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Monte-Carlo Simulation-Based Statistical Modeling.

By: Chen, Ding-Geng (Din).
Contributor(s): Chen, John Dean.
Material type: TextTextSeries: eBooks on Demand.ICSA Book Series in Statistics Ser: Publisher: Singapore : Springer, 2017Copyright date: ©2017Description: 1 online resource (440 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9789811033070.Subject(s): Statistical methodsGenre/Form: Electronic books.Additional physical formats: Print version:: Monte-Carlo Simulation-Based Statistical ModelingDDC classification: 519.5 LOC classification: QA276-280Online resources: Click here to view this ebook.
Contents:
Intro -- Preface -- About the Book -- Contents -- Editors and Contributors -- Part I Monte-Carlo Techniques -- Joint Generation of Binary, Ordinal, Count, and Normal Data with Specified Marginal and Association Structures in Monte-Carlo Simulations -- 1 Introduction -- 2 Algorithm -- 3 Some Operational Details and an Illustrative Example -- 4 Future Directions -- References -- Improving the Efficiency of the Monte-Carlo Methods Using Ranked Simulated Approach -- 1 Introduction -- 2 Steady-State Ranked Simulated Sampling (SRSIS) -- 3 Monte-Carlo Methods for Multiple Integration Problems -- 3.1 Importance Sampling Method -- 3.2 Using Bivariate Steady-State Sampling (BVSRSIS) -- 3.3 Simulation Study -- 4 Steady-State Ranked Gibbs Sampler -- 4.1 Traditional (standard) Gibbs Sampling Method -- 4.2 Steady-State Gibbs Sampling (SSGS): The Proposed Algorithms -- 4.3 Simulation Study and Illustrations -- References -- Normal and Non-normal Data Simulations for the Evaluation of Two-Sample Location Tests -- 1 Introduction -- 2 Statistical Tests -- 2.1 t-Test -- 2.2 Wilcoxon Rank-Sum Test -- 2.3 Two-Stage Test -- 2.4 Permutation Test -- 3 Simulations -- 4 Results -- 4.1 Heterogeneous Variance -- 4.2 Skewness -- 4.3 Kurtosis -- 5 Discussion -- References -- Anatomy of Correlational Magnitude Transformations in Latency and Discretization Contexts in Monte-Carlo Studies -- 1 Introduction -- 2 Building Blocks -- 2.1 Dichotomous Case: Normality -- 2.2 Dichotomous Case: Beyond Normality -- 2.3 Polytomous Case: Normality -- 2.4 Polytomous Case: Beyond Normality -- 3 Algorithms and Illustrative Examples -- 4 Simulations in a Multivariate Setting -- 5 Discussion -- References -- Monte-Carlo Simulation of Correlated Binary Responses -- 1 Introduction -- 1.1 Binary Data Issues -- 2 Fully Specified Joint Probability Distributions.
2.1 Simulating Binary Data with a Joint PDF -- 2.2 Explicit Specification of the Joint PDF -- 2.3 Derivation of the Joint PDF -- 3 Specification by Mixture Distributions -- 3.1 Mixtures Involving Discrete Distributions -- 3.2 Mixtures Involving Continuous Distributions -- 4 Simulation by Dichotomizing Variates -- 4.1 Dichotomizing Normal Variables -- 4.2 Iterated Dichotomization -- 4.3 Dichotomizing Non-normal Variables -- 5 Conditionally Specified Distributions -- 5.1 The Linear Conditional Probability Model -- 5.2 Non-linear Dynamic Conditional Probability Model -- 6 Software Discussion -- References -- Quantifying the Uncertainty in Optimal Experiment Schemes via Monte-Carlo Simulations -- 1 Introduction -- 2 Quantifying the Uncertainty in the Optimal Experiment Scheme -- 2.1 Comparing Experimental Schemes -- 2.2 Comparing Values of Objective Functions -- 3 Progressive Censoring with Location-Scale Family of Distributions -- 3.1 Maximum Likelihood Estimation -- 3.2 Optimal Criteria -- 3.3 Numerical Illustrations -- 3.4 Discussions -- 4 Illustrative Example -- 5 Concluding Remarks -- References -- Part II Monte-Carlo Methods in Missing Data -- Markov Chain Monte-Carlo Methods for Missing Data Under Ignorability Assumptions -- 1 Introduction -- 2 Missing Data Mechanisms -- 3 Data Augmentation -- 4 Missing Response -- 4.1 Method: Multivariate Normal Model -- 4.2 Simulation -- 4.3 Prostate Specific Antigen (PSA) Data -- 5 Missing Covariates -- 5.1 Method -- 5.2 Simulation -- 5.3 BRFSS Data -- 6 Discussion -- References -- A Multiple Imputation Framework for Massive Multivariate Data of Different Variable Types: A Monte-Carlo Technique -- 1 Introduction -- 2 Background on RNG -- 3 Missing Data and MI -- 4 Connecting RNG and MI, Outline of a Unified MI Algorithm for Mixed Data -- 5 Some Remarks and Discussion -- References.
Hybrid Monte-Carlo in Multiple Missing Data Imputations with Application to a Bone Fracture Data -- 1 Introduction -- 2 The Bone Fracture Data -- 3 Imputation Modeling and Inference -- 3.1 Multiple Imputation to Missing Data Problems -- 3.2 Odds Ratio Models for Complete Data -- 3.3 Multiple Imputation Under the Framework -- 4 Hybrid Monte-Carlo -- 5 Implementing HMC for Model Fitting -- 5.1 Assigning Prior Distributions -- 5.2 Tuning Proposal Distribution -- 5.3 Starting Values -- 5.4 Determining Burn-In -- 5.5 Determining Iteration Intervals to Obtain Imputed Values -- 5.6 Determining Stopping Time -- 5.7 Output Analysis -- 6 Conclusion -- References -- Statistical Methodologies for Dealing with Incomplete Longitudinal Outcomes Due to Dropout Missing at Random -- 1 Introduction -- 2 Notation and Basic Concepts -- 3 Dropout Analysis Strategies in Longitudinal Continuous Data -- 3.1 Likelihood Analysis -- 3.2 Multiple Imputation (MI) -- 3.3 Illustration -- 3.4 Simulation of Missing Values -- 3.5 Results -- 4 Dropout Analysis Strategies in Longitudinal Binary Data -- 4.1 Weighted Generalized Estimating Equation (WGEE) -- 4.2 Multiple Imputation Based GEE (MI-GEE) -- 4.3 Generalized Linear Mixed Model (GLMM) -- 4.4 Simulation Study -- 4.5 Analysis -- 4.6 Application Example: Dermatophyte Onychomycosis Study -- 5 Discussion and Conclusion -- References -- Applications of Simulation for Missing Data Issues in Longitudinal Clinical Trials -- 1 Introduction -- 2 Generation of Study Data with a Specified MDM and Cumulative Drop-Out Rates -- 3 Tipping Point Analysis to Assess the Robustness of MMRM Analyses -- 4 Monte-Carlo Approaches for Control-Based Imputation Analysis -- 5 Discussions and Remarks -- References.
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 -- 1 Introduction -- 2 Multiple Imputation to Deal with Missing Data -- 2.1 Multiple Imputation via MCMC -- 2.2 Combining Inferences from Imputed Data Sets -- 3 Example of Clinical Trial and Sample Data -- 3.1 Introduction of a Simulated Longitudinal Clinical Trial -- 3.2 Assuming Data of Primary Efficacy Endpoint to Have Normal Distribution -- 3.3 Not Assuming Data of Primary Efficacy Endpoint to Have Normal Distribution -- 4 Discussion -- References -- Part III Monte-Carlo in Statistical Modellings and Applications -- Monte-Carlo Simulation in Modeling for Hierarchical Generalized Linear Mixed Models -- 1 Introduction -- 2 Generalized Linear Model -- 3 Hierarchical Models -- 3.1 Approaches with Binary Outcomes -- 4 Three-Level Hierarchical Models -- 4.1 With Random Intercepts -- 4.2 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes -- 4.3 Nested Higher Level Logistic Regression Models -- 5 Possible Problems with Hierarchical Model -- 5.1 Issues in Hierarchical Modeling -- 5.2 Parameter Estimations -- 5.3 Convergence Issues in SAS -- 6 Simulation of Data -- 6.1 Simulation Setup -- 6.2 Simulation Results -- 7 Analysis of Data -- 7.1 Description -- 7.2 Data Analysis -- 8 Conclusions -- References -- Monte-Carlo Methods in Financial Modeling -- 1 Hierarchical Modeling in Market Microstructure Studies -- 1.1 The Model -- 1.2 Bayesian Inference via MCMC Algorithms -- 1.3 Simulation Study -- 1.4 Empirical Study -- 1.5 Economic Interpretation -- 1.6 Appendix 1 -- 2 Monte-Carlo Strategies in Option Pricing for SABR Model -- 2.1 SABR Model and Option Pricing for the Case β= 1 -- 2.2 Approximating the Distribution of (Σ2, X2).
2.3 Numerical Experiments and Empirical Calibration of SABR -- References -- Simulation Studies on the Effects of the Censoring Distribution Assumption in the Analysis of Interval-Censored Failure Time Data -- 1 Introduction -- 2 Methodology -- 2.1 Case I -- 2.2 Case II -- 3 Simulation Studies -- 3.1 Case I -- 3.2 Case II -- 4 Conclusions and Discussion -- References -- Robust Bayesian Hierarchical Model Using Monte-Carlo Simulation -- 1 Parkinson's Disease as an Example -- 2 MLIRT Model -- 3 MLIRT Model with NI Distribution -- 3.1 NI Distribution -- 3.2 NI Distribution in MLIRT Model -- 4 Bayesian Inference and Model Selection Criteria -- 5 Monte Carlo Simulation Scheme and Some Results -- 6 Application to Trial Study Data -- 7 More Extended Modeling -- 7.1 Joint MLIRT Model -- 7.2 MLIRT Model with Skew-Normal/Independent (SNI) Distributions -- 8 Discussions -- References -- A Comparison of Bootstrap Confidence Intervals for Multi-level Longitudinal Data Using Monte-Carlo Simulation -- 1 Introduction -- 2 Linear Mixed Effects Model -- 2.1 Statistical Models -- 2.2 Estimation Methods -- 3 Bootstrap Methods -- 3.1 Bootstrap Estimates -- 3.2 Bootstrap Confidence Intervals -- 4 Monte-Carlo Simulation Study -- 4.1 The Simulation Design -- 4.2 Simulation Results Five Students per Classroom -- 4.3 Simulation Results 15 Students per Classroom -- 4.4 Comparison of Simulation Results for Five Students per Classroom and 15 Students per Classroom -- 5 Application -- 6 Conclusions -- References -- Bootstrap-Based LASSO-Type Selection to Build Generalized Additive Partially Linear Models for High-Dimensional Data -- 1 Introduction -- 2 Framework of the Procedure to Build GAPLM -- 3 Generalized Additive Partial Linear Models -- 3.1 Spline Approximation -- 3.2 Penalized Regression -- 4 Real Data Examples -- 4.1 Breast Cancer Data -- 4.2 HIV Data.
5 A Simulation Study.
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Electronic Book UT Tyler Online
Online
QA276-280 (Browse shelf) http://ebookcentral.proquest.com/lib/uttyler/detail.action?docID=4799566 Available EBC4799566

Intro -- Preface -- About the Book -- Contents -- Editors and Contributors -- Part I Monte-Carlo Techniques -- Joint Generation of Binary, Ordinal, Count, and Normal Data with Specified Marginal and Association Structures in Monte-Carlo Simulations -- 1 Introduction -- 2 Algorithm -- 3 Some Operational Details and an Illustrative Example -- 4 Future Directions -- References -- Improving the Efficiency of the Monte-Carlo Methods Using Ranked Simulated Approach -- 1 Introduction -- 2 Steady-State Ranked Simulated Sampling (SRSIS) -- 3 Monte-Carlo Methods for Multiple Integration Problems -- 3.1 Importance Sampling Method -- 3.2 Using Bivariate Steady-State Sampling (BVSRSIS) -- 3.3 Simulation Study -- 4 Steady-State Ranked Gibbs Sampler -- 4.1 Traditional (standard) Gibbs Sampling Method -- 4.2 Steady-State Gibbs Sampling (SSGS): The Proposed Algorithms -- 4.3 Simulation Study and Illustrations -- References -- Normal and Non-normal Data Simulations for the Evaluation of Two-Sample Location Tests -- 1 Introduction -- 2 Statistical Tests -- 2.1 t-Test -- 2.2 Wilcoxon Rank-Sum Test -- 2.3 Two-Stage Test -- 2.4 Permutation Test -- 3 Simulations -- 4 Results -- 4.1 Heterogeneous Variance -- 4.2 Skewness -- 4.3 Kurtosis -- 5 Discussion -- References -- Anatomy of Correlational Magnitude Transformations in Latency and Discretization Contexts in Monte-Carlo Studies -- 1 Introduction -- 2 Building Blocks -- 2.1 Dichotomous Case: Normality -- 2.2 Dichotomous Case: Beyond Normality -- 2.3 Polytomous Case: Normality -- 2.4 Polytomous Case: Beyond Normality -- 3 Algorithms and Illustrative Examples -- 4 Simulations in a Multivariate Setting -- 5 Discussion -- References -- Monte-Carlo Simulation of Correlated Binary Responses -- 1 Introduction -- 1.1 Binary Data Issues -- 2 Fully Specified Joint Probability Distributions.

2.1 Simulating Binary Data with a Joint PDF -- 2.2 Explicit Specification of the Joint PDF -- 2.3 Derivation of the Joint PDF -- 3 Specification by Mixture Distributions -- 3.1 Mixtures Involving Discrete Distributions -- 3.2 Mixtures Involving Continuous Distributions -- 4 Simulation by Dichotomizing Variates -- 4.1 Dichotomizing Normal Variables -- 4.2 Iterated Dichotomization -- 4.3 Dichotomizing Non-normal Variables -- 5 Conditionally Specified Distributions -- 5.1 The Linear Conditional Probability Model -- 5.2 Non-linear Dynamic Conditional Probability Model -- 6 Software Discussion -- References -- Quantifying the Uncertainty in Optimal Experiment Schemes via Monte-Carlo Simulations -- 1 Introduction -- 2 Quantifying the Uncertainty in the Optimal Experiment Scheme -- 2.1 Comparing Experimental Schemes -- 2.2 Comparing Values of Objective Functions -- 3 Progressive Censoring with Location-Scale Family of Distributions -- 3.1 Maximum Likelihood Estimation -- 3.2 Optimal Criteria -- 3.3 Numerical Illustrations -- 3.4 Discussions -- 4 Illustrative Example -- 5 Concluding Remarks -- References -- Part II Monte-Carlo Methods in Missing Data -- Markov Chain Monte-Carlo Methods for Missing Data Under Ignorability Assumptions -- 1 Introduction -- 2 Missing Data Mechanisms -- 3 Data Augmentation -- 4 Missing Response -- 4.1 Method: Multivariate Normal Model -- 4.2 Simulation -- 4.3 Prostate Specific Antigen (PSA) Data -- 5 Missing Covariates -- 5.1 Method -- 5.2 Simulation -- 5.3 BRFSS Data -- 6 Discussion -- References -- A Multiple Imputation Framework for Massive Multivariate Data of Different Variable Types: A Monte-Carlo Technique -- 1 Introduction -- 2 Background on RNG -- 3 Missing Data and MI -- 4 Connecting RNG and MI, Outline of a Unified MI Algorithm for Mixed Data -- 5 Some Remarks and Discussion -- References.

Hybrid Monte-Carlo in Multiple Missing Data Imputations with Application to a Bone Fracture Data -- 1 Introduction -- 2 The Bone Fracture Data -- 3 Imputation Modeling and Inference -- 3.1 Multiple Imputation to Missing Data Problems -- 3.2 Odds Ratio Models for Complete Data -- 3.3 Multiple Imputation Under the Framework -- 4 Hybrid Monte-Carlo -- 5 Implementing HMC for Model Fitting -- 5.1 Assigning Prior Distributions -- 5.2 Tuning Proposal Distribution -- 5.3 Starting Values -- 5.4 Determining Burn-In -- 5.5 Determining Iteration Intervals to Obtain Imputed Values -- 5.6 Determining Stopping Time -- 5.7 Output Analysis -- 6 Conclusion -- References -- Statistical Methodologies for Dealing with Incomplete Longitudinal Outcomes Due to Dropout Missing at Random -- 1 Introduction -- 2 Notation and Basic Concepts -- 3 Dropout Analysis Strategies in Longitudinal Continuous Data -- 3.1 Likelihood Analysis -- 3.2 Multiple Imputation (MI) -- 3.3 Illustration -- 3.4 Simulation of Missing Values -- 3.5 Results -- 4 Dropout Analysis Strategies in Longitudinal Binary Data -- 4.1 Weighted Generalized Estimating Equation (WGEE) -- 4.2 Multiple Imputation Based GEE (MI-GEE) -- 4.3 Generalized Linear Mixed Model (GLMM) -- 4.4 Simulation Study -- 4.5 Analysis -- 4.6 Application Example: Dermatophyte Onychomycosis Study -- 5 Discussion and Conclusion -- References -- Applications of Simulation for Missing Data Issues in Longitudinal Clinical Trials -- 1 Introduction -- 2 Generation of Study Data with a Specified MDM and Cumulative Drop-Out Rates -- 3 Tipping Point Analysis to Assess the Robustness of MMRM Analyses -- 4 Monte-Carlo Approaches for Control-Based Imputation Analysis -- 5 Discussions and Remarks -- References.

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 -- 1 Introduction -- 2 Multiple Imputation to Deal with Missing Data -- 2.1 Multiple Imputation via MCMC -- 2.2 Combining Inferences from Imputed Data Sets -- 3 Example of Clinical Trial and Sample Data -- 3.1 Introduction of a Simulated Longitudinal Clinical Trial -- 3.2 Assuming Data of Primary Efficacy Endpoint to Have Normal Distribution -- 3.3 Not Assuming Data of Primary Efficacy Endpoint to Have Normal Distribution -- 4 Discussion -- References -- Part III Monte-Carlo in Statistical Modellings and Applications -- Monte-Carlo Simulation in Modeling for Hierarchical Generalized Linear Mixed Models -- 1 Introduction -- 2 Generalized Linear Model -- 3 Hierarchical Models -- 3.1 Approaches with Binary Outcomes -- 4 Three-Level Hierarchical Models -- 4.1 With Random Intercepts -- 4.2 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes -- 4.3 Nested Higher Level Logistic Regression Models -- 5 Possible Problems with Hierarchical Model -- 5.1 Issues in Hierarchical Modeling -- 5.2 Parameter Estimations -- 5.3 Convergence Issues in SAS -- 6 Simulation of Data -- 6.1 Simulation Setup -- 6.2 Simulation Results -- 7 Analysis of Data -- 7.1 Description -- 7.2 Data Analysis -- 8 Conclusions -- References -- Monte-Carlo Methods in Financial Modeling -- 1 Hierarchical Modeling in Market Microstructure Studies -- 1.1 The Model -- 1.2 Bayesian Inference via MCMC Algorithms -- 1.3 Simulation Study -- 1.4 Empirical Study -- 1.5 Economic Interpretation -- 1.6 Appendix 1 -- 2 Monte-Carlo Strategies in Option Pricing for SABR Model -- 2.1 SABR Model and Option Pricing for the Case β= 1 -- 2.2 Approximating the Distribution of (Σ2, X2).

2.3 Numerical Experiments and Empirical Calibration of SABR -- References -- Simulation Studies on the Effects of the Censoring Distribution Assumption in the Analysis of Interval-Censored Failure Time Data -- 1 Introduction -- 2 Methodology -- 2.1 Case I -- 2.2 Case II -- 3 Simulation Studies -- 3.1 Case I -- 3.2 Case II -- 4 Conclusions and Discussion -- References -- Robust Bayesian Hierarchical Model Using Monte-Carlo Simulation -- 1 Parkinson's Disease as an Example -- 2 MLIRT Model -- 3 MLIRT Model with NI Distribution -- 3.1 NI Distribution -- 3.2 NI Distribution in MLIRT Model -- 4 Bayesian Inference and Model Selection Criteria -- 5 Monte Carlo Simulation Scheme and Some Results -- 6 Application to Trial Study Data -- 7 More Extended Modeling -- 7.1 Joint MLIRT Model -- 7.2 MLIRT Model with Skew-Normal/Independent (SNI) Distributions -- 8 Discussions -- References -- A Comparison of Bootstrap Confidence Intervals for Multi-level Longitudinal Data Using Monte-Carlo Simulation -- 1 Introduction -- 2 Linear Mixed Effects Model -- 2.1 Statistical Models -- 2.2 Estimation Methods -- 3 Bootstrap Methods -- 3.1 Bootstrap Estimates -- 3.2 Bootstrap Confidence Intervals -- 4 Monte-Carlo Simulation Study -- 4.1 The Simulation Design -- 4.2 Simulation Results Five Students per Classroom -- 4.3 Simulation Results 15 Students per Classroom -- 4.4 Comparison of Simulation Results for Five Students per Classroom and 15 Students per Classroom -- 5 Application -- 6 Conclusions -- References -- Bootstrap-Based LASSO-Type Selection to Build Generalized Additive Partially Linear Models for High-Dimensional Data -- 1 Introduction -- 2 Framework of the Procedure to Build GAPLM -- 3 Generalized Additive Partial Linear Models -- 3.1 Spline Approximation -- 3.2 Penalized Regression -- 4 Real Data Examples -- 4.1 Breast Cancer Data -- 4.2 HIV Data.

5 A Simulation Study.

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