Related papers: Updating Sets of Probabilities
I propose a framework for an agent to change its probabilistic beliefs when a new piece of propositional information $\alpha$ is observed. Traditionally, belief change occurs by either a revision process or by an update process, depending…
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a…
Bayesian inference provides a natural framework for updating knowledge as new information becomes available, often in a sequential manner by incorporating datasets in stages or reusing previous posteriors as priors. In practice, this is…
The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore…
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables $X$ and $Y$ given a random variable $Z$.…
We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…
Fairness is an emerging and challenging topic in recommender systems. In recent years, various ways of evaluating and therefore improving fairness have emerged. In this study, we examine existing evaluation measures of fairness in…
Conditioning on some set of confounders that causally affect both treatment and outcome variables can be sufficient for eliminating bias introduced by all such confounders when estimating causal effect of the treatment on the outcome from…
You measure the value of a quantity x for a number of systems (cells, molecules, people, chunks of metal, DNA vectors, etc.). You repeat the whole set of measures in different occasions or assays, which you try to design as equal to one…
This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a…
Scoring rules serve to quantify predictive performance. A scoring rule is proper if truth telling is an optimal strategy in expectation. Subject to customary regularity conditions, every scoring rule can be made proper, by applying a…
Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with…
We investigate the inverse problem of identifying a conditional probability measure in a measure-dependent dynamical system. We provide existence and well-posedness results and outline a discretization scheme for approximating a measure.…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning…
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…