Related papers: J. B. S. Haldane's Rule of Succession

Laplace's "add-one" rule of succession modifies the observed frequencies in a sequence of heads and tails by adding one to the observed counts. This improves prediction by avoiding zero probabilities and corresponds to a uniform Bayesian…

Induction is a form of reasoning that starts with a particular example and generalizes to a rule, namely, a hypothesis. However, establishing the truth of a hypothesis is problematic due to the potential occurrence of conflicting events,…

This article brings attention to some historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to…

The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…

In a review on the contribution of J.B.S. Haldane to the development of the Bayes factor hypothesis test (arXiv:1511.08180), Etz and Wagenmakers focus on Haldane's proposition of a mixture prior in a genetic example (Haldane 1932, A note on…

An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly…

In 1922, JBS Haldane discovered an intriguing bias of postzygotic isolation during early speciation: the heterogametic sex of F1 hybrids between closely related species or subspecies is more susceptible to sterility or inviability than the…

Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…

(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…

An agent observes a clue, and an analyst observes an inference: a ranking of events on the basis of how corroborated they are by the clue. We prove that if the inference satisfies the axioms of Villegas (1964) except for the classic…

I propose a normative updating rule, extended Bayesianism, for the incorporation of probabilistic information arising from the process of becoming more aware. Extended Bayesianism generalizes standard Bayesian updating to allow the…

In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). This is a fundamental problem, and of particular interest for Bayesian networks.…

Generalization of the Lambalgen's theorem is studied with the notion of Hippocratic (blind) randomness without assuming computability of conditional probabilities. In [Bauwence 2014], a counter-example for the generalization of Lambalgen's…

We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently,…