators despite its convergence guarantees. To remedy this shortcoming, we instead propose to use adaptive optimisers (such as AdaGrad and Adam) to improve the stability of the OAIS. We provide convergence results for AdaOAIS in a similar manner to OAIS. We also provide empirical demonstration on a variety of examples and show that AdaOAIS lead to stable importance sampling estimators in practice.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Contributions to binary-output computer experiments and large-scale computer experiments

Computer experiments have played an increasingly important role in science and technology and received enormous attention from industries and research institutes. One prominent example is the redesign of a new rocket engine by the U.S. Air Force (Mak et al., 2018). This dissertation makes contributions in two important aspects of computer experiments: (i) binary-output computer experiments and (ii) large-scale computer experiments. For (i), the dissertation contains two chapters: a new emulation method in Chapter 1 and a novel calibration method in Chapter 2, respectively. For (ii), the dissertation contains two chapters, in which new computationally efficient search limiting techniques for local Gaussian process approximation are developed in Chapter 3, and a new model, which is called multi-resolution function ANOVA, is proposed in Chapter 4.Ph.D

A Study of Treatment-by-Site Interaction in Multisite Clinical Trials

Currently, there is little discussion about methods to explain treatment-by-site interaction in multisite clinical trials, so investigators are left to explain these differences post-hoc with no formal statistical tests in the literature. Using mediated moderation techniques, three significance tests used to detect mediation are extended to the multisite setting. Explicit power functions are derived and compared. In the two-site case, the mediated moderation framework is utilized to test two difference-in-coefficients and one product-of-coefficients type tests. The test in the latter group is based on the product of two independent standard normal variables, which is a modified Bessel function of the second kind. Because the alternative distribution does not have a closed form expression, power is approximated using Gauss-Hermite quadrature. This test suffers from an inflated type I error, so two modifications are proposed: a combination of intersection-union and union-intersection tests; and one based on a variance stabilizing transformation. In addition, a modification of one of the difference-in-coefficients tests is proposed. The tests are also extended to deal with multiple sites in the ANOVA and logistic regres- sion models, and the groundwork has been laid to account for multiple mediators as well. The contribution of this is a group of formal significance tests for explaining treatment- by-site interaction in the multisite clinical trial setting. This will serve to inform the design of future clinical trials by accounting for this site-level variability. The proposed methodol- ogy is illustrated in the analysis of the Treatment of SSRI-Resistant Depression in Adolescents study conducted across six sites coordinated at the University of Pittsburgh