scholarly journals Possibility Measure of Accepting Statistical Hypothesis

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 551
Author(s):  
Jung-Lin Hung ◽  
Cheng-Che Chen ◽  
Chun-Mei Lai
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Statistical Testing ◽  
Statistical Hypothesis ◽  
Statistical Hypothesis Testing ◽  
Test Statistic ◽  
Possibility Measure ◽  
Testing Approach ◽  
Hypothesis Testing Approach

Taking advantage of the possibility of fuzzy test statistic falling in the rejection region, a statistical hypothesis testing approach for fuzzy data is proposed in this study. In contrast to classical statistical testing, which yields a binary decision to reject or to accept a null hypothesis, the proposed approach is to determine the possibility of accepting a null hypothesis (or alternative hypothesis). When data are crisp, the proposed approach reduces to the classical hypothesis testing approach.

A parametric approach to kinship hypothesis testing using identity-by-descent parameters

2015 ◽  
Vol 14 (5) ◽  
Author(s):  
Manuel García-Magariños ◽  
Thore Egeland ◽  
Ignacio López-de-Ullibarri ◽  
Nils L. Hjort ◽  
Antonio Salas
Keyword(s):  
Hypothesis Testing ◽  
Family Relationships ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Statistical Hypothesis ◽  
Statistical Hypothesis Testing ◽  
Test Statistic ◽  
Identity By Descent ◽  
Classical Statistics ◽  
Competing Ideas

AbstractThere is a large number of applications where family relationships need to be determined from DNA data. In forensic science, competing ideas are in general verbally formulated as the two hypotheses of a test. For the most common paternity case, the null hypothesis states that the alleged father is the true father against the alternative hypothesis that the father is an unrelated man. A likelihood ratio is calculated to summarize the evidence. We propose an alternative framework whereby a model and the hypotheses are formulated in terms of parameters representing identity-by-descent probabilities. There are several advantages to this approach. Firstly, the alternative hypothesis can be completely general. Specifically, the alternative does not need to specify an unrelated man. Secondly, the parametric formulation corresponds to the approach used in most other applications of statistical hypothesis testing and so there is a large theory of classical statistics that can be applied. Theoretical properties of the test statistic under the null hypothesis are studied. An extension to trios of individuals has been carried out. The methods are exemplified using simulations and a real dataset of 27 Spanish Romani individuals.

scholarly journals A BAYESIAN HYPOTHESIS TESTING APPROACH FOR FINDING UPPER BOUNDS FOR PROBABILITIES THAT PAIRS OF SOFTWARE COMPONENTS FAIL SIMULTANEOUSLY

2011 ◽  
Vol 18 (03) ◽  
pp. 209-236 ◽  
Author(s):  
MONICA KRISTIANSEN ◽  
RUNE WINTHER ◽  
BENT NATVIG
Keyword(s):  
Hypothesis Testing ◽  
Prior Probability ◽  
Probability Distributions ◽  
Upper Bounds ◽  
Statistical Testing ◽  
Software Components ◽  
Reliability Models ◽  
Bayesian Hypothesis Testing ◽  
Testing Approach ◽  
Hypothesis Testing Approach

Predicting the reliability of software systems based on a component-based approach is inherently difficult, in particular due to failure dependencies between software components. One possible way to assess and include dependency aspects in software reliability models is to find upper bounds for probabilities that software components fail simultaneously and then include these into the reliability models. In earlier research, it has been shown that including partial dependency information may give substantial improvements in predicting the reliability of compound software compared to assuming independence between all software components. Furthermore, it has been shown that including dependencies between pairs of data-parallel components may give predictions close to the system's true reliability. In this paper, a Bayesian hypothesis testing approach for finding upper bounds for probabilities that pairs of software components fail simultaneously is described. This approach consists of two main steps: (1) establishing prior probability distributions for probabilities that pairs of software components fail simultaneously and (2) updating these prior probability distributions by performing statistical testing. In this paper, the focus is on the first step in the Bayesian hypothesis testing approach, and two possible procedures for establishing a prior probability distribution for the probability that a pair of software components fails simultaneously are proposed.

scholarly journals An introductory tutorial on Bayesian inference using a simple pedagogical tool

2017 ◽  
Author(s):  
Guillermo CAMPITELLI
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Traditional Approach ◽  
Postgraduate Students ◽  
Data Table ◽  
Null Hypothesis Testing ◽  
Testing Approach ◽  
Hypothesis Testing Approach

This tutorial on Bayesian inference targets psychological researchers who are trained in the null hypothesis testing approach and use of SPSS software. There a number ofexcellent quality tutorials on Bayesian inference, but their problem is that, they assume mathematical knowledge that most psychological researchers do not possess. Thistutorial starts from the idea that Bayesian inference is not more difficult than the traditional approach, but before being introduced to probability theory notation is necessary for the newcomer to understand simple probability principles, which could be explained without mathematical formulas or probability notation. For this purpose in this tutorial I use a simple tool-the parameter-data table-to explain how probability theory can easily be used to make inferences in research. Then I compare the Bayesian and the null hypothesis testing approach using the same tool. Only after having introduced these principles I show the formulas and notations and explain how they relate to the parameter-data table. It is to be expected that this tutorial will increase the use of Bayesian inference by psychological researchers. Moreover, Bayesian researchers may use this tutorial to teach Bayesian inference to undergraduate or postgraduate students.

scholarly journals Diferencias entre coeficientes alfa, con muestras y partes pequeñas; adenda

2021 ◽  
Author(s):  
Cesar Merino-Soto
Keyword(s):  
Clinical Practice ◽  
Measurement Error ◽  
Computer Program ◽  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Small Samples ◽  
Testing Approach ◽  
The Difference ◽  
Hypothesis Testing Approach ◽  
Reliability Coefficients

This paper presenting a computer program written in VB 6.0, to calculate the difference between internal consistency coefficients (Cronbach’s alpha) obtained in independent small samples and with instruments have a small number of parts or items. The comparison of reliability coefficients allow to identify possible differences in amount of measurement error in instruments; this methodology use the hypothesis testing approach for test the null hypothesis of equally reliability coefficients. This situation is tending to be common in clinical practice between psychologists or allied career, and even in the construction phases of instruments of measurement, for example in pilot samples. The proposed technique is from the work of Feldt and Kim (2006), and offers a viable and interesting methodological proposal that expands the analysis of the reliability of instruments of psychological and educational measurement.

scholarly journals Identification of dominant hydrological mechanisms using Bayesian inference, multiple statistical hypothesis testing and flexible models

2021 ◽  
Author(s):  
Cristina Prieto ◽  
Dmitri Kavetski ◽  
Nataliya Nataliya Le Vine ◽  
César Álvarez ◽  
Raúl Medina
Keyword(s):  
Hypothesis Testing ◽  
Real Data ◽  
Hydrological Modelling ◽  
Statistical Hypothesis ◽  
Model Errors ◽  
Statistical Hypothesis Testing ◽  
Test Statistic ◽  
Identification Method ◽  
Study Results ◽  
Model Structures

<p>In hydrological modelling, the identification of hydrological model mechanisms best suited for representing individual hydrological (physical) processes is a major research and operational challenge. We present a statistical hypothesis-testing perspective to identify dominant hydrological mechanism. The method combines: (i) Bayesian estimation of posterior probabilities of individual mechanisms from a given ensemble of model structures; (ii) a test statistic that defines a “dominant” mechanism as a mechanism more probable than all its alternatives given observed data; (iii) a flexible modelling framework to generate model structures using combinations of available mechanisms. The uncertainty in the test statistic is approximated via bootstrap from the ensemble of model structures. Synthetic and real data experiments are conducted using 624 model structures from the hydrological modelling system FUSE and data from the Leizarán catchment in northern Spain. The findings show that the mechanism identification method is reliable: it identifies the correct mechanism as dominant in all synthetic trials where an identification is made. As data/model errors increase, statistical power (identifiability) decreases, manifesting as trials where no mechanism is identified as dominant. The real data case study results are broadly consistent with the synthetic analysis, with dominant mechanisms identified for 4 of 7 processes. Insights on which processes are most/least identifiable are also reported. The mechanism identification method is expected to contribute to broader community efforts on improving model identification and process representation in hydrology.</p>

scholarly journals Diferencias entre coeficientes alfa de Cronbach, con muestras y partes pequeñas: Un programa VB

2016 ◽  
Vol 32 (2) ◽  
pp. 587 ◽  
Author(s):  
César Merino-Soto
Keyword(s):  
Clinical Practice ◽  
Measurement Error ◽  
Computer Program ◽  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Small Samples ◽  
Testing Approach ◽  
The Difference ◽  
Hypothesis Testing Approach ◽  
Reliability Coefficients

<p>This paper presenting a computer program written in VB 6.0, to calculate the difference between internal consistency coefficients (Cronbach’s alpha) obtained in independent small samples and with instruments have a small number of parts or items. The comparison of reliability coefficients allow to identify possible differences in amount of measurement error in instruments; this methodology use the hypothesis testing approach for test the null hypothesis of equally reliability coefficients. This situation is tending to be common in clinical practice between psychologists or allied career, and even in the construction phases of instruments of measurement, for example in pilot samples. The proposed technique is from the work of Feldt and Kim (2006), and offers a viable and interesting methodological proposal that expands the analysis of the reliability of instruments of psychological and educational measurement.</p>

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