Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications

Taper, Mark L.; Ponciano, José Miguel; Dennis, B. R.

doi:10.3390/e24091273

Cited by 3 publications

(4 citation statements)

References 54 publications

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“…How does this perspective, complementary to Taper et al (2022) connect to philosophical approaches to statistics including evidential statistics?…”

Section: It Is About Science!mentioning

confidence: 99%

“…This preference does not mean that we have no difficulties in representing meta-notions under the evidential theory, however. Using replications and reproducibility as a running example, it is currently not clear whether some of the desiderata in Taper et al (2022) can be satisfied for some components of an idealized experiment. Specifically:…”

Section: It Is About Science!mentioning

confidence: 99%

“…To round up our perspective, we offer a slightly revised version of the question raised by Royall (2004) and reiterated in the call for this special issue by Taper et al (2022). We believe that the crux of problem in philosophical and theoretical approaches to statistics is the failure in addressing: "When does a given set of observations support one scientific hypothesis over another?…”

Section: It Is About Science!mentioning

confidence: 99%

“…Our tone is philosophical, stemming from our theoretical research program on statistical theory in and of metascience, and we hope it complements Taper et al (2022). We raise a number of questions about improving scientific inference via statistical inference.…”

Section: Introductionmentioning

confidence: 99%

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Statistics in service of metascience: Measuring replication distance with reproducibility rate

Buzbas,

Devezer

2024

Preprint

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Motivated by the recent putative reproducibility crisis, we discuss the relationship between replicability of scientific studies, reproducibility of results obtained in these replications, and the philosophy of statistics. Our approach focuses on challenges in specifying scientific studies for scientific inference via statistical inference, and is complementary to classical discussions in philosophy of statistics. We particularly consider the challenges in replicating studies exactly, using the notion of the idealized experiment. We argue against treating reproducibility as an inherently desirable property of scientific results, and in favor of viewing it as a tool to measure distance between an original study and its replications. To sensibly study the implications of replicability and results reproducibility on inference, such a measure of replication distance is needed. We present an effort to delineate such a framework here, addressing some challenges in capturing the components of scientific studies while identifying others as ongoing issues. We illustrate our measure of replication distance by simulations using a toy example. Rather than replications, we present purposefully planned modifications as an appropriate tool to inform scientific inquiry. Our ability to measure replication distance serves scientists in their search for replication-ready studies. We believe that likelihood-based and evidential approaches may play a critical role towards building a statistics that effectively serves the practical needs of science.

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“…How does this perspective, complementary to Taper et al (2022) connect to philosophical approaches to statistics including evidential statistics?…”

Section: It Is About Science!mentioning

confidence: 99%

Section: It Is About Science!mentioning

confidence: 99%

Section: It Is About Science!mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Statistics in service of metascience: Measuring replication distance with reproducibility rate

Buzbas,

Devezer

2024

Preprint

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Statistics in Service of Metascience: Measuring Replication Distance with Reproducibility Rate

Buzbas,

Devezer

2024

Entropy

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Motivated by the recent putative reproducibility crisis, we discuss the relationship between the replicability of scientific studies, the reproducibility of results obtained in these replications, and the philosophy of statistics. Our approach focuses on challenges in specifying scientific studies for scientific inference via statistical inference and is complementary to classical discussions in the philosophy of statistics. We particularly consider the challenges in replicating studies exactly, using the notion of the idealized experiment. We argue against treating reproducibility as an inherently desirable property of scientific results, and in favor of viewing it as a tool to measure the distance between an original study and its replications. To sensibly study the implications of replicability and results reproducibility on inference, such a measure of replication distance is needed. We present an effort to delineate such a framework here, addressing some challenges in capturing the components of scientific studies while identifying others as ongoing issues. We illustrate our measure of replication distance by simulations using a toy example. Rather than replications, we present purposefully planned modifications as an appropriate tool to inform scientific inquiry. Our ability to measure replication distance serves scientists in their search for replication-ready studies. We believe that likelihood-based and evidential approaches may play a critical role towards building statistics that effectively serve the practical needs of science.

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Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models

Dennis,

Taper,

Ponciano

2024

Entropy

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Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of the worrisome aspects of statistical hypothesis testing can be ameliorated with concepts and methods from evidential analysis. The model family we treat is the familiar normal linear model with fixed effects, embracing multiple regression and analysis of variance, a warhorse of everyday science in labs and field stations. Questions about study design, the applicability of the null hypothesis, the effect size, error probabilities, evidence strength, and model misspecification become more naturally housed in an evidential setting. We provide a completely worked example featuring a two-way analysis of variance.

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Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications

Abstract: Scope and Goals of the Special Issue: There is a growing realization that despite being the essential tool of modern data-based scientific discovery and model testing, statistics has major problems [...]

Cited by 3 publications

References 54 publications

Statistics in service of metascience: Measuring replication distance with reproducibility rate

Statistics in service of metascience: Measuring replication distance with reproducibility rate

Statistics in Service of Metascience: Measuring Replication Distance with Reproducibility Rate

Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models

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