Related papers: My Statistics is Better than Yours
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original…
This book presents our case in defense of a constructivist epistemological framework and the use of compatible statistical theory and inference tools. The basic metaphor of decision theory is the maximization of a gambler's expected…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
Current developments in the statistics community suggest that modern statistics education should be structured holistically, that is, by allowing students to work with real data and to answer concrete statistical questions, but also by…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…
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,…
There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
The increasing ease of data capture and storage has led to a corresponding increase in the choice of data, the type of analysis performed on that data, and the complexity of the analysis performed. The main contribution of this paper is to…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…