Related papers: Random Variables aren't Random
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
Statistical pragmatism embraces all efficient methods in statistical inference. Augmentation of the collected data is used herein to obtain representative population information from a large class of non-representative population's units.…
Sampling distribution, a foundational concept in statistics, is difficult to understand, since we usually have only one realization of the estimator of interest. In this work, we present an innovative method for helping university students…
The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data -> decision]. An SDF need not perform…
Spurious association arises from covariance between propensity for the treatment and individual risk for the outcome. For sensitivity analysis with stochastic counterfactuals we introduce a methodology to characterize uncertainty in causal…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To…
This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…
We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non-stationary…