Related papers: Using Random Variables to Predict Experimental Out…
When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is…
We prove the explicit formula for the probability of a run of r successes in n trials.
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…
The problem of inferring the binomial parameter p from x successes obtained in n trials is reviewed and extended to take into account the presence of background, that can affect the data in two ways: a) fake successes are due to a…
This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
The probabilities of causation are commonly used to solve decision-making problems. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…
Given the complexity of combinations of tasks, languages, and domains in natural language processing (NLP) research, it is computationally prohibitive to exhaustively test newly proposed models on each possible experimental setting. In this…
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…
We want to find the convex combination $S$ of iid Bernoulli random variables that maximizes $\textbf{P}(S\geq t)$ for a given threshold~$t$. Cs\'oka conjectured that such an $S$ is an average if $t\geq p$, where $p$ is the success…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…
Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical…
The Bernoulli convolution with parameter $\lambda\in(0,1)$ is the measure on $\bf R$ that is the distribution of the random power series $\sum\pm\lambda^n$, where $\pm$ are independent fair coin-tosses. This paper surveys recent progress on…
When testing a set of data for randomness according to a probability distribution that depends on a parameter, access to this parameter can be considered as a computational resource. We call a randomness test Hippocratic if it is not…
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…