scholarly journals On the Measure-Theoretic Premises of Bayes Factor and Full Bayesian Significance Tests: a Critical Reevaluation

2021 ◽  
Author(s):  
Riko Kelter
Keyword(s):  
Bayes Factor ◽  
Critical Evaluation ◽  
Significance Test ◽  
Statistical Hypothesis ◽  
P Value ◽  
Specific Class ◽  
Statistical Hypothesis Testing ◽  
Specific Measure ◽  
Bayesian Evidence ◽  
Relationship Of

AbstractThe Full Bayesian Significance Test (FBST) and the Bayesian evidence value recently have received increasing attention across a variety of sciences including psychology. Ly and Wagenmakers (2021) have provided a critical evaluation of the method and concluded that it suffers from four problems which are mostly attributed to the asymptotic relationship of the Bayesian evidence value to the frequentist p-value. While Ly and Wagenmakers (2021) tackle an important question about the best way of statistical hypothesis testing in the cognitive sciences, it is shown in this paper that their arguments are based on a specific measure-theoretic premise. The identified problems hold only under a specific class of prior distributions which are required only when adopting a Bayes factor test. However, the FBST explicitly avoids this premise, which resolves the problems in practical data analysis. In summary, the analysis leads to the more important question whether precise point null hypotheses are realistic for scientific research, and a shift towards the Hodges-Lehmann paradigm may be an appealing solution when there is doubt on the appropriateness of a precise hypothesis.

scholarly journals Normalisr: normalization and association testing for single-cell CRISPR screen and co-expression

2021 ◽  
Author(s):  
Lingfei Wang
Keyword(s):  
Single Cell ◽  
Regulatory Networks ◽  
Large Scale ◽  
High Sensitivity ◽  
Statistical Hypothesis ◽  
P Value ◽  
Statistical Hypothesis Testing ◽  
Experimental Conditions ◽  
Library Size ◽  
Association Testing

AbstractSingle-cell RNA sequencing (scRNA-seq) provides unprecedented technical and statistical potential to study gene regulation but is subject to technical variations and sparsity. Here we present Normalisr, a linear-model-based normalization and statistical hypothesis testing framework that unifies single-cell differential expression, co-expression, and CRISPR scRNA-seq screen analyses. By systematically detecting and removing nonlinear confounding from library size, Normalisr achieves high sensitivity, specificity, speed, and generalizability across multiple scRNA-seq protocols and experimental conditions with unbiased P-value estimation. We use Normalisr to reconstruct robust gene regulatory networks from trans-effects of gRNAs in large-scale CRISPRi scRNA-seq screens and gene-level co-expression networks from conventional scRNA-seq.

scholarly journals Pengaruh Penggunaan Lahan Dan Kinerja Lalu Lintas Terhadap Iklim Perkotaan Di Wilayah Peri-Urban Mamminasata

2021 ◽  
Vol 3 (2) ◽  
pp. 41-51
Author(s):  
Sri Hidayat ◽  
Syafri Syafri ◽  
Syahriar Tato
Keyword(s):  
Land Use ◽  
Anthropogenic Activities ◽  
Urban Climate ◽  
Climatic Conditions ◽  
Statistical Hypothesis ◽  
Anthropogenic Activity ◽  
P Value ◽  
Spatial Transformation ◽  
Statistical Hypothesis Testing ◽  
Traffic Performance

Koridor ruas jalan Hertasning-Tun Abdul Razak merupakan wilayah peri-urban yang mengalami dinamika cukup tinggi akibat kebutuhan permukiman dan sarana kegiatan baru. Hal ini memicu terjadinya transformasi spasial. Transformasi spasial memberikan dampak pada peningkatan aktivitas antropogenik yang dapat mengubah iklim perkotaan. Peningkatan aktivitas antropogenik ditandai dengan perbedaan penggunaan lahan dan kinerja lalu lintas sepanjang koridor. Penelitian ini menggunakan metode kuantitatif untuk mengetahui hubungan variabel penggunaan lahan dan kinerja lalu lintas terhadap kondisi iklim perkotaan dengan analisis data menggunakan SEM PLS.  Hasil pengujian hipotesis secara statistik terhadap pengaruh masing-masing variabel independen terhadap variabel dependennya menghasilkan kesimpulan penggunaan lahan berpengaruh signifikan terhadap kondisi iklim dimana nilai T-Statistik sebesar 2,752 > 1,96 atau nilai P sebesar 0,040 < 0,05. Sementara kinerja lalu lintas tidak berpengaruh signifikan terhadap kondisi iklim perkotaan dengan nilai T-Statistik sebesar 1,071 < 1,96 atau nilai P sebesar 0,285 > 0,05. Hasil ini juga menunjukkan bahwa penggunaan lahan di koridor ruas jalan Hertasning-Tun Abdul Razak dapat menyebabkan meningkatnya suhu perkotaan dikawasan tersebut. Namun peningkatan suhu perkotaan pada kawasan tersebut lebih disebabkan oleh aktivitas antropogenik pada penggunaan lahannya dan tidak dipengaruhi oleh luas area yang terbangun. The corridor of the Hertasning-Tun Abdul Razak road section is a peri-urban area experiencing high dynamics due to the need for new housing and activity facilities. This triggers a spatial transformation. Spatial transformation has an impact on increasing anthropogenic activities that can change the urban climate. The increase in anthropogenic activity is indicated by differences in land use and traffic performance along the corridor. This study uses a quantitative method to determine the relationship between land use variables and traffic performance on urban climatic conditions with data analysis using SEM PLS. The results of statistical hypothesis testing on the effect of each independent variable on the dependent variable resulted in the conclusion that land use had a significant effect on climatic conditions where the T-statistic value was 2.752> 1.96 or the P value was 0.040 <0.05. Meanwhile, traffic performance has no significant effect on urban climatic conditions with a T-statistic value of 1.071 <1.96 or a P value of 0.285> 0.05. These results also indicate that land use in the Hertasning-Tun Abdul Razak road corridor can cause an increase in urban temperatures in the area. However, the increase in urban temperature in these areas is more due to anthropogenic activities in land use and is not influenced by the area that is built.

scholarly journals Statistical hypothesis testing in wavelet analysis: theoretical developments and applications to Indian rainfall

2019 ◽  
Vol 26 (2) ◽  
pp. 91-108 ◽  
Author(s):  
Justin A. Schulte
Keyword(s):  
Wavelet Analysis ◽  
Statistical Significance ◽  
Persistent Homology ◽  
Testing Procedure ◽  
Significance Test ◽  
Wavelet Spectrum ◽  
Statistical Hypothesis ◽  
Statistical Hypothesis Testing ◽  
Testing Procedures ◽  
Indian Rainfall

Abstract. Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity (e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arclength, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

scholarly journals Entropic Ranks: A Methodology for Enhanced, Threshold-Free, Information-Rich Data Partition and Interpretation

2020 ◽  
Vol 10 (20) ◽  
pp. 7077
Author(s):  
Hector-Xavier de Lastic ◽  
Irene Liampa ◽  
Alexandros G. Georgakilas ◽  
Michalis Zervakis ◽  
Aristotelis Chatziioannou
Keyword(s):  
Information Content ◽  
Selection Method ◽  
Differentially Expressed ◽  
Statistical Hypothesis ◽  
P Value ◽  
Data Partition ◽  
Statistical Hypothesis Testing ◽  
Data Types ◽  
Parametric Statistics ◽  
Rich Data

Background: Here, we propose a threshold-free selection method for the identification of differentially expressed features based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques, based on fixed thresholds. This work aims to propose a methodology, which automates and standardizes the statistical selection, through the utilization of established measures like that of entropy, already used in information retrieval from large biomedical datasets, thus departing from classical fixed-threshold based methods, relying in arbitrary p-value and fold change values as selection criteria, whose efficacy also depends on degree of conformity to parametric distributions,. Methods: Our work extends the rank product (RP) methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP entropy of the distribution, to isolate the features of interest by their contribution to its information content. Goal is a methodology of threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under study. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterizations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and rich in information, indicating phenotypic aspects specific to the tissue and biological phenomenon investigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresh-holding, thus facilitating the full automation of the analysis.

scholarly journals Entropic Ranks: A Methodology for Enhanced, Threshold-Free, Information-Rich Data Partition and Interpretation

2020 ◽  
Author(s):  
Hector - Xavier de Lastic ◽  
Irene Liampa ◽  
Alexandros G. Georgakilas ◽  
Michalis Zervakis ◽  
Aristotelis Chatziioannou
Keyword(s):  
Information Content ◽  
Selection Method ◽  
Statistical Hypothesis ◽  
P Value ◽  
Data Partition ◽  
Statistical Hypothesis Testing ◽  
Data Types ◽  
Extraction Capacity ◽  
Parametric Statistics ◽  
Rich Data

Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution&rsquo;s entropy to isolate the features of interest by their contribution to the distribution&rsquo;s information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.

scholarly journals A Critical Evaluation of the FBST ev for Bayesian Hypothesis Testing

2021 ◽  
Author(s):  
Alexander Ly ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Critical Evaluation ◽  
Significance Test ◽  
P Value ◽  
Bayesian Hypothesis Testing ◽  
Absence Of Evidence ◽  
Evidence Of Absence ◽  
Foregone Conclusion

he “Full Bayesian Significance Test e-value”, henceforth FBST ev, has received increasing attention across a range of disciplines including psychology. We show that the FBST ev leads to four problems: (1) the FBST ev cannot quantify evidence in favor of a null hypothesis and therefore also cannot discriminate “evidence of absence” from “absence of evidence”; (2) the FBST ev is susceptible to sampling to a foregone conclusion; (3) the FBST ev violates the principle of predictive irrelevance, such that it is affected by data that are equally likely to occur under the null hypothesis and the alternative hypothesis; (4) the FBST ev suffers from the Jeffreys-Lindley paradox in that it does not include a correction for selection. These problems also plague the frequentist p-value. We conclude that although the FBST ev may be an improvement over the p-value, it does not provide a reasonable measure of evidence against the null hypothesis.

A Comment on “Beyond P-value: the Rigor and Power of Study"

2019 ◽  
pp. 7-9 ◽  
Author(s):  
Helena Kraemer
Keyword(s):  
Hypothesis Testing ◽  
Present Situation ◽  
Hypothesis Generation ◽  
Statistical Hypothesis ◽  
P Value ◽  
Exploratory Research ◽  
Statistical Hypothesis Testing ◽  
P Values

“As ye sow. So shall ye reap”: For almost 100 years, researchers have been taught that the be-all and end-all in data-based research is the p-value. The resulting problems have now generated concern, often from us who have long so taught researchers. We must bear a major responsibility for the present situation and must alter our teachings. Despite the fact that the Zhang and Hughes paper is titled “Beyond p-value”, the total focus remains on statistical hypothesis testing studies (HTS) and p-values(1). Instead, I would propose that there are three distinct, necessary, and important phases of research: 1) Hypothesis Generation Studies (HGS) or Exploratory Research (2-4); 2) Hypothesis Testing Studies (HTS); 3) Replication and Application of Results. Of these, HTS is undoubtedly the most important, but without HGS, HTS is often weak and wasteful, and without Replication and Application, the results of HTS are often misleading.

scholarly journals Simulation data for the analysis of Bayesian posterior significance and effect size indices for the two-sample t-test to support reproducible medical research

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Riko Kelter
Keyword(s):  
Medical Research ◽  
Effect Size ◽  
Bayes Factor ◽  
Significance Test ◽  
T Test ◽  
P Value ◽  
Type I ◽  
Type I Errors ◽  
Statistical Programming ◽  
Region Of Practical Equivalence

Abstract Objectives The data presented herein represents the simulated datasets of a recently conducted larger study which investigated the behaviour of Bayesian indices of significance and effect size as alternatives to traditional p-values. The study considered the setting of Student’s and Welch’s two-sample t-test often used in medical research. It investigated the influence of the sample size, noise, the selected prior hyperparameters and the sensitivity to type I errors. The posterior indices used included the Bayes factor, the region of practical equivalence, the probability of direction, the MAP-based p-value and the e-value in the Full Bayesian Significance Test. The simulation study was conducted in the statistical programming language R. Data description The R script files for simulation of the datasets used in the study are presented in this article. These script files can both simulate the raw datasets and run the analyses. As researchers may be faced with different effect sizes, noise levels or priors in their domain than the ones studied in the original paper, the scripts extend the original results by allowing to recreate all analyses of interest in different contexts. Therefore, they should be relevant to other researchers.

DETECTION OF AN EMERGING NEW CLASS USING STATISTICAL HYPOTHESIS TESTING AND DENSITY ESTIMATION

2010 ◽  
Vol 24 (01) ◽  
pp. 1-14 ◽  
Author(s):  
CHEONG HEE PARK ◽  
HONGSUK SHIM
Keyword(s):  
Data Collection ◽  
Density Estimation ◽  
Statistical Significance ◽  
Significance Test ◽  
Statistical Hypothesis ◽  
Statistical Hypothesis Testing ◽  
New Class ◽  
Statistical Significance Test ◽  
Class Distribution ◽  
Over Time

Most traditional classifiers implicitly assume that data samples belong to at least one class among predefined several classes. However, all data patterns may not be known at the time of data collection or a new pattern can be emerging over time. In this paper, a new method is presented for monitoring the change in class distribution and detecting an emerging class. First a statistical significance test is designed which can signal for a change in class distribution. When an alarm for new class generation is set on, retrieval of new class members is performed using density estimation and entropy-based thresholding. Our experimental results demonstrate competent performances of the proposed method.

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