Assessing the Distribution Consistency of Sequential Data

Posterior Consistency of Bayesian Inverse Regression and Inverse Reference Distributions

We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian inverse regression problemsunder appropriate priors in a leave-one-out cross-validation setup. We relate this to posterior consistency of inverse reference distributions (Bhattacharya (2013)) for assessing model adequacy. We illustrate our theory and methods with various examples of Bayesian inverse regression, along with adequate simulation experiments.

Assessing transfer functions in control systems

When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural breaks and other abberations that require monitoring and quantification to aid decision making. The present paper develops such a methodology, which is based on an index of increase that naturally arises as the solution to an optimization problem. We show theoretically and illustrate numerically that the empirical counterpart of the index needs to be used wit…

A supermartingale approach to Gaussian process based sequential design of experiments

Gaussian process (GP) models have become a well-established frameworkfor the adaptive design of costly experiments, and notably of computerexperiments. GP-based sequential designs have been found practicallyefficient for various objectives, such as global optimization(estimating the global maximum or maximizer(s) of a function),reliability analysis (estimating a probability of failure) or theestimation of level sets and excursion sets. In this paper, we studythe consistency of an important class of sequential designs, known asstepwise uncertainty reduction (SUR) strategies. Our approach relies…

基于向量值高斯过程的序贯实验设计策略在极值集估计中的一致性

Consistency of some sequential experimental design strategies for excursion set estimation based on vector-valued Gaussian processes

本文扩展了逐步不确定性减少序贯设计的一致性结果至向量值高斯过程，澄清了连续高斯过程与高斯测度的联系，并应用于极值集估计的不确定性泛函。

Consistency of Binary Segmentation For Multiple Change-Points Estimation With Functional Data

For sequentially observed functional data exhibiting multiple change points in the mean function, we establish consistency results for the estimated number and locations of the change points based on the norm of the functional CUSUM process and standard binary segmentation. In addition to extending similar results in Venkatraman (1992) and Fryzlewicz (2014) for scalar data to the general Hilbert space setting, our main results are established without assuming the Gaussianity of the data, and under general linear process conditions on the model errors.

Non-Asymptotic Sequential Tests for Overlapping Hypotheses and application to near optimal arm identification in bandit models

In this paper, we study sequential testing problems with \emph{overlapping} hypotheses. We first focus on the simple problem of assessing if the mean $μ$ of a Gaussian distribution is smaller or larger than a fixed $ε>0$; if $μ\in(-ε,ε)$, both answers are considered to be correct. Then, we consider PAC-best arm identification in a bandit model: given $K$ probability distributions on $\mathbb{R}$ with means $μ_1,\dots,μ_K$, we derive the asymptotic complexity of identifying, with risk at most $δ$, an index $I\in\{1,\dots,K\}$ such that $μ_I\geq \max_iμ_i -ε$. We provide non-asymptotic bounds on…