We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of the random payoff vector of each player belongs to a distributional uncertainty set. Using distributionally robust approach, we define a chance-constrained game with respect to the worst-case chanceconstraint. We call s...

For chance-constrained programming (CCP) with non-Gaussian uncertainty, the optimization is generally intractable owing to the complicated probability density function (PDF). Using a simple fitted distribution with Kullback-Leibler (KL) divergence to represent the PDF mismatch is a systematic way to tackle CCP with non-Gaussian uncertainty. However, the essential difficulty of this methodology ...

It is no doubt that the evolutionary process is affected by chance, but the question is to what extent the chance plays its role. The random analysis can throw light on the underlying reasoning for the primary structure of proteins. With the use of random principles, we have explored three approaches to analyse protein primary structure, i.e. the randomness in the construction of amino-acid seq...

A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold , over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to approximate the joint chance ...

We tested the core prediction of the Trace Deletion Hypothesis (TDH) of agrammatic Broca's aphasia, which contends that such patients' comprehension performance is normal for active reversible sentences but at chance level for passive reversible sentences. We analyzed the comprehension performance of 38 Italian Broca's aphasics with verified damage to Broca's area, who completed sentence-to-pic...

In this paper, we propose a distributionally robust chance constrained (DRCC) optimization problem for the operation of an active distribution network (ADN). The ADN’s operator uses proposed to centrally optimize dispatch plan his resources, namely photovoltaic (PV) and battery energy storage (BES) systems, participate in wholesale real/reactive power flexibility markets. We model uncertainties...

In our day-to-day discourse on uncertainty, words like belief, chance, plausible, likelihood and probability are commonly encountered. Often, these words are used interchangeably, because they are intended to encapsulate some loosely articulated notions about the unknowns. The purpose of this paper is to propose a framework that is able to show how each of these terms can be made precise, so th...