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Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be…
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…
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an ultra-chaos are sensitive to tiny disturbances. We…
The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue…
Increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow a carefully crafted set of scientific hypotheses with statistical analysis, researchers can now test…
Analysis of credibility is a reverse-Bayes technique that has been proposed by Matthews (2001) to overcome some of the shortcomings of significance tests. A significant result is deemed credible if current knowledge about the effect size is…
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
There are various mathematical models proposed in the recent literature for estimating the h-index through bibliometric measures, such as number of articles (P) and citations received (C). These models have been previously empirically…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
The reproducibility crisis has led to an increasing number of replication studies being conducted. Sample sizes for replication studies are often calculated using conditional power based on the effect estimate from the original study.…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
Social sciences were built from comparison methods assembling field works and data, either quantitative or qualitative. Big Data offers new opportunities to extend this requirement to build commensurable data sets. The paper tells the story…
We study the detection capability of the weak-value amplification on the basis of the statistical hypothesis testing. We propose a reasonable testing method in the physical and statistical senses to find that the weak measurement with the…
Shafer (2021) offers a betting perspective on statistical testing which may be useful for foundational debates, given that disputes over such testing continue to be intense. To be helpful for researchers, however, this perspective will need…
Scientific and technological progress has historically been very beneficial to humanity but this does not always need to be true. Going forward, science may enable bad actors to cause genetically engineered pandemics that are more frequent…
The replication crisis, the failure of scientific claims to be validated by further research, is one of the most pressing issues for empirical research. This is partly an incentive problem: replication is costly and less well rewarded than…
We show that publishing results using the statistical significance filter---publishing only when the p-value is less than 0.05---leads to a vicious cycle of overoptimistic expectation of the replicability of results. First, we show…
The replicability crisis in the social, behavioral, and data sciences has led to the formulation of algorithm frameworks for replicability -- i.e., a requirement that an algorithm produce identical outputs (with high probability) when run…
The reproducibility of academic research has long been a persistent issue, contradicting one of the fundamental principles of science. What is even more concerning is the increasing number of false claims found in academic manuscripts…