Related papers: Frequentist vs Bayesian statistics - a non-statist…
The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…
Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian…
News articles of varying degrees of truthfulness and political alignment, and their influences on the political opinions of the media consumers are modeled as a Bayesian network incorporating a mixture of ideas from dual-reasoning models of…
Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…
This study aims to show the fundamental difference between logistic regression and Bayesian classifiers in the case of exponential and unexponential families of distributions, yielding the following findings. First, the logistic regression…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
Discussions of political disagreement emphasize two patterns: polarization, where beliefs diverge toward opposite extremes on each issue dimension; and issue alignment, where individuals' views across issues become more internally…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
Data can be collected in scientific studies via a controlled experiment or passive observation. Big data is often collected in a passive way, e.g. from social media. In studies of causation great efforts are made to guard against bias and…
Starting with the neo-Bayesian revival of the 1950s, many statisticians argued that it was inappropriate to use Bayesian methods, and in particular subjective Bayesian methods in governmental and public policy settings because of their…
Generalist mathematics journals exhibit bias toward the branches of mathematics by publishing articles about some subjects in quantities far disproportionate to the production of papers in those areas within all of mathematics.
Defining interdisciplinary physics today requires first a reformulation of what is physics today, which in turn calls for clarifying what makes a physicist. This assessment results from my forty year journey arguing and fighting to build…
The choice of priors may become an insoluble problem if priors and Bayes' rule are not seen and accepted in the framework of subjectivism. Therefore, the meaning and the role of subjectivity in science is considered and defended from the…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds.…
The classic frequentist theory of hypothesis testing developed by Neyman, Pearson and Fisher has a claim to being the twentieth century's most influential piece of applied mathematics. Something new is happening in the twenty-first century:…