相关论文: Wrong Priors
Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version…
Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…
Transition from Fourier series to Fourier integrals is considered and error introduced by ordinary substitution of integration for summing is estimated. Ambiguity caused by transition from discrete function to continuous one is examined and…
Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical…
Ray Solomonoff invented the notion of universal induction featuring an aptly termed "universal" prior probability function over all possible computable environments. The essential property of this prior was its ability to dominate all other…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
We propose a model for diffusion of two opposite opinions. Here, the decision to be taken by each individual is a random variable which depends on the tendency of the population, as well on its own trend characteristic. The influence of the…
Poor research design and data analysis encourage false-positive findings. Such poor methods persist despite perennial calls for improvement, suggesting that they result from something more than just misunderstanding. The persistence of poor…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
Counterfactual explanations provide a potentially significant solution to the Explainable AI (XAI) problem, but good, native counterfactuals have been shown to rarely occur in most datasets. Hence, the most popular methods generate…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
The beliefs of physicists can bias their results towards their expectations in a number of ways. We survey a variety of historical cases of expectation bias in observations, experiments, and calculations.
This volume is a collection of six papers on the use of auxiliary information and 'a priori' values in construction of improved estimators. The work included here will be of immense application for researchers and students who emply…
Take a look around you -- in your family, your school or workplace, in the streets, and you see boys & girls in about equal proportion, and without any easily visible gender patterns in case of siblings. So, to the famous first order of…
In many large multiple testing problems the hypotheses are divided into families. Given the data, families with evidence for true discoveries are selected, and hypotheses within them are tested. Neither controlling the error-rate in each…
The unparalleled ability of machine learning algorithms to learn patterns from data also enables them to incorporate biases embedded within. A biased model can then make decisions that disproportionately harm certain groups in society. Much…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
While the general form of even perfect numbers is well-known, the existence or non-existence of odd perfect numbers is still an open problem. We address this problem and prove that if a natural number is odd, then it's not perfect.