scholarly journals An Implementation of Empirical Bayesian Inference and Non-Null Bootstrapping for Threshold Selection and Power Estimation in Multiple and Single Statistical Testing

2018 ◽  
Author(s):  
Bahman Nasseroleslami
Keyword(s):  
Bayesian Inference ◽  
Probability Density ◽  
Statistical Power ◽  
Statistical Tests ◽  
Gaussian Mixture ◽  
Statistical Testing ◽  
Test Statistics ◽  
Empirical Bayesian ◽  
Statistical Measures ◽  
Wide Range

AbstractThe majority of conclusions and interpretations in quantitative sciences such as neuroscience are based on statistical tests. However, the statistical inferences, especially in multivariate analyses, commonly rely on the p-values, but not on more expressive measures such as posterior probabilities, false discovery rates (FDR) and statistical power (1 − β). The aim of this report is to make these statistical measures further accessible in single and multiple statistical testing. For multiple testing, the Empirical Bayesian Inference (Efron et al., 2001; Efron, 2007) was implemented using non-parametric test statistics (e.g. the Area Under the Curve of the Receiving Operator Characteristics Curve or Spearman’s rank correlation) and Gaussian Mixture Model estimation of the probability density function of the original and bootstrapped data. For single statistical tests, the same test statistics were used to construct and estimate the null and non-null probability density functions using bootstrapping under null and non-null grouping assumptions. Simulations were used to test the reliability of the results under a wide range of conditions. The results show conformity to the real truth in the simulated conditions, which is held under various conditions imposed on the simulated data. The open-source MATLAB codes are provided and the utility of the approach has been exemplified and discussed for real-world electroencephalographic signals. This implementation of Empirical Bayesian Inference and informed selection of statistical thresholds are expected to facilitate more realistic scientific deductions in versatile fields, especially in neuroscience, neural signal analysis and neuro-imaging.

scholarly journals Inferring exemplar discriminability in brain representations

2016 ◽  
Author(s):  
Hamed Nili ◽  
Alexander Walther ◽  
Arjen Alink ◽  
Nikolaus Kriegeskorte
Keyword(s):  
Fixed Effects ◽  
Statistical Tests ◽  
Random Effect ◽  
Nonparametric Tests ◽  
Test Statistics ◽  
Brain Response ◽  
Test Statistic ◽  
Mahalanobis Distances ◽  
Linear Discriminant ◽  
Wide Range

AbstractRepresentational distinctions within categories are important in all perceptual modalities and also in cognitive and motor representations. Recent pattern-information studies of brain activity have used condition-rich designs to sample the stimulus space more densely. To test whether brain response patterns discriminate among a set of stimuli (e.g. exemplars within a category) with good sensitivity, we can pool statistical evidence over all pairwise comparisons. A popular test statistic reflecting exemplar information is the exemplar discriminability index (EDI), which is defined as the average of the pattern dissimilarity estimates between different exemplars minus the average of the pattern dissimilarity estimates between repetitions of identical exemplars. The EDI is commonly tested with a t test (H0: population mean EDI = 0) across subjects (subject as random effect). However, it is unclear whether this approach is either valid or optimal. Here we describe a wide range of statistical tests of exemplar discriminability and assess the validity (specificity) and power (sensitivity) of each test. The tests include previously used and novel, parametric and nonparametric tests, which treat subject as a random or fixed effect, and are based on different dissimilarity measures, different test statistics, and different inference procedures. We use simulated and real data to determine which tests are valid and which are most sensitive. The popular across-subject t test of the EDI (typically using correlation distance as the pattern dissimilarity measure) requires the assumption that the EDI is 0-mean normal under H0, which is not strictly true. Reassuringly, our simulations suggest that the test controls the false-positives rate at the nominal level and is thus valid in practice. However, test statistics based on average Mahalanobis distances or average linear-discriminant t values (both accounting for the multivariate error covariance among responses) are substantially more powerful for both random- and fixed-effects inference. We suggest preferred procedures for safely and sensitively detecting subtle pattern differences between exemplars.

scholarly journals A robust and adaptive framework for interaction testing in quantitative traits between multiple genetic loci and exposure variables

2021 ◽  
Author(s):  
Julian Hecker ◽  
Dmitry Prokopenko ◽  
Matthew Moll ◽  
Sanghun Lee ◽  
Wonji Kim ◽  
...  
Keyword(s):  
Statistical Power ◽  
Quantitative Traits ◽  
Risk Scores ◽  
Environment Interaction ◽  
Test Statistics ◽  
Robust Test ◽  
Gene Environment Interaction ◽  
Gene Environment ◽  
Wide Range ◽  
Interaction Testing

AbstractThe identification and understanding of gene-environment interactions can provide insights into the pathways and mechanisms underlying complex diseases. However, testing for gene-environment interaction remains a challenge since statistical power is often limited, the specification of environmental effects is nontrivial, and such misspecifications can lead to false positive findings. To address the lack of statistical power, recent methods aim to identify interactions on an aggregated level using, for example, polygenic risk scores. While this strategy increases power to detect interactions, identifying contributing key genes and pathways is difficult based on these global results.Here, we propose RITSS (Robust Interaction Testing using Sample Splitting), a gene-environment interaction testing framework for quantitative traits that is based on sample splitting and robust test statistics. RITSS can incorporate multiple genetic variants and/or multiple environmental factors. Using sample splitting, a screening step enables the selection and combination of potential interactions into scores with improved interpretability, based on the user’s unrestricted choices for statistical/machine learning approaches. In the testing step, the application of robust test statistics minimizes the susceptibility of the results to main effect misspecifications.Using extensive simulation studies, we demonstrate that RITSS controls the type 1 error rate in a wide range of scenarios. In an application to lung function phenotypes and human height in the UK Biobank, RITSS identified genome-wide significant interactions with subcomponents of genetic risk scores. While the contributing single variant interactions are moderate, our analysis results indicate interesting interaction patterns that result in strong aggregated signals that provide further insights into gene-environment interaction mechanisms.

scholarly journals On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3837
Author(s):  
Rafael Orellana ◽  
Rodrigo Carvajal ◽  
Pedro Escárate ◽  
Juan C. Agüero
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dynamic Systems ◽  
Gaussian Mixture ◽  
Error Model ◽  
Fault Detection And Diagnosis ◽  
Deterministic Models ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

The Measurement of Performance in Probabilistic Diagnosis

1978 ◽  
Vol 17 (04) ◽  
pp. 227-237 ◽  
Author(s):  
J. Hilden ◽  
J. D. F. Habbema ◽  
B. Bjerregaard
Keyword(s):  
Acute Abdomen ◽  
External Validity ◽  
Statistical Tests ◽  
Computer Aided Diagnosis ◽  
Discriminatory Power ◽  
Statistical Measures ◽  
Computer Aided ◽  
Size Bias ◽  
Aided Diagnosis ◽  
Probabilistic Diagnosis

Attention is focused on one important aspect of good performance in probabilistic diagnosis, the »reliability« (external validity) of probabilistic assertions: a diagnostic alternative claimed to be 90% certain, say, must occur neither more nor less than nine times out of ten on the average. Statistical measures are offered by which departures from such perfect reliability can be estimated, and statistical tests are developed in order to test the hypothesis of perfect reliability. The specific reliability defects looked for include overconfident diagnoses and so-called size bias (common diseases being over diagnosed). Reliability is contrasted with discriminatory power and other performance aspects. The illustrative data derive from a study of computer-aided diagnosis of the acute abdomen.

scholarly journals Seismic fragility of bridges: An approach coupling multiple-stripe analysis and Gaussian mixture for multicomponent structures

2021 ◽  
pp. 875529302110361
Author(s):  
Pedro Alexandre Conde Bandini ◽  
Jamie Ellen Padgett ◽  
Patrick Paultre ◽  
Gustavo Henrique Siqueira
Keyword(s):  
Statistical Tests ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Seismic Fragility ◽  
Correlated Response ◽  
Eastern Canada ◽  
Seismic Engineering ◽  
Response Data ◽  
Demand Models ◽  
Mean Annual Frequency

An approach is developed to build multivariate probabilistic seismic demand models (PSDMs) of multicomponent structures based on the coupling of multiple-stripe analysis and Gaussian mixture models. The proposed methodology is eminently flexible in terms of adopted assumptions, and a classic highway bridge in Eastern Canada is used to present an application of the new approach and to investigate its impact on seismic fragility analysis. Traditional PSDM methods employ lognormal distribution and linear correlation between pairs of components to fit the seismic response data, which may lead to poor statistical modeling. Using ground motion records rigorously selected for the investigated site, data are generated via response history analysis, and appropriate statistical tests are then performed to show that these hypotheses are not always valid on the response data of the case-study bridge. The clustering feature of the proposed methodology allows the construction of a multivariate PSDM with refined fitting to the correlated response data, introducing low bias into the fragility functions and mean annual frequency of violating damage states, which are crucial features for decision making in the context of performance-based seismic engineering.

scholarly journals Analysis of lithofacies cyclicity in the Miocene Coal Complex of the Bełchatów lignite deposit, south-central Poland

Geologos ◽  
2015 ◽  
Vol 21 (4) ◽  
pp. 285-302 ◽  
Author(s):  
Wojciech Mastej ◽  
Tomasz Bartuś ◽  
Jerzy Rydlewski
Keyword(s):  
Statistical Tests ◽  
Surface Flow ◽  
Alluvial Fan ◽  
Statistical Testing ◽  
New Approach ◽  
Sedimentary Environments ◽  
Carbonate Sedimentation ◽  
South Central ◽  
Sedimentation Model ◽  
Almost All

Abstract Markov chain analysis was applied to studies of cyclic sedimentation in the Coal Complex of the Bełchatów mining field (part of the Bełchatów lignite deposit). The majority of ambiguous results of statistical testing that were caused by weak, statistically undetectable advantage of either cyclicity over environmental barriers or vice versa, could be explained if only the above-mentioned advantages appeared in the neighbourhood. Therefore, in order to enhance the credibility of statistical tests, a new approach is proposed here in that matrices of observed transition numbers from different boreholes should be added to increase statistical reliability if they originated in a homogeneous area. A second new approach, which consists of revealing statistically undetectable cyclicity of lithofacies alternations, is proposed as well. All data were derived from the mining data base in which differentiation between lithology and sedimentary environments was rather weak. For this reason, the methodological proposals are much more important than details of the sedimentation model in the present paper. Nevertheless, they did reveal some interesting phenomena which may prove important in the reconstruction of peat/lignite environmental conditions. First of all, the presence of cyclicity in the sedimentation model, i.e., cyclic alternation of channel and overbank deposits, represents a fluvial environment. It was also confirmed that the lacustrine subenvironment was cut off from a supply of clastic material by various types of mire barriers. Additionally, our analysis revealed new facts: (i) these barriers also existed between lakes in which either carbonate or clay sedimentation predominated; (ii) there was no barrier between rivers and lakes in which clay sedimentation predominated; (iii) barriers were less efficient in alluvial fan areas but were perfectly tight in regions of phytogenic or carbonate sedimentation; (iv) groundwater, rather than surface flow, was the main source of CaCO3 in lakes in which carbonate sedimentation predominated; (v) a lack of cyclic alternation between abandoned channels and pools with clayey sedimentation; (vi) strong evidence for autocyclic alternation of phytogenic subenvironments and lakes in which carbonate sedimentation predominated was found in almost all areas studied.

Contribution of green manufacturing for realizing business performance in Indian small and medium scale organizations (SME’s)

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mahakdeep Singh ◽  
Kanwarpreet Singh ◽  
Amanpreet Singh Sethi
Keyword(s):  
Business Performance ◽  
Discriminant Validity ◽  
Statistical Tests ◽  
Pearson Correlation ◽  
Green Manufacturing ◽  
Statistical Testing ◽  
Content Type ◽  
Medium Scale ◽  
Green Practices ◽  
Significant Factors

Purpose The current manuscript is focused on evaluating the capabilities of green practices that affect various business performance (BP) parameters of small and medium scale Indian manufacturing enterprises (SME’s). This study aims to obtain multiple significant factors that influence the implementation of green practices. Design/methodology/approach The manuscript focuses on statistical testing of responses obtained from 168 Indian SMEs to determine the relationship between input parameters and BP parameters. This paper starts with deploying tests such as Cronbach alpha and inter-item covariance test to obtain confidence in data collected, followed by various statistical tests such as Pearson correlation, multiple regression, canonical correlation to extract various significant factors the study. Further Games-Howell post hoc test is deployed to evaluate the significant improvements in BP gained over a reasonable duration of time. Finally, a discriminant validity test is used to find out the success or failure of the organizations that participated in the survey. Findings This research contributes to the holistic effect of green manufacturing (GM) toward gaining improvements in terms of different BP parameters taken for the study. It has been found that various input factors such as customer attributes, adoption of new technology, social pressure and government pressure are the main parameters for GM implementation. Further, it is observed that those at the maturity phase of GM implementation are reaping higher benefits than the organizations at the transition and stability phase. Originality/value The current study has been accomplished in Indian SME manufacturing organizations to investigate the effects of GM implementation in the organization. Although research findings imply the effective use of green practices within the organization to reap BP parameters and improve the market’s competitive image, the study cannot be generalized and can be used as an insight for both academicians and end-users in understanding the overall achievements of GM.

The null-hypothesis significance-test procedure is still warranted

1998 ◽  
Vol 21 (2) ◽  
pp. 228-235 ◽  
Author(s):  
Siu L. Chow
Keyword(s):  
Null Hypothesis ◽  
Statistical Power ◽  
Meta Analysis ◽  
Statistical Significance ◽  
Test Procedure ◽  
Significance Test ◽  
Null Hypothesis Significance Test ◽  
Wide Range ◽  
Statistical Hypotheses ◽  
Alternative Hypotheses

Entertaining diverse assumptions about empirical research, commentators give a wide range of verdicts on the NHSTP defence in Statistical significance. The null-hypothesis significance-test procedure (NHSTP) is defended in a framework in which deductive and inductive rules are deployed in theory corroboration in the spirit of Popper's Conjectures and refutations (1968b). The defensible hypothetico-deductive structure of the framework is used to make explicit the distinctions between (1) substantive and statistical hypotheses, (2) statistical alternative and conceptual alternative hypotheses, and (3) making statistical decisions and drawing theoretical conclusions. These distinctions make it easier to show that (1) H0 can be true, (2) the effect size is irrelevant to theory corroboration, and (3) “strong” hypotheses make no difference to NHSTP. Reservations about statistical power, meta-analysis, and the Bayesian approach are still warranted.

Comparison of Several Acoustic Modeling Techniques for Speech Emotion Recognition

2016 ◽  
Vol 7 (1) ◽  
pp. 58-68 ◽  
Author(s):  
Imen Trabelsi ◽  
Med Salim Bouhlel
Keyword(s):  
Emotion Recognition ◽  
Linear Prediction ◽  
Recognition Rate ◽  
Gaussian Mixture ◽  
Speech Emotion Recognition ◽  
Support Vector ◽  
Emotional States ◽  
Wide Range ◽  
Leibler Divergence ◽  
Perceptual Linear Prediction

Automatic Speech Emotion Recognition (SER) is a current research topic in the field of Human Computer Interaction (HCI) with a wide range of applications. The purpose of speech emotion recognition system is to automatically classify speaker's utterances into different emotional states such as disgust, boredom, sadness, neutral, and happiness. The speech samples in this paper are from the Berlin emotional database. Mel Frequency cepstrum coefficients (MFCC), Linear prediction coefficients (LPC), linear prediction cepstrum coefficients (LPCC), Perceptual Linear Prediction (PLP) and Relative Spectral Perceptual Linear Prediction (Rasta-PLP) features are used to characterize the emotional utterances using a combination between Gaussian mixture models (GMM) and Support Vector Machines (SVM) based on the Kullback-Leibler Divergence Kernel. In this study, the effect of feature type and its dimension are comparatively investigated. The best results are obtained with 12-coefficient MFCC. Utilizing the proposed features a recognition rate of 84% has been achieved which is close to the performance of humans on this database.

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