Related papers: Where do statistical models come from? Revisiting …
There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the…
Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370--418; 54 296--325] introduced the observed likelihood function to statistical inference and provided a weight function to calibrate the parameter; he also introduced a confidence…
This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
These notes provide a pedagogical introduction to the role of transversality theory in the analysis of statistical degeneracies within the framework of distributional statistical models. The classical question of when a statistical model is…
Several tasks in information retrieval (IR) rely on assumptions regarding the distribution of some property (such as term frequency) in the data being processed. This thesis argues that such distributional assumptions can lead to incorrect…
In this article we revisit the definition of Precision-Recall (PR) curves for generative models proposed by Sajjadi et al. (arXiv:1806.00035). Rather than providing a scalar for generative quality, PR curves distinguish mode-collapse (poor…
Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We…
Model steering, which involves intervening on hidden representations at inference time, has emerged as a lightweight alternative to finetuning for precisely controlling large language models. While steering efficacy has been widely studied,…
A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
The traditional calculus-based introduction to statistical inference consists of a semester of probability followed by a semester of frequentist inference. Cobb (2015) challenges the statistical education community to rethink the…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
There have been many claims in the media and a bit of respectable research about the causes of variation in firearm sales. The challenges for causal inference can be quite daunting. This paper reports an analysis of daily handgun sales in…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the…
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…