Some recent advances in mathematics and statistics : proceedings of Statistics 2011 Canada/IMST 2011-FIM XX, Montreal, Canada, 1-4 July 2011

This volume consists of a series of research papers presented at the conference Statistics 2011 Canada: 5th Canadian Conference in Applied Statistics held together with the 20th conference of the Forum for Interdisciplinary Mathematics titled, “Interdisciplinary Mathematical & Statistical Techniques”. These papers cover a wide range of topics from applications of Mathematics and Statistics such as Selection Bias in Surveys, Biomarker Discovery, Analysis of Earth Temperature, Supply Chain Management, Trimmed ANOVA, Zero-inflated Data, Non-Gaussian Time Series, and Stochastic Ordering; Classification, Nonparametric Test, and Jackknifed Ridge Estimator; Bayes Factor; Random Graphs and Error Correcting Codes; Meta Analysis; and National Health Plans and Risk Reduction through Supply Chain.The topics have been reviewed by experts in the field and the selected papers are expected to provide a topical resource on the subjects concerned. CONTENTS 8 (1) Preface 6 (2) Hypothesis Assessment Using the Bayes Factor and Relative Belief Ratio Z. Baskurt and M. Evans 10 1. Introduction 10 2. General Definition 13 3. The Method of Concentration 17 4. Calibration 20 5. Conclusions 22 References 23 (3) An Analysis of 1990-2011 Ontario Surface Air Temperatures D. R. Brillinger 25 1. Introduction 25 2. The Data 26 3. Models and Preliminary Analyses 27 4. Results 29 5. Model Assessment 32 6. Discussion/Conclusions 35 Acknowledgments 36 References 36 (4) A Markov Chain Monte Carlo Sampler for Gene Genealogies Conditional on Haplotype Data K. M. Burkett, B. McNeney and J. Graham 38 1. Introduction 38 2. Notation 39 3. Overview of The ZP Algorithm 40 3.1. A distribution for ( x,T) conditional on haplotypes H 41 3.2. Overview of the proposal distributions used in the ZP algorithm 43 4. Description of Our Genealogy Sampler 45 4.1. The target distribution: f(A|H) 45 4.2. Proposal distributions for ti, ri and si 45 4.3. Update schemes for our sampler 48 4.4. Software and application 51 5. Discussion 51 Acknowledgments 52 References 52 (5) Jackknifing Stochastic Restricted Ridge Estimator with Heteroscedastic Errors Y. P. Chaubey, M. Khurana and S. Chandra 54 1. Introduction 54 2. Jackknifed SRR Estimator 58 3. Comparison between SRR and Jackknifed SRR Estimators 59 4. Numerical Illustration 61 5. A Simulation Study 64 6. Concluding Remarks 67 Acknowledgments 67 References 67 (6) Molecular Classification of Acute Leukemia G. Chen and J. Wu 69 1. Introduction 69 2. Data Description 70 3. Methodology 71 3.1. A two-sample semiparametric model 72 3.2. Maximum likelihood estimation 73 3.3. Minimum Hellinger distance estimation 74 4. Marker Gene Selection 76 5. Classification 77 5.1. Classification rule 77 5.2. Classification results and discussion 80 6. Further Discussion 83 References 83 (7) A Note on a Nonparametric Trend Test and its Competitors K. Deka and B. Gogoi 84 1. Introduction 84 2. Model and the Tests 85 2.1. Parametric tests 86 2.2. Nonparametric tests 87 3. A Simulation Study 92 4. Results and Discussion 92 4.1. Comparison of level of the tests 92 4.2. Comparison of the power of the tests 92 5. Conclusions 93 References 93 (8) Local Search for Identifying Communities in Large Random Graphs N. Deo and M. Vasudevan 95 1. Introduction 95 2. Defining a Community 97 3. Community Detection Algorithms 99 4. Proposed Community Identification Algorithm 101 5. Experimental Results 102 5.1 Synthetic graphs 102 5.2 Real-world networks 105 6. Conclusion 106 Acknowledgement 106 References 106 (9) Data Mining Approaches to Multivariate Biomarker Discovery D. M. Dziuda 109 1. Introduction 109 2. The Informative Set of Genes 110 3. The Modified Bagging Schema 111 4. Identification of Multivariate Biomarkers that are Robust and Biologically Interpretable 112 5. A Case Study 114 6. Conclusions 118 References 118 (10) On Sequential Change-Point Detection Strategies E. Gombay 119 1. Introduction 119 2. An Open Ended Strategy 121 3. Truncated Procedures 125 4. Theoretical Comparisons 127 5. Empirical Comparisons 127 6. Conclusions 130 Appendix: Asymptotic Properties 131 Acknowledgements 132 References 132 (11) Multi-Item Two-Stage EOQ Model Incorporating Quantity and Freight Discounts D. Gupta, K. Gandhi, S. Makkar and P. C. Jha 134 1. Introduction 134 2. Model’s Assumptions, Sets, and Symbols 137 2.1. Assumptions 137 2.2. Sets 137 2.3. Parameters 137 2.4. Decision Variables 138 3. Problem Formulation 139 3.1. Mathematical Model Formulation 139 3.2. Analysis of Model Formulation 140 3.3. Solution 141 4. Conclusions 142 Appendix A: Data Set 143 Appendix B: Solution 145 References 146 (12) An Improved Bound on Average Codeword Length of Variable Length Error Correcting Codes R. Gupta and B. Sharma 147 1. Introduction 147 2. Preliminaries and Earlier Results 148 3. An Improved Bound on Average Codeword Length 151 3.1. Examples 153 4. Conclusion 154 Appendix A. The Range of s2 for Example 1 154 Appendix B. The Range of s2 for Example 2 155 References 157 (13) Trimmed Analysis Of Variance: A Robust Modification of ANOVA G. S. Mudholkar, D. K. Srivastava, C. E. Marchetti and A. G. Mudholkar 159 1. Introduction 160 2. Trimmed-Means ANOVA 162 2.1. The Robust F -statistic: Construction 165 3. Operating Characteristics 169 4. Conclusions 175 Acknowledgments 176 References 176 (14) Bayesian Predictive Inference under Sequential Sampling with Selection Bias B. Nandram and D. Kim 178 1. Introduction 178 2. Ignorable and Nonignorable Selection Models 181 3. Bayesian Computations 184 4. An Illustrative Example on Cystic Fibrosis 188 5. Concluding Remarks 192 Acknowledgments 193 APPENDIX A 194 APPENDIX B 194 References 195 (15) Tests For and Against Uniform Stochastic Ordering on Multinomial Parameters Based on -Divergences J. Peng 196 1. Introduction 196 2. Maximum Likelihood Estimator P of P under P U Q 198 3. Test Statistics Based on -Divergence 199 4. An Example 201 Acknowledgments 202 References 203 (16) Development and Management of National Health Plans: Health Economics and Statistical Perspectives P. K. Sen 204 1. Introduction 204 2. An Inventory of Points to Ponder 205 3. Whither Statistics? 206 4. BPL, AAL, MIC and Nested Inequalities 207 5. Clinical and Environmental Perspectives 208 6. Statistics: Perspectives and Task Ahead 213 7. Integrating Measures of Socio-economic Features 216 Acknowledgments 226 References 226 (17) A Unified Approach between Population-Averaged and Cluster-Specific Analyses for Multilevel Zero-Inflated Count Data G. Sneddon, M. T. Hasan and R. Ma 228 1. Introduction 228 2. Zero-Inflated Poisson Mixed Model for Multilevel Longitudinal Data 230 2.1. The Model 230 2.2. Mean and Covariance structure 232 3. Parameter Estimation 233 3.1. Estimation of regression parameters 234 3.2. Estimation of random effects parameters 234 4. Application 235 5. Discussion 237 Acknowledgments 238 References 238 (18) Meta-Analysis of Binary Outcomes Data in Clinical Trials P. Subbaiah, A. Mallick and T. K. Desai 240 1. Introduction 241 2. Confidence Intervals for the Proportion of Interest 241 3. Meta Analysis of Binary Outcome Data 243 4. Example to Study the Success Rate of Antifungal Onychomycosis Lacquers 247 5. Example to Study the Incidence of Esophageal Adenocarcinoma (EAC) in Non-dysplastic Barrett’s Esophagus (NDBE) 250 6. Modification of the Methods for Comparative Studies 253 References 256 (19) Risk Reduction of the Supply Chain through Pooling Losses in Case of Bankruptcy of Suppliers Using the Black-Scholes-Merton Pricing Model R. Valvarde and M. Talla 257 1. Introduction 257 2. Black-Scholes-Merton Option Pricing Model 258 3. Risk Reduction through Pooling Independent Losses 261 4. Illustration of the Methods on Real Data 261 5. Conclusions and Future Research 264 References 265 (20) Random Effects Modelling of Non-Gaussian Time Series Responses with Covariates G. Yan, M. T. Hasan and R. Ma 266 1. Introduction 266 2. Mixed Model for Non-Gaussian Time Series Responses 268 2.1. The model 268 2.2. Moment structure 269 3. Best Linear Unbiased Predictors of Random Effects 269 4. Estimation of Parameters 270 4.1. Estimation of regression parameters 270 4.2. Estimation of random effects parameters 271 4.3. Estimation of correlation parameter 271 5. Application 272 5.1. Daily counts of emergency room visit data 272 5.2. Los Angeles air pollution data 274 6. Discussion 275 Ackowledgements 276 References 276 This volume consists of a series of research papers presented at the conference Statistics 2011 Canada: 5th Canadian Conference in Applied Statistics held together with the 20th conference of the Forum for Interdisciplinary Mathematics titled, "Interdisciplinary Mathematical & Statistical Techniques". These papers cover a wide range of topics from applications of Mathematics and Statistics such as Selection Bias in Surveys, Biomarker Discovery, Analysis of Earth Temperature, Supply Chain Management, Trimmed ANOVA, Zero-inflated Data, Non-Gaussian Time Series, and Stochastic Ordering; Classification, Nonparametric Test, and Jackknifed Ridge Estimator; Bayes Factor; Random Graphs and Error Correcting Codes; Meta Analysis; and National Health Plans and Risk Reduction through Supply Chain. The topics have been reviewed by experts in the field and the selected papers are expected to provide a topical resource on the subjects concerned "The present volume consists of 19 papers dealing with current issues in mathematical and statistical methods that were presented at Statistics 2011 Canada Conference in Applied Statistics that was held together with the 20th conference of the Forum for Interdisciplinary Mathematics titled, "Interdisciplinary Mathematical & Statistical Techniques" from July 1 to July 4, 2011"--Preface