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The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality…
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…
One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from…
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born's rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative…
Conventional survival analysis approaches estimate risk scores or individualized time-to-event distributions conditioned on covariates. In practice, there is often great population-level phenotypic heterogeneity, resulting from (unknown)…
Probabilities in eternal inflation are traditionally defined as limiting frequency distributions, but a unique and unambiguous probability measure remains elusive. In this paper, we present a different approach, based on Bayesian reasoning.…
Life emerged on the Earth within the first quintile of its habitable window, but a technological civilization did not blossom until its last. Efforts to infer the rate of abiogenesis, based on its early emergence, are frustrated by the…
We provide a reason for Bayesian updating, in the Bernoulli case, even when it is assumed that observations are independent and identically distributed with a fixed but unknown parameter $\theta_0$. The motivation relies on the use of loss…
This expository paper discusses Bayesian decision analysis perspectives on problems of constrained forecasting. Foundational and pedagogic discussion contrasts decision analytic approaches with the traditional, but typically inappropriate,…
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…
Where is everybody? This phrase distills the foreboding of what has come to be known as the Fermi Paradox - the disquieting idea that, if extraterrestrial life is probable in the Universe, then why have we not encountered it? This conundrum…
It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
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.
Planned and ongoing searches for life, both biological and technological, confront an epistemic barrier concerning false positives - namely, that we don't know what we don't know. The most defensible and agnostic approach is to adopt…
Following the observational evidence for cosmic acceleration which may exclude a possibility for the universe to recollapse to a second singularity, we review alternative scenarios of its future evolution. Although the de Sitter asymptotic…
In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a…
Concerns about artificial intelligence (AI) and its potential existential risks have garnered significant attention, with figures like Geoffrey Hinton and Dennis Hassabis advocating for robust safeguards against catastrophic outcomes.…
In 1957, Lindley published "A statistical paradox" in Biometrika, revealing a fundamental conflict between frequentist and Bayesian inference as sample size approaches infinity. We present a new paradox of a different kind: a conflict…
It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information…