Related papers: An attempt at reading Keynes' Treatise on Probabil…
If we accept Savage's set of axioms, then all uncertainties must be treated like ordinary probability. Savage espoused subjective probability, allowing, for example, the probability of Donald Trump's re-election. But Savage's probability…
J. Willard Gibbs published a book in 1902 on statistical mechanics that quickly received significant attention from his contemporaries because of the reputation that he had secured with his prior work on thermodynamics. People reading…
One of the greatest contributors of the 20th century among all academician in the field of statistical finance, M. F. M. Osborne published in 1956 [6] an essential paper and proposed to treat the question of stock market motion through the…
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…
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
The fiducial argument of Fisher (1973) has been described as his biggest blunder, but the recent review of Hannig et al. (2016) demonstrates the current and increasing interest in this brilliant idea. This short note analyses an example…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
This article reviews and develops an epistemological tradition in the philosophy of science, known as convergentism, which holds that inference methods should be assessed based on their ability to converge to the truth across a range of…
This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to…
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…
We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
Many of you reading these words will have been attracted by the discussion paper [McShane and Wyner (2011)], in which case, this may be the first, but hopefully not the last, time you will have read anything in a statistics journal. I would…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…