Related papers: Optimal Multistage Sampling in a Boundary-Crossing…
The world is rarely static -- many problems need not only be solved once but repeatedly, under changing conditions. This setting is addressed by the "multistage" view on computational problems. We study the "diverse multistage" variant,…
How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not…
In this paper, a general stochastic model with controls applied at the moments when the random process hits the boundary of a given subset of the state set is proposed and studied. The general concept of the model is formulated and its…
This paper studies closed-loop chance constrained control problems with disturbance feedback (equivalently state feedback) where state and input vectors must remain in a prescribed polytopic safe region with a predefined confidence level.…
This work investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one "most informative"…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to…
Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in…
We examine a fundamental problem that models various active sampling setups, such as network tomography. We analyze sampling of a multivariate normal distribution with an unknown expectation that needs to be estimated: in our setup it is…
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At…
A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or…
Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…
We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary…
We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or…
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity…
Conventional multiple hypothesis tests use step-up, step-down, or closed testing methods to control the overall error rates. We will discuss marrying these methods with adaptive multistage sampling rules and stopping rules to perform…
We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide…
In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this…