Bayesian Reliability Assessment Based on Dirichlet Prior Information

2010 ◽  
Vol 108-111 ◽  
pp. 1147-1151
Author(s):  
Hong Sheng Su
Keyword(s):  
Test Data ◽  
Prior Distribution ◽  
Prior Information ◽  
Reliability Assessment ◽  
Bayesian Theory ◽  
New Method ◽  
Small Samples ◽  
Complex Products ◽  
Dirichlet Prior ◽  
Direct Solid

To resolve the reliability assessment of the large-sized complex products under small samples, with the aid of the Dirichlet prior distribution and Bayesian theory, a new method is proposed in this paper. The method can fully apply Dirichlet prior information and test data to estimate the reliabilities of the products, and forecasting the success times during the products test. Compared other methods, it is simple, direct, solid, and high-effective. The investigations show that the method is quit handy and effective.

A Comparison of Approaches to Select the Informativeness of Priors in BVARs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jan Prüser ◽  
Christoph Hanck
Keyword(s):  
Impulse Response ◽  
Prior Information ◽  
Hierarchical Modeling ◽  
Small Samples ◽  
Model Parameters ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Vector Autoregressions ◽  
The Rich ◽  
Bayesian Vars

Abstract Vector autoregressions (VARs) are richly parameterized time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, in small samples the rich parametrization of VAR models may come at the cost of overfitting the data, possibly leading to imprecise inference for key quantities of interest such as impulse response functions (IRFs). Bayesian VARs (BVARs) can use prior information to shrink the model parameters, potentially avoiding such overfitting. We provide a simulation study to compare, in terms of the frequentist properties of the estimates of the IRFs, useful strategies to select the informativeness of the prior. The study reveals that prior information may help to obtain more precise estimates of impulse response functions than classical OLS-estimated VARs and more accurate coverage rates of error bands in small samples. Strategies based on selecting the prior hyperparameters of the BVAR building on empirical or hierarchical modeling perform particularly well.

scholarly journals Measurement of technical efficiency in the case of heterogeneity of technologies used between firms – Based on evidence from Polish crop farms

2021 ◽  
Author(s):  
Jerzy Marzec ◽  
Andrzej Pisulewski
Keyword(s):  
Technical Efficiency ◽  
Production Function ◽  
Prior Distribution ◽  
Prior Information ◽  
Stochastic Frontier ◽  
Returns To Scale ◽  
Random Coefficients ◽  
Point Of View ◽  
Model Specification ◽  
Stochastic Frontier Models

In the present study, we have investigated several competing stochastic frontier models which differ in terms of the form of the production function (Cobb-Douglas or translog), inefficiency distribution (half-normal or exponential distribution) and type of prior distribution for the parameters (hierarchical or non-hierarchical from the Bayesian point of view). This last distinction corresponds to a difference between random coefficients and fixed coefficients models. Consequently, this study aims to examine to what extent inferences about estimates of farms' efficiency depend on the above assumptions. Moreover, the study intends to investigate how far the production function's characteristics are affected by the choice of the type of prior distribution for the parameters. First of all, it was found that the form of the production function does not impact the efficiency scores. Secondly, we found that measures of technical efficiency are sensitive to distributional assumptions about the inefficiency term. Finally, we have revealed that estimates of technical efficiency are reasonably robust to the prior information about the parameters of crop farms' production technology. There is also a resemblance in the elasticity of output with respect to inputs between the models considered in this paper. Additionally, the measurement of returns to scale is not sensitive to model specification.

scholarly journals A new method for the determination of the δ18O composition of bone phosphate: applications to the thermal physiology of vertebrates

1992 ◽  
Vol 6 ◽  
pp. 269-269
Author(s):  
William J. Showers ◽  
Bernard Genna ◽  
Reese E. Barrick ◽  
Alfred G. Fischer
Keyword(s):  
Isotopic Analysis ◽  
Xrd Analysis ◽  
Exchange Chromatography ◽  
New Method ◽  
Small Samples ◽  
Thermal Physiology ◽  
Fossil Bone ◽  
Thin Sections ◽  
Bone Material ◽  
Silver Phosphate

A new method for the preparation of bone samples for δ18O-PO4 analysis has been developed. The phosphate from bone samples is separated and purified using ion exchange chromatography, and then precipitated as silver phosphate using the Firsching method. O2 is then extracted by reaction with bromine pentafluoride and converted to CO2 for isotopic analysis. Advantages of the silver phosphate technique over the bismuth phosphate technique are (1) the simplicity of the method, (2) silver phosphate is not hygroscopic so atmospheric water is not an oxygen contaminate, and (3) very small samples (2 mg to 10 mg) can be analyzed with an increase of precision compared to previous techniques. Iron and silica oxides added to Ag3PO4 standards produce no offset, which suggests that this new technique is not sensitive to interferences from cements commonly found in fossil bone material. Analyses have been performed on standards ranging in size from 30 mg to 2 mg with a σ1 of ± 0.05 per mil.The δ18O-PO4 compositional pattern of the bones of modern vertebrates have been analyzed to provide a base for the interpretation of the δ18O-PO4 pattern of fossil vertebrates. The average %PO4 in modern mammals and reptiles is approximately 15% with a σ1 of 2-3 %. The average %PO4 of fossil reptiles range from 10 to 25% with σ1 variations of up to 10%. The %PO4 variation can be related to cementation of void spaces in the bone material. XRD analysis reveals that calcite, dolomite, ankerite, and silica cements are commonly present. FTIR (Fourier Transform Infrared Spectroscopy) yields low indices calculated according to the formula of Shemesh, 1990 [GCA 54(9):2433]. Thin sections of the fossil bone material show detailed structures. All this evidence suggests that the fossil bone δ18O-PO4 composition is pristine and not altered by diagenesis. The total δ18O-PO4 σ1 variation of 10 or more skeletal elements analyzed for each individual specimen varies from 0.1 per mil for a domestic cow (Bos) to 0.8 per mil for a Komodo dragon (Varanus). Variations in between appear to be related to thermal physiology and variations in drinking water δ18O due to seasonality or migration.

A Non-Stationary Uncertainty Model and Bayesian Calibration of Strain-Life Models

2020 ◽  
Author(s):  
Arinan Dourado ◽  
Firat Irmak ◽  
Felipe Viana ◽  
Ali Gordon
Keyword(s):  
Fatigue Life ◽  
Test Data ◽  
Model Calibration ◽  
Prior Information ◽  
Bayesian Framework ◽  
Applied Strain ◽  
Prediction Intervals ◽  
Bayesian Calibration ◽  
Uncertainty Model ◽  
Inconel 617

Abstract The Coffin-Manson-Basquin-Haford (CMBH) model is a well-accepted strain-life relationship to model fatigue life as a function of applied strain. In this paper, we propose a non-stationary uncertainty model for the CMBH model, alongside a Bayesian framework for model calibration and estimation of confidence and prediction intervals. Using Inconel 617 coupon test data, we compared our approach to traditional stationary variance models. The proposed uncertainty model successfully captures the fact that the variance of fatigue life decreases as the applied strain decreases. Additionally, a discussion on how to use the proposed Bayesian framework to compensate for the lack of data by using prior information coming from a similar alloys is also presented considering Hastealloy-X and Inconel 617 coupon data.

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