Related papers: The Epic Story of Maximum Likelihood
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
We show that the incorporation of any new piece of information allows for improved decision making in the sense that the expected costs of an optimal decision decrease (or, in boundary cases where no or not enough new information is…
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
This article reviews and develops an epistemological tradition in the philosophy of science, known as convergentism, which holds that inference methods should be assessed based on their ability to converge to the truth across a range of…
Graphical and sparse (inverse) covariance models have found widespread use in modern sample-starved high dimensional applications. A part of their wide appeal stems from the significantly low sample sizes required for the existence of…
We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson [14]. We develop a…
The paper by Mayo claims to provide a new clarification and critique of Birnbaum's argument for showing that sufficiency and conditionality principles imply the likelihood principle. However, much of the arguments go back to arguments made…
We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…
Meta analysis is commonly-used to synthesize multiple results from individual studies. However, its validation is usually threatened by publication bias and between-study heterogeneity, which can be captured by the Copas selection model.…
We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax…
The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…
The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli's Theorem in 1713, through De Moivre's Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob…
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
In proofs of L_2-differentiability, Lebesgue densities of a central distribution are often assumed right from the beginning. Generalizing Theorem 4.2 of Huber[81], we show that in the class of smooth parametric group models these densities…
The Availability bias, manifested in the over-representation of extreme eventualities in decision-making, is a well-known cognitive bias, and is generally taken as evidence of human irrationality. In this work, we present the first…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
The Expectation-Maximization (EM) algorithm (Dempster, Laird and Rubin, 1977) is a popular method for computing maximum likelihood estimates (MLEs) in problems with missing data. Each iteration of the al- gorithm formally consists of an…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.