Application of Markov Chain Monte-Carlo Multiple Imputation Method to Deal with Missing Data from the Mechanism of MNAR in Sensitivity Analysis for a Longitudinal Clinical Trial

2017 ◽  
pp. 233-252 ◽  
Author(s):  
Wei Sun
Keyword(s):  
Clinical Trial ◽  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Missing Data ◽  
Multiple Imputation ◽  
Imputation Method ◽  
Multiple Imputation Method

Markov Chain Monte Carlo Multiple Imputation Using Bayesian Networks for Incomplete Intelligent Transportation Systems Data

2005 ◽  
Vol 1935 (1) ◽  
pp. 57-67 ◽  
Author(s):  
Daiheng Ni ◽  
John D. Leonard
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Missing Data ◽  
Bayesian Network ◽  
Intelligent Transportation Systems ◽  
Intelligent Transportation ◽  
Transportation Systems ◽  
Imputation Method ◽  
Raw Data

The rich data on intelligent transportation systems (ITS) are a precious resource for transportation researchers and practitioners. However, the usability of this resource is greatly limited by missing data. Many imputation methods have been proposed in the past decade. However, some issues are still not addressed or are not sufficiently addressed, for example, the missing of entire records, temporal correlation in observations, natural characteristics in raw data, and unbiased estimates for missing values. This paper proposes an advanced imputation method based on recent development in other disciplines, especially applied statistics. The method uses a Bayesian network to learn from the raw data and a Markov chain Monte Carlo technique to sample from the probability distributions learned by the Bayesian network. It imputes the missing data multiple times and makes statistical inferences about the result. In addition, the method incorporates a time series model so that it allows data missing in entire rows–-an unfavorable missing pattern frequently seen in ITS data. Empirical study shows that the proposed method is robust and accurate. It is ideal for use as a high-quality imputation method for off-line application.

Sensitivity analysis of an urban stormwater microorganism model

2010 ◽  
Vol 62 (6) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. T. McCarthy ◽  
A. Deletic ◽  
V. G. Mitchell ◽  
C. Diaper
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Analysis ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Urban Stormwater ◽  
Urban Catchments ◽  
Two Parameters

This paper presents the sensitivity analysis of a newly developed model which predicts microorganism concentrations in urban stormwater (MOPUS—MicroOrganism Prediction in Urban Stormwater). The analysis used Escherichia coli data collected from four urban catchments in Melbourne, Australia. The MICA program (Model Independent Markov Chain Monte Carlo Analysis), used to conduct this analysis, applies a carefully constructed Markov Chain Monte Carlo procedure, based on the Metropolis-Hastings algorithm, to explore the model's posterior parameter distribution. It was determined that the majority of parameters in the MOPUS model were well defined, with the data from the MCMC procedure indicating that the parameters were largely independent. However, a sporadic correlation found between two parameters indicates that some improvements may be possible in the MOPUS model. This paper identifies the parameters which are the most important during model calibration; it was shown, for example, that parameters associated with the deposition of microorganisms in the catchment were more influential than those related to microorganism survival processes. These findings will help users calibrate the MOPUS model, and will help the model developer to improve the model, with efforts currently being made to reduce the number of model parameters, whilst also reducing the slight interaction identified.

Regression multiple imputation for missing data analysis

2020 ◽  
Vol 29 (9) ◽  
pp. 2647-2664
Author(s):  
Lili Yu ◽  
Liang Liu ◽  
Karl E Peace
Keyword(s):  
Data Analysis ◽  
Missing Data ◽  
Multiple Imputation ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Imputation Method ◽  
Missing Data Analysis ◽  
Multiple Imputation Method ◽  
Asymptotically Efficient ◽  
Parameter Estimators

Iterative multiple imputation is a popular technique for missing data analysis. It updates the parameter estimators iteratively using multiple imputation method. This technique is convenient and flexible. However, the parameter estimators do not converge point-wise and are not efficient for finite imputation size m. In this paper, we propose a regression multiple imputation method. It uses the parameter estimators obtained from multiple imputation method to estimate the parameter estimators based on expectation maximization algorithm. We show that the resulting estimators are asymptotically efficient and converge point-wise for small m values, when the iteration k of the iterative multiple imputation goes to infinity. We evaluate the performance of the new proposed methods through simulation studies. A real data analysis is also conducted to illustrate the new method.

Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods

2019 ◽  
Vol 233 (6) ◽  
pp. 943-957 ◽  
Author(s):  
Pengfei Wei ◽  
Chenghu Tang ◽  
Yuting Yang
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Failure Surface ◽  
Sensitivity Indices ◽  
Parametric Reliability ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Global Reliability Sensitivity

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

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