scholarly journals Bayesian Methods of Representative Values of Variable Actions

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 346
Author(s):  
Xudong Wang ◽  
Jitao Yao
Keyword(s):  
Standard Deviation ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Engineering Practice ◽  
Regression Estimation ◽  
Type I ◽  
Statistical Uncertainty ◽  
Good Precision ◽  
Classical Statistics ◽  
Informative Prior Distribution

In engineering practice, it is sometimes necessary to infer the representative value of variable action under the condition that the test data is insufficient, but the classical statistics methods adopted now do not take into account the influences of statistical uncertainty, and the inferring results are always small, especially when characteristic and frequent values are inferred. Variable actions usually obey a type I maximum distribution, so the linear regression estimation of the tantile of type I minimum distribution can be employed to infer their characteristic and frequent values. However, it is inconvenient to apply and cannot totally meet the demands of characteristic and frequent values inference. Applying Jeffreys non-informative prior distribution, Bayesian methods for inferring characteristic and frequent values of variable actions are put forward, including that with known standard deviation, which could yield more advantageous results. The methods proposed are convenient and flexible, possessing good precision.

scholarly journals Estimating the Gumbel-Barnett copula parameter of dependence

2018 ◽  
Vol 41 (1) ◽  
pp. 53-73 ◽  
Author(s):  
Jennyfer Portilla Yela ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Empirical Evaluation ◽  
Bayesian Estimator ◽  
Dependence Structure ◽  
Type I ◽  
Copula Parameter

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

scholarly journals Variance prior specification for a basket trial design using Bayesian hierarchical modeling

2018 ◽  
Vol 16 (2) ◽  
pp. 142-153 ◽  
Author(s):  
Kristen M Cunanan ◽  
Alexia Iasonos ◽  
Ronglai Shen ◽  
Mithat Gönen
Keyword(s):  
Standard Deviation ◽  
Prior Distribution ◽  
Hierarchical Modeling ◽  
Bayesian Hierarchical Modeling ◽  
Bayesian Hierarchical ◽  
Inverse Gamma ◽  
Wide Range ◽  
Basket Trial ◽  
Basket Trials ◽  
Variance Parameter

Background: In the era of targeted therapies, clinical trials in oncology are rapidly evolving, wherein patients from multiple diseases are now enrolled and treated according to their genomic mutation(s). In such trials, known as basket trials, the different disease cohorts form the different baskets for inference. Several approaches have been proposed in the literature to efficiently use information from all baskets while simultaneously screening to find individual baskets where the drug works. Most proposed methods are developed in a Bayesian paradigm that requires specifying a prior distribution for a variance parameter, which controls the degree to which information is shared across baskets. Methods: A common approach used to capture the correlated binary endpoints across baskets is Bayesian hierarchical modeling. We evaluate a Bayesian adaptive design in the context of a non-randomized basket trial and investigate three popular prior specifications: an inverse-gamma prior on the basket-level variance, a uniform prior and half-t prior on the basket-level standard deviation. Results: From our simulation study, we can see that the inverse-gamma prior is highly sensitive to the input hyperparameters. When the prior mean value of the variance parameter is set to be near zero [Formula: see text], this can lead to unacceptably high false-positive rates [Formula: see text] in some scenarios. Thus, use of this prior requires a fully comprehensive sensitivity analysis before implementation. Alternatively, we see that a prior that places sufficient mass in the tail, such as the uniform or half-t prior, displays desirable and robust operating characteristics over a wide range of prior specifications, with the caveat that the upper bound of the uniform prior and the scale parameter of the half-t prior must be larger than 1. Conclusion: Based on the simulation results, we recommend that those involved in designing basket trials that implement hierarchical modeling avoid using a prior distribution that places a majority of the density mass near zero for the variance parameter. Priors with this property force the model to share information regardless of the true efficacy configuration of the baskets. Many commonly used inverse-gamma prior specifications have this undesirable property. We recommend to instead consider the more robust uniform prior or half-t prior on the standard deviation.

A Characterization of the Exponential Distribution

1994 ◽  
Vol 44 (1-2) ◽  
pp. 123-126
Author(s):  
E. S. Jebvanand ◽  
N. Unnikrishnan Nair
Keyword(s):  
Exponential Distribution ◽  
Prior Distribution ◽  
Future Observation ◽  
Informative Prior ◽  
Informative Prior Distribution ◽  
Continuous Population

In this note we prove that the exponential distribution is characterized by the property [Formula: see text] where Y is a future observation and x1, x2,…, x n are identical and independently distributed observations from a continuous population with density f( x; a), where a is assumed to have a non-informative prior distribution

scholarly journals Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System

2019 ◽  
Vol 42 (1) ◽  
pp. 223-143
Author(s):  
Víctor H. Salinas Torres ◽  
Cristián A. Vásquez ◽  
José S. Romeo
Keyword(s):  
Prior Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Coherent System ◽  
Repairable System ◽  
Unit System ◽  
System A ◽  
Informative Prior ◽  
Informative Prior Distribution

 This work presents a Bayesian approach for estimating the limiting availability of an one-unit repairable system. A Bayesian analysis is developed considering an informative prior and a less informative prior distribution, respectively. Simulations are presented to study the performance of the Bayesian solutions. The maximum likelihood method is also revisited. Finally, a case study is considered, the Bayesian methodology is applied to estimate the limiting availability of a palletizer, which is used in the packaging of glass bottles. Extensions to a coherent system are also discussed.

scholarly journals Estimating Remaining Useful Life for Degrading Systems with Large Fluctuations

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Dang-Bo Du ◽  
Jian-Xun Zhang ◽  
Zhi-Jie Zhou ◽  
Xiao-Sheng Si ◽  
Chang-Hua Hu
Keyword(s):  
Stochastic Process ◽  
Standard Deviation ◽  
Health Management ◽  
Prediction Method ◽  
Remaining Useful Life ◽  
Threshold Function ◽  
Engineering Practice ◽  
Practical Case ◽  
Degradation Data ◽  
Useful Life

Remaining useful life (RUL) prediction method based on degradation trajectory has been one of the most important parts in prognostics and health management (PHM). In the conventional model, the degradation data are usually used for degradation modeling directly. In engineering practice, the degradation of many systems presents a volatile situation, that is, fluctuation. In fact, the volatility of degradation data shows the stability of system, so it could be used to reflect the performance of system. As such, this paper proposes a new degradation model for RUL estimation based on the volatility of degradation data. Firstly the degradation data are decomposed into trend items and random items, which are defined as a stochastic process. Then the standard deviation of the stochastic process is defined as another performance variable because standard deviation reflects the system performance. Finally the Wiener process and the normal stochastic process are used to model the trend items and random items separately, and then the probability density function (PDF) of the RUL is obtained via a redefined failure threshold function that combines the trend items and the standard deviation of the random items. Two practical case studies demonstrate that, compared with traditional approaches, the proposed model can deal with the degradation data with many fluctuations better and can get a more reasonable result which is convenient for maintenance decision.

The Duration of Undiagnosed Bipolar Disorder: Impact of Substance use Disorders co-morbidity

2017 ◽  
Vol 41 (S1) ◽  
pp. S132-S132
Author(s):  
S. Ben Mustapha ◽  
W. Homri ◽  
L. Jouini ◽  
R. Labbane
Keyword(s):  
Bipolar Disorder ◽  
Substance Use ◽  
Standard Deviation ◽  
Substance Use Disorders ◽  
Mood Stabilizer ◽  
Type I ◽  
Addictive Behaviour ◽  
Bipolar Disease ◽  
Co Morbidity ◽  
The Impact

AimsStudy the impact of substance use disorders (SUD) co-morbidity on the duration of undiagnosed bipolar disorder (DUBP).MethodsCase-control study during a period of six months from July 2015 to December 2015. One hundred euthymic patients with BD (type I, II or unspecified) were recruited in the department of psychiatry C Razi Hospital, during their follow-up. Two groups were individualized by the presence or not of a SUD co-morbidity. In our study DUBP was defined as the period between the first symptoms and the beginning of treatment by a mood stabilizer.ResultsThe beginning of addictive behaviour preceded the installation of bipolar disease in 32% of cases. Installation of bipolar disorder preceded the installation of addictive behaviour in 12% of cases. The beginning of addictive behaviour was concomitant with the installation of bipolar disease in 6% of cases. The average DUBP in the full sample was 4.80 years with a standard deviation of 8.04 and extremes ranging from 0.08 to 37.5.The average DUBP in patients with SUD co-morbidity was 5.91 years with a standard deviation of 8.16 and extremes ranging from 0.08 to 35, and 3.68 years with a standard deviation of 7.84 and extremes ranging from 0.08 to 37.5 in patients without SUD co-morbidity.ConclusionsAccording to studies over two thirds of patients with bipolar disorder received misdiagnoses before diagnosis of BD, and among the factors involved can report the presence of SUD co-morbidity. Hence, we should detect BD among patients with SUD.Disclosure of interestThe authors have not supplied their declaration of competing interest.

scholarly journals An Introduction to Fuzzy Testing of Multialternative Hypotheses for Group of Samples with the Single Parameter: Through the Fuzzy Confidence Interval of Region of Acceptance

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Manikandan Harikrishnan ◽  
Jeyabharathi Sundarrajan ◽  
Muthuraj Rengasamy
Keyword(s):  
Standard Deviation ◽  
Statistical Significance ◽  
Group Testing ◽  
Fuzzy Group ◽  
Classical Statistics ◽  
Two Samples ◽  
Significant Difference ◽  
Alternative Hypotheses ◽  
Sole Criterion ◽  
First Time

Classical statistics and many data mining methods rely on “statistical significance” as a sole criterion for evaluating alternative hypotheses. It is very useful to find out the significant difference existing between the samples as well as the population or between two samples. But in this paper, the researchers try to apply the concepts of fuzzy group testing of hypothesis problem between multi group of samples of same size or different, through comparing the parameters like mean, standard deviation, and so forth. Hence we can compare multigroups such that they have the significant difference in their mean or standard deviation or other parameters through the fuzzy group testing of multihypotheses. The authors introduced and investigated the concepts very first time through fuzzy analysis that can decide which group(s) or samples can be taken for further investigation and eitherH0is rejected or accepted and hence the next discussion provides the properties of group of samples which may result in the optimized solution for the problem.

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