This paper is about the estimation of the maximum expected value of a set of independent random variables. The performance of several learning algorithms (e.g., Q-learning) is affected by the accuracy of such estimation. Unfortunately, no unbiased estimator exists. The usual approach of taking the maximum of the sample means leads to large overestimates that may significantly harm the performan...

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to ...

This article elaborates a bounding approximation scheme for convex multistage stochastic programs (MSP) that constrain the conditional expectation of some decision-dependent random variables. Expected value constraints of this type are useful for modelling a decision maker’s risk preferences, but they may also arise as artefacts of stage-aggregation. It is shown that the gap between certain upp...

Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such processes and are processes with state space {0, 1, . . . , N} and where each transition is of size one. We derive explicit bounds on the expected value of such a process, bracketing it between the mean-field model and ...

This paper introduces the option to conduct discovery into a model of settlement bargaining and negative expected value (NEV) suits under asymmetric information. We find that the option to conduct discovery has important effects on the standard model of settlement under asymmetric information for several reasons. First, because discovery is typically cheaper than litigation, it reduces the defe...

Measures of decision sensitivity that have been applied to medical decision problems were examined. Traditional threshold proximity methods have recently been supplemented by probabilistic sensitivity analysis, and by entropy-based measures of sensitivity. The authors propose a fourth measure based upon the expected value of perfect information (EVPI), which they believe superior both methodolo...

Based upon the upper expected value, lower expected value and expected value operators of a fuzzy variable, this paper first presents three types of multicriteria maximum expected value models. Then a theorem about the connection of Pareto solutions among the maximum expected value models is proved. In addition, the relationship between maximum and minimum expected value models is discussed. At...

Risk assessors attempting to use probabilistic approaches to describe uncertainty often find themselves in a data-sparse situation: available data are only partially relevant to the parameter of interest, so one needs to adjust empirical distributions, use explicit judgmental distributions, or collect new data. In determining whether or not to collect additional data, whether by measurement or ...

The dopamine system has been linked to anhedonia in depression and both the positive and negative symptoms of schizophrenia, but it remains unclear how dopamine dysfunction could mechanistically relate to observed symptoms. There is considerable evidence that phasic dopamine signals encode prediction error (differences between expected and actual outcomes), with reinforcement learning theories ...

The minimum k-assignment of an m×n matrix X is the minimum sum of k entries of X, no two of which belong to the same row or column. If X is generated by choosing each entry independently from the exponential distribution with mean 1, then Coppersmith and Sorkin conjectured that the expected value of its minimum k-assignment is