Related papers: Approximate Expected Utility Rationalization
The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint…
A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…
With the emergence of energy communities, where a number of prosumers invest in shared generation and storage, the issue of fair allocation of benefits is increasingly important. The Shapley value has attracted increasing interest for…
Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by…
Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Normality, in the colloquial sense, has historically been considered an aspirational trait, synonymous with ideality. The arithmetic average and, by extension, statistics including linear regression coefficients, have often been used to…
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit…
This paper studies whether rationality can be computed. Rationality is defined as the use of complete information, which is processed with a perfect biological or physical brain, in an optimized fashion. To compute rationality one needs to…
Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
To choose between two discrete goods, a consumer pays attention to only those with prices below a threshold. From these, she chooses her most preferred good. We assume consumers in a population have the same preference but may have…
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…
The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
We introduce a new class of graphical representations, expected utility networks (EUNs), and discuss some of its properties and potential applications to artificial intelligence and economic theory. In EUNs not only probabilities, but also…
The maximum utility estimation proposed by Elliott and Lieli (2013) can be viewed as cost-sensitive binary classification; thus, its in-sample overfitting issue is similar to that of perceptron learning. A utility-maximizing prediction rule…
Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug's effects on a relevant set of patients and controls. Sometimes,…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Data is a cornerstone of empirical software engineering (ESE) research and practice. Data underpin numerous process and project management activities, including the estimation of development effort and the prediction of the likely location…