相关论文: Infinite lotteries, spinners, and the applicabilit…
A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon…
We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes' own…
We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model…
In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to…
Improper priors are not allowed for the computation of the Bayesian evidence $Z=p({\bf y})$ (a.k.a., marginal likelihood), since in this case $Z$ is not completely specified due to an arbitrary constant involved in the computation. However,…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
We modify the definable ultrapower construction of Kanovei and Shelah (2004) to develop a ZF-definable extension of the continuum with transfer provable using countable choice only, with an additional mild hypothesis on well-ordering…
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…
The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong to a…
We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of mathematical techniques in the sciences, and introduce a…
We bound features of counterfactual choices in the nonparametric random utility model of demand, i.e. if observable choices are repeated cross-sections and one allows for unrestricted, unobserved heterogeneity. In this setting, tight bounds…
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…
Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
The lottery ticket hypothesis conjectures the existence of sparse subnetworks of large randomly initialized deep neural networks that can be successfully trained in isolation. Recent work has experimentally observed that some of these…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably…
The use of improper priors in the context of Bayesian hierarchical linear mixed models has been studied under the assumption of normality of the random effects. We study the propriety of the posterior under more flexible distributional…
The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas…
Parametric complexity is a central concept in MDL model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML…