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Stochastic variational Bayes algorithms have become very popular in the machine learning literature, particularly in the context of nonparametric Bayesian inference. These algorithms replace the true but intractable posterior distribution…

We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…

Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a…

We study the stochastic convergence of the Ces\`{a}ro mean of a sequence of random variables. These arise naturally in statistical problems that have a sequential component, where the sequence of random variables is typically derived from a…

We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We…

Resetting plays a pivotal role in optimizing the completion time of complex first passage processes with single or multiple outcomes/exit possibilities. While it is well established that the coefficient of variation -- a statistical…

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal…

This paper explores the challenges of constructing suitable inferential models in scenarios where the parameter of interest is determined in light of the data, such as regression after variable selection. Two compelling arguments for…

Using theory and experiments, this paper shows that the difficulty of making tradeoffs offers a parsimonious explanation for a wide range of behavioral phenomena. We develop a model of imprecise comparisons applicable to multiattribute,…

A number of writers have supposed that for the full specification of belief, higher order probabilities are required. Some have even supposed that there may be an unending sequence of higher order probabilities of probabilities of…

In this paper, we consider the problem of order preservation under addition and multiplication operators over the vector space of univariate real-valued random variables. Consistent with the case of usual order over the real numbers-as…

We present here two examples of stochastic modelings of social phenomena. The first topic is pedestrian counter flow. Two groups of model pedestrians move in opposite directions and create congestions. It will be shown that this congestion…

In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…

For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…

Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice. We estimate all parameters, the strength of the objects and the boundaries of equal decision,…

Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not…

The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…

Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…