Related papers: Continuous time asymptotic representations for ada…
Recently, it has been shown how sampling actions from the predictive distribution over the optimal action-sometimes called Thompson sampling-can be applied to solve sequential adaptive control problems, when the optimal policy is known for…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…
Adaptive experiments such as multi-arm bandits adapt the treatment-allocation policy and/or the decision to stop the experiment to the data observed so far. This has the potential to improve outcomes for study participants within the…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…
We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…
Estimating treatment effects from observational data is of central interest across numerous application domains. Individual treatment effect offers the most granular measure of treatment effect on an individual level, and is the most useful…
We propose an adaptive sequential framework for testing two simple hypotheses that analytically ensures finite exposure to the less effective treatment. Our proposed procedure employs a likelihood ratio-driven adaptive allocation rule,…
Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference…
Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time.…
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…
We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional…
We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
Adaptive experiments are used extensively in online platforms, healthcare and biotechnology, and a variety of other settings. In many of these applications, the main goal is not to precisely estimate a treatment effect, but to demonstrate…