Quantifying uncertainty in statistical distribution of small sample data using Bayesian inference of unbounded Johnson distribution

2012 ◽  
Vol 6 (4) ◽  
pp. 311 ◽  
Author(s):  
Kun Marhadi ◽  
Satchi Venkataraman ◽  
Shantaram S. Pai
Keyword(s):  
Bayesian Inference ◽  
Small Sample ◽  
Statistical Distribution ◽  
Sample Data ◽  
Johnson Distribution ◽  
Quantifying Uncertainty

scholarly journals A Performance Prediction Method Based on Sliding Window Grey Neural Network for Inertial Platform

2021 ◽  
Vol 13 (23) ◽  
pp. 4864
Author(s):  
Langfu Cui ◽  
Qingzhen Zhang ◽  
Liman Yang ◽  
Chenggang Bai
Keyword(s):  
Neural Network ◽  
Prediction Models ◽  
Prediction Method ◽  
Sliding Window ◽  
Small Sample ◽  
Grey Theory ◽  
Sensing System ◽  
Performance Change ◽  
Sample Data ◽  
Platform System

An inertial platform is the key component of a remote sensing system. During service, the performance of the inertial platform appears in degradation and accuracy reduction. For better maintenance, the inertial platform system is checked and maintained regularly. The performance change of an inertial platform can be evaluated by detection data. Due to limitations of detection conditions, inertial platform detection data belongs to small sample data. In this paper, in order to predict the performance of an inertial platform, a prediction model for an inertial platform is designed combining a sliding window, grey theory and neural network (SGMNN). The experiments results show that the SGMNN model performs best in predicting the inertial platform drift rate compared with other prediction models.

scholarly journals Abnormal Detection to Big Data Using Deep Neural Networks

2021 ◽  
Vol 2068 (1) ◽  
pp. 012025
Author(s):  
Jian Zheng ◽  
Zhaoni Li ◽  
Jiang Li ◽  
Hongling Liu
Keyword(s):  
Neural Network ◽  
Big Data ◽  
Risk Model ◽  
Small Sample ◽  
Small Samples ◽  
Small Data ◽  
Data Segmentation ◽  
Sample Data ◽  
Segmentation Algorithms ◽  
The Common

Abstract It is difficult to detect the anomalies in big data using traditional methods due to big data has the characteristics of mass and disorder. For the common methods, they divide big data into several small samples, then analyze these divided small samples. However, this manner increases the complexity of segmentation algorithms, moreover, it is difficult to control the risk of data segmentation. To address this, here proposes a neural network approch based on Vapnik risk model. Firstly, the sample data is randomly divided into small data blocks. Then, a neural network learns these divided small sample data blocks. To reduce the risks in the process of data segmentation, the Vapnik risk model is used to supervise data segmentation. Finally, the proposed method is verify on the historical electricity price data of Mountain View, California. The results show that our method is effectiveness.

Bayesian jackknife empirical likelihood

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 981-988
Author(s):  
Y Cheng ◽  
Y Zhao
Keyword(s):  
Bayesian Inference ◽  
Empirical Likelihood ◽  
Small Sample ◽  
New Approach ◽  
U Statistics ◽  
Posterior Inference ◽  
Jackknife Empirical Likelihood ◽  
General Tool ◽  
Control Study ◽  
Better Than

Summary Empirical likelihood is a very powerful nonparametric tool that does not require any distributional assumptions. Lazar (2003) showed that in Bayesian inference, if one replaces the usual likelihood with the empirical likelihood, then posterior inference is still valid when the functional of interest is a smooth function of the posterior mean. However, it is not clear whether similar conclusions can be obtained for parameters defined in terms of $U$-statistics. We propose the so-called Bayesian jackknife empirical likelihood, which replaces the likelihood component with the jackknife empirical likelihood. We show, both theoretically and empirically, the validity of the proposed method as a general tool for Bayesian inference. Empirical analysis shows that the small-sample performance of the proposed method is better than its frequentist counterpart. Analysis of a case-control study for pancreatic cancer is used to illustrate the new approach.

Variation analysis driven by small-sample data for compliant aero-structure assembly

2019 ◽  
Vol 39 (1) ◽  
pp. 101-112 ◽  
Author(s):  
Biao Mei ◽  
Weidong Zhu ◽  
Yinglin Ke ◽  
Pengyu Zheng
Keyword(s):  
Probability Distributions ◽  
Small Sample ◽  
Accurate Estimation ◽  
Production Volume ◽  
Analysis Method ◽  
Variation Analysis ◽  
Content Type ◽  
Aircraft Manufacturing ◽  
Sample Data ◽  
Structure Assembly

Purpose Assembly variation analysis generally demands probability distributions of variation sources. However, due to small production volume in aircraft manufacturing, especially prototype manufacturing, the probability distributions are hard to obtain, and only the small-sample data of variation sources can be consulted. Thus, this paper aims to propose a variation analysis method driven by small-sample data for compliant aero-structure assembly. Design/methodology/approach First, a hybrid assembly variation model, integrating rigid effects with flexibility, is constructed based on the homogeneous transformation and elasticity mechanics. Then, the bootstrap approach is introduced to estimate a variation source based on small-sample data. The influences of bootstrap parameters on the estimation accuracy are analyzed to select suitable parameters for acceptable estimation performance. Finally, the process of assembly variation analysis driven by small-sample data is demonstrated. Findings A variation analysis method driven by small-sample data, considering both rigid effects and flexibility, is proposed for aero-structure assembly. The method provides a good complement to traditional variation analysis methods based on probability distributions of variation sources. Practical implications With the proposed method, even if probability distribution information of variation sources cannot be obtained, accurate estimation of the assembly variation could be achieved. The method is well suited for aircraft assembly, especially in the stage of prototype manufacturing. Originality/value A variation analysis method driven by small-sample data is proposed for aero-structure assembly, which can be extended to deal with other similar applications.

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