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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…
In cell biology, statistical analysis means testing the hypothesis that there was no effect. This weak form of hypothesis testing neglects effect size, is universally misinterpreted, and is disastrously prone to error when combined with…
Information flow analysis has largely ignored the setting where the analyst has neither control over nor a complete model of the analyzed system. We formalize such limited information flow analyses and study an instance of it: detecting the…
For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and…
Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
Methods for addressing missing data have become much more accessible to applied researchers. However, little guidance exists to help researchers systematically identify plausible missing data mechanisms in order to ensure that these methods…
We provide an approach to exploratory data analysis in matched observational studies with a single intervention and multiple endpoints. In such settings, the researcher would like to explore evidence for actual treatment effects among these…
Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of…
Statistical inference has undergone a profound transformation over the past decade, evolving from a significance-testing paradigm toward a comprehensive, transparency-driven framework embedded within the broader open science ecosystem.…
While running any experiment, we often have to consider the statistical power to ensure an effective study. Statistical power or power ensures that we can observe an effect with high probability if such a true effect exists. However,…
In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…
Meta-analysis employs statistical techniques to synthesize the results of individual studies, providing an estimate of the overall effect size for a specific outcome of interest. The direction and magnitude of this estimate, along with its…
Data analysis requires translating higher level questions and hypotheses into computable statistical models. We present a mixed-methods study aimed at identifying the steps, considerations, and challenges involved in operationalizing…
This paper serves as a literature review of methodology concerning the (modern) causal inference methods to address the causal estimand with observational/survey data that have been or will be used in social science research. Mainly, this…
Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly,…
This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…
In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would…
Experimental datasets are growing rapidly in size, scope, and detail, but the value of these datasets is limited by unwanted measurement noise. It is therefore tempting to apply analysis techniques that attempt to reduce noise and enhance…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…