Related papers: The Bayes cost in the binary decision problem
This paper discusses a class of combinatorial optimization problems with uncertain costs in the objective function. It is assumed that a sample of the cost realizations is available, which defines an empirical probability distribution for…
We show that quantum state discrimination sits neatly in the framework of Bayesian experimental design. In this setting, the two main branches of quantum state discrimination (minimal error and maximal confidence) simply correspond to two…
We discuss a novel implementation of the minimum error state discrimination measurement, originally introduced by Helstrom. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the…
Bayesian classification labels observations based on given prior information, namely class-a priori and class-conditional probabilities. Bayes' risk is the minimum expected classification cost that is achieved by the Bayes' test, the…
Binary decision theory has been applied to the general interferometric problem. Optimal detection scheme-according to the Neyman-Pearson criterion-has been considered for different phase-enhanced states of radiation field, and the…
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology…
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative…
We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
We address the problem of discriminating with minimal error probability two given quantum operations. We show that the use of entangled input states generally improves the discrimination. For Pauli channels we provide a complete comparison…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…
In classification with a reject option, the classifier is allowed in uncertain cases to abstain from prediction. The classical cost-based model of a reject option classifier requires the cost of rejection to be defined explicitly. An…
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the…