scholarly journals Inference of Adaptive methods for Multi-Stage skew-t Simulated Data

2017 ◽  
Vol 13 (24) ◽  
pp. 448
Author(s):  
Loai M. A. Al-Zou’bi ◽  
Amer I. Al-Omari ◽  
Ahmad M. Al-Khazalah ◽  
Raed A. Alzghool
Keyword(s):  
Multilevel Models ◽  
Variance Estimation ◽  
Simulated Data ◽  
Adaptive Methods ◽  
Multi Stage ◽  
Simple Simulation ◽  
Level Model ◽  
Variance Estimates ◽  
Cluster Correlation ◽  
Cluster Level

Multilevel models can be used to account for clustering in data from multi-stage surveys. In some cases, the intra-cluster correlation may be close to zero, so that it may seem reasonable to ignore clustering and fit a single level model. This article proposes several adaptive strategies for allowing for clustering in regression analysis of multi-stage survey data. The approach is based on testing whether the cluster-level variance component is zero. If this hypothesis is retained, then variance estimates are calculated ignoring clustering; otherwise, clustering is reflected in variance estimation. A simple simulation study is used to evaluate the various procedures.

scholarly journals Bayesian Multilevel Models for Count Data

2021 ◽  
pp. 224-233
Author(s):  
Olumide Sunday Adesina
Keyword(s):  
Count Data ◽  
Multilevel Models ◽  
Geometric Model ◽  
Real Life ◽  
Simulated Data ◽  
Data Set ◽  
K Value ◽  
Real Life Data ◽  
Level Model ◽  
Multi Level

The traditional Poisson regression model for fitting count data is considered inadequate to fit over-or under-dispersed count data and new models have been developed to make up for such inadequacies inherent in the model. In this study, Bayesian Multi-level model was proposed using the No-U-Turn Sampler (NUTS) sampler to sample from the posterior distribution. A simulation was carried out for both over-and under-dispersed data from discrete Weibull distribution. Pareto k diagnostics was implemented, and the result showed that under-dispersed and over-dispersed simulated data has all its k value to be less than 0.5, which indicate that all the observations are good. Also all WAIC were the same as LOO-IC except for Poisson in the over-dispersed simulated data. Real-life data set from National Health Insurance Scheme (NHIS) was used for further analysis. Seven multi-level models were f itted and the Geometric model outperformed other model. 

scholarly journals Hierarchical Scheduling Scheme for AC/DC Hybrid Active Distribution Network Based on Multi-Stakeholders

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2830 ◽  
Author(s):  
Chang Ye ◽  
Shihong Miao ◽  
Yaowang Li ◽  
Chao Li ◽  
Lixing Li
Keyword(s):  
Optimization Model ◽  
Distribution Network ◽  
Hierarchical Optimization ◽  
Active Distribution Network ◽  
Scheduling Scheme ◽  
Multi Stage ◽  
Flexible Loads ◽  
Level Model ◽  
Load Regulation ◽  
Upper Level

This paper presents a hierarchical multi-stage scheduling scheme for the AC/DC hybrid active distribution network (ADN). The load regulation center (LRC) is considered in the developed scheduling strategy, as well as the AC and DC sub-network operators. They are taken to be different stakeholders. To coordinate the interests of all stakeholders, a two-level optimization model is established. The flexible loads are dispatched by LRC in the upper-level optimization model, the objective of which is minimizing the loss of the entire distribution network. The lower-level optimization is divided into two sub-optimal models, and they are carried out to minimize the operating costs of the AC/DC sub-network operators respectively. This two-level model avoids the difficulty of solving multi-objective optimization and can clarify the role of various stakeholders in the system scheduling. To solve the model effectively, a discrete wind-driven optimization (DWDO) algorithm is proposed. Then, considering the combination of the proposed DWDO algorithm and the YALMIP toolbox, a hierarchical optimization algorithm (HOA) is developed. The HOA can obtain the overall optimization result of the system through the iterative optimization of the upper and lower levels. Finally, the simulation results verify the effectiveness of the proposed scheduling scheme.

Bayesian Multi-Level Modelling for Improved Prediction of Corrosion Growth Rate

2020 ◽  
Author(s):  
Domenic Di Francesco ◽  
Marios Chryssanthopoulos ◽  
Michael Havbro Faber ◽  
Ujjwal Bharadwaj
Keyword(s):  
Epistemic Uncertainty ◽  
Simulated Data ◽  
Steel Structures ◽  
Pressure Vessels ◽  
Mathematical Basis ◽  
Management Planning ◽  
Integrity Management ◽  
Level Model ◽  
Multi Level ◽  
Inspection Data

Abstract In pipelines, pressure vessels and various other steel structures, the remaining thickness of a corroding ligament can be measured directly and repeatedly over time. Statistical analysis of these measurements is a common approach for estimating the rate of corrosion growth, where the uncertainties associated with the inspection activity are taken into account. An additional source of variability in such calculations is the epistemic uncertainty associated with the limited number of measurements that are available to engineers at any point in time. Traditional methods face challenges in fitting models to limited or missing datasets. In such cases, deterministic upper bound values, as recommended in industrial guidance, are sometimes assumed for the purpose of integrity management planning. In this paper, Bayesian inference is proposed as a means for representing available information in consistency with evidence. This, in turn, facilitates decision support in the context of risk-informed integrity management. Aggregating inspection data from multiple locations does not account for the possible variability between the locations, and creating fully independent models can result in excessive levels of uncertainty at locations with limited data. Engineers intuitively acknowledge that the areas with more sites of corrosion should, to some extent, inform estimates of growth rates in other locations. Bayesian multi-level (hierarchical) models provide a mathematical basis for achieving this by means of the appropriate pooling of information, based on the homogeneity of the data. Included in this paper is an outline of the process of fitting a Bayesian multi-level model and a discussion of the benefits and challenges of pooling inspection data between distinct locations, using example calculations and simulated data.

scholarly journals Exploring the assumptions of multi-stock assessment models for humpback whales (Megaptera novaeangliae) in the Southern Hemisphere: using Breeding Stocks D and E as an example

2020 ◽  
pp. 119-128
Author(s):  
Rebecca Leaper ◽  
Samantha Peel ◽  
David Peel ◽  
Nick Gales
Keyword(s):  
Density Dependence ◽  
Population Model ◽  
Stock Assessment ◽  
Simulated Data ◽  
Megaptera Novaeangliae ◽  
Humpback Whales ◽  
Simulation Approach ◽  
Potential Value ◽  
Simple Simulation ◽  
Feeding Area

There is potential value in exploring multi-stock models to address situations where humpback stocks are mixing. However, sensitivity to the assumptions underlying these models has yet to be fully explored. Using a simple simulation approach, the assumptions of a population model that allows for mixing of humpback whale (Megaptera novaeangliae) stocks D and E on feeding areas has been explored by relaxing the assumptions of the original Johnston and Butterworth model in a number of plausible ways. First the ability of the model to estimate parameters was checked for a situation where simulated data are generated from an underlying model of exactly the same form for which the actual values of these parameters are known (Scenario 1). Then the ability of the model to estimate these parameters when alternative forms and assumptions were used for the underlying model generating the data was investigated. Specifically, stocks were allowed to mix non-uniformly across each feeding area and catch was non-uniformly distributed across each feeding area (Scenario 2). The consequences of density dependence implemented on feeding rather than breeding areas (Scenario 3) were also examined. The original mixing model was robust to alternate mixing and catch allocation scenarios in all but one of the simulations, but when density dependence acted at the level of the feeding rather than the breeding areas, the model produced estimates that were quite different from the underlying population. It is recommend that the inclusion of density dependence on feeding areas in models that allow for mixing of whales on these grounds be investigated further.

scholarly journals Investigation On Sleep Status and Its Influencing Factors in Children Aged 3-14 in Beijing

2021 ◽  
Author(s):  
Li Hongbin ◽  
Li Zhuo ◽  
Li Xiaodan ◽  
Zhao Jing ◽  
Wang Guixiang ◽  
...  
Keyword(s):  
Sleep Quality ◽  
Influencing Factors ◽  
Current Status ◽  
School Age Children ◽  
Older Children ◽  
Related Factors ◽  
Multi Stage ◽  
Level Model ◽  
Multi Level ◽  
Children’S Sleep

Abstract Objective: To investigate the current status of children's sleep in Beijing and analyze the influencing factors that affect it. Methods:Using multi-stage stratified cluster random sampling, a total of 11420 children aged 3-14 in 7 districts in Beijing were included in the study. The Pediatric Sleep Questionnaire (PSQ) was used to investigate and analyze various factors influencing sleep. Multi-level model was used to analyze the relationship between PSQ score and related factors. Results: The average PSQ score of the children surveyed was 3.60 ± 2.69 points. If the score is greater than 7, it is considered that there may be sleep quality problems . The proportion of children with sleep quality problems was more than 8%. Multi-level model analysis results show that younger children have higher PSQ scores than older children. Boys have higher PSQ scores than girls. Conclusion: The sleep quality of children in Beijing is not optimistic. The PSQ score of preschool children is higher than school age children. It is recommended that parents pay attention to children’s sleep status and try to remove influencing factors.

A Bayesian approach for multi-stage models with linear time-dependent hazard rate

2019 ◽  
Vol 25 (4) ◽  
pp. 307-316
Author(s):  
Hoa Pham ◽  
Huong T. T. Pham
Keyword(s):  
Hazard Rate ◽  
Linear Time ◽  
Simulated Data ◽  
Time Dependent ◽  
Stage Model ◽  
Stage Duration ◽  
Stage Models ◽  
Multi Stage ◽  
Mh Algorithm ◽  
Number Of Individuals

Abstract Multi-stage models have been used to describe progression of individuals which develop through a sequence of discrete stages. We focus on the multi-stage model in which the number of individuals in each stage is assessed through destructive samples for a sequence of sampling time. Moreover, the stage duration distributions of the model are effected by a time-dependent hazard rate. The multi-stage models become complex with a stage having time-dependent hazard rate. The main aim of this paper is to derive analytically the approximation of the likelihood of the model. We apply the approximation to the Metropolis–Hastings (MH) algorithm to estimate parameters for the model. The method is demonstrated by applying to simulated data which combine non-hazard rate, stage-wise constant hazard rate and time-dependent hazard rates in stage duration distributions.

A comparison of gravity prediction methods on actual and simulated data

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1774-1780 ◽  
Author(s):  
F. Foster Morrison ◽  
Bruce C. Douglas
Keyword(s):  
Gravity Data ◽  
Random Number Generator ◽  
Simulated Data ◽  
Gravity Anomalies ◽  
Computer Time ◽  
Actual Data ◽  
Distance Weighting ◽  
Buried Point ◽  
Variance Estimates ◽  
The Cost

A comparison was made between Shepard’s method (inverse‐distance weighting) and collocation (linear filtering) for the purpose of predicting gravity anomalies. Tests were made with actual data from southern California and with simulated data created from buried point masses generated by a random number generator. The autocorrelation functions of the simulated and actual gravity data behaved very much alike. In general, the sophisticated collocation method did produce better results and very good variance estimates, compared with Shepard’s method, for simulated data. The advantage was less for actual data. The cost of the better results is the use of more computer time. The most important scientific conclusion of this study is that careful trend removal must be done and an adequate data sample obtained to produce truly optimal results from collocation. The variance estimates are much more sensitive to the form and calibration of the model autocorrelation function than are the prediction results.

The Application of Multiscale Modelling for the Prediction of Plastic Anisotropy and Deformation Textures

2007 ◽  
Vol 550 ◽  
pp. 13-22 ◽  
Author(s):  
Paul van Houtte ◽  
Albert Van Bael ◽  
Marc Seefeldt
Keyword(s):  
Constitutive Model ◽  
Multilevel Models ◽  
Plastic Anisotropy ◽  
Forming Limit ◽  
Stress And Strain ◽  
Finite Element Models ◽  
Identification Procedure ◽  
Macro Scale ◽  
Deformation Textures ◽  
Level Model

Finite element models for metal forming and models for the prediction of forming limit strains should be as accurate as possible, and hence should take effects due to texture, microstructure and substructure (dislocation patterns) into account. To achieve this, a hierarchical type of modelling is proposed in order to maintain the balance between calculation speed (required for engineering applications) and accuracy. This means that the FE models work with an analytical constitutive model, the parameters of which are identified using results of multilevel models. The analytical constitutive model will be discussed, as well as the identification procedure. The multilevel models usually connect the macro-scale with a meso-scale (grain level) via a homogenisation procedure. They can also be used to make predictions of deformation textures. These will be quantitatively compared with experimentally obtained rolling textures of steel and aluminium alloys. It was found that only models which to some extent take both stress and strain interactions between adjacent grains into account perform well. Finally an example of a three level model, also including the micro-scale (i.e. the dislocation substructure), will be given.

scholarly journals On the Interpretation of Parameters in Multivariate Multilevel Models Across Different Combinations of Model Specification and Estimation

2019 ◽  
Vol 2 (3) ◽  
pp. 288-311 ◽  
Author(s):  
Lesa Hoffman
Keyword(s):  
Latent Variables ◽  
Structural Equation ◽  
Multilevel Models ◽  
Structural Equation Models ◽  
Simulated Data ◽  
Recent Change ◽  
Model Specification ◽  
Predictor Variables ◽  
Random Slopes ◽  
Multivariate Multilevel Models

The increasing availability of software with which to estimate multivariate multilevel models (also called multilevel structural equation models) makes it easier than ever before to leverage these powerful techniques to answer research questions at multiple levels of analysis simultaneously. However, interpretation can be tricky given that different choices for centering model predictors can lead to different versions of what appear to be the same parameters; this is especially the case when the predictors are latent variables created through model-estimated variance components. A further complication is a recent change to Mplus (Version 8.1), a popular software program for estimating multivariate multilevel models, in which the selection of Bayesian estimation instead of maximum likelihood results in different lower-level predictors when random slopes are requested. This article provides a detailed explication of how the parameters of multilevel models differ as a function of the analyst’s decisions regarding centering and the form of lower-level predictors (i.e., observed or latent), the method of estimation, and the variant of program syntax used. After explaining how different methods of centering lower-level observed predictor variables result in different higher-level effects within univariate multilevel models, this article uses simulated data to demonstrate how these same concepts apply in specifying multivariate multilevel models with latent lower-level predictor variables. Complete data, input, and output files for all of the example models have been made available online to further aid readers in accurately translating these central tenets of multivariate multilevel modeling into practice.

scholarly journals On the Use of Empirical Bayes Estimates as Measures of Individual Traits

Assessment ◽  
2019 ◽  
pp. 107319111988501
Author(s):  
Siwei Liu ◽  
Peter Kuppens ◽  
Laura Bringmann
Keyword(s):  
Random Effects ◽  
Empirical Bayes ◽  
Multilevel Models ◽  
Simulated Data ◽  
Residual Variance ◽  
Data Set ◽  
Number Of Factors ◽  
Individual Traits ◽  
Level 1

Empirical Bayes (EB) estimates of the random effects in multilevel models represent how individuals deviate from the population averages and are often extracted to detect outliers or used as predictors in follow-up analysis. However, little research has examined whether EB estimates are indeed reliable and valid measures of individual traits. In this article, we use statistical theory and simulated data to show that EB estimates are biased toward zero, a phenomenon known as “shrinkage.” The degree of shrinkage and reliability of EB estimates depend on a number of factors, including Level-1 residual variance, Level-1 predictor variance, Level-2 random effects variance, and number of within-person observations. As a result, EB estimates may not be ideal for detecting outliers, and they produce biased regression coefficients when used as predictors. We illustrate these issues using an empirical data set on emotion regulation and neuroticism.

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