Related papers: An Information Theoretic Analysis of Sequential De…
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests…
Medical research has evolved conventions for choosing sample size in randomized clinical trials that rest on the theory of hypothesis testing. Bayesians have argued that trials should be designed to maximize subjective expected utility in…
It is often of interest to study the association between covariates and the cumulative incidence of a right-censored time-to-event outcome. When time-varying covariates are measured on a fixed discrete time scale, it is desirable to account…
Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…
We consider a residuals-based distributionally robust optimization (DRO) model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt both parametric and nonparametric regression models to learn…
Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing…
In this paper, a new and convenient $\chi^2$ wald test based on MCMC outputs is proposed for hypothesis testing. The new statistic can be explained as MCMC version of Wald test and has several important advantages that make it very…
In this work, we consider a binary hypothesis testing problem involving a group of human decision-makers. Due to the nature of human behavior, each human decision-maker observes the phenomenon of interest sequentially up to a random length…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables. However, MI is an aggregate statistic and cannot be used…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
Observational learning is an important information aggregation mechanism. However, it occasionally leads to a state in which an entire population chooses a sub-optimal option. When it occurs and whether it is a phase transition remain…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
In this paper we explore partial coherence as a tool for evaluating causal influence of one signal sequence on another. In some cases the signal sequence is sampled from a time- or space-series. The key idea is to establish a connection…
The focus of this paper is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use…
This paper develops a conditional independence (CI) test from a conditional density ratio (CDR) for weakly dependent data. The main contribution is presenting a closed-form expression for the estimated conditional density ratio function…
We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We propose a method of detecting non-self-correcting information cascades in experiments in which subjects choose an option sequentially by observing the choices of previous subjects. The method uses the correlation function $C(t)$ between…
The problem of simple $M-$ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule…