We investigate the ability of a quantum measurement device to discriminate two states or, generically, two hypotheses. In full generality, the measurement can be performed a number n of times, and arbitrary preprocessing of the states and postprocessing of the obtained data are allowed. There is an intrinsic error associated with the measurement device, which we aim to quantify, that limits its...

The testing of multiple null hypotheses in a single study is a common occurrence in applied research. The problem of Type I error inflation or probability pyramiding in such contexts has been well-known for many years. General procedures for the control of Type I error rates in multiple testing are the Bonferroni procedure and its’ more recent modifications. These procedures partition a desired...

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities...

In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling probabilities. The sampling dependent error bound (i) allows us to better understand the tradeoff in the reconstruction error due to sampling probabilities, (ii) exhi...

We give a survey of several methods to obtain sharp concentration results, typically with exponentially small error probabilities, for random variables occuring in combinatorial probability.

Simple analytic estimates and corresponding error bounds are provided for communication or broadcast systems with state dependent message loss probabilities, such as slotted ALOHA loss systems.

I have developed an interactive microcomputer simulation program for the design, comparison, and evaluation of alternative quality-control (QC) procedures. The program estimates the probabilities for rejection under different conditions of random and systematic error when these procedures are used and plots their power function graphs. It also estimates the probabilities for detection of critic...

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown...

Exact small-sample methods for discrete data use probability distributions that do not depend on unknown parameters. However, they are conservative inferentially: the actual error probabilities for tests and confidence intervals are bounded above by the nominal level. This article surveys ways of reducing or even eliminating the conservatism. Fuzzy inference is a recent innovation that enables ...

In this paper, an adaptive fusion algorithm is proposed for an environment where the observations and local decisions are dependent from one sensor to another. An optimal decision rule, based on the maximum posterior probability (MAP) detection criterion for such an environment, is derived and compared to the adaptive approach. In the algorithm, the log-likelihood ratio function can be expresse...