Related papers: Resolving Jeffreys-Lindley Paradox
A theory of quantitative inference about the parameters of sampling distributions is constructed deductively by following very general rules, referred to as the Cox-Polya-Jaynes Desiderata. The inferences are made in terms of probability…
Recently, the educational initiative TED-Ed has published a popular brain teaser coined the 'frog riddle', which illustrates non-intuitive implications of conditional probabilities. In its intended form, the frog riddle is a reformulation…
In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different…
We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…
Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…
We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model…
Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…
The Benjamini-Hochberg (BH) procedure remains widely popular despite having limited theoretical guarantees in the commonly encountered scenario of correlated test statistics. Of particular concern is the possibility that the method could…
Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such…
Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…
We perform extensive Monte Carlo simulations to systematically compare the frequentist and Bayesian treatments of the Lomb--Scargle periodogram. The goal is to investigate whether the Bayesian period search is advantageous over the…
When it is acknowledged that all candidate parameterised statistical models are misspecified relative to the data generating process, the decision maker (DM) must currently concern themselves with inference for the parameter value…
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…
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter $\theta_j$ was equal or lay close to a specified value…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
We argue that the Bayesian paradigm, of a prior which represents the beliefs of the statistician before observing the data, is not feasible in ultra-high-dimensional models. We claim that natural priors that represent the a priori beliefs…
Experiments are once again under way at the LHC. This time around, however, the mood in the high-energy physics community is pessimistic. There is a growing suspicion that naturalness arguments that predict new physics near the weak scale…