Empirical Model Building : Data, Models, and Reality.

By: Thompson, James RMaterial type: TextTextSeries: Wiley Series in Probability and Statistics SerPublisher: Hoboken : John Wiley & Sons, Incorporated, 2011Copyright date: ©2011Edition: 2nd edDescription: 1 online resource (460 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118109625Subject(s): Experimental design | Mathematical models | Mathematical statisticsGenre/Form: Electronic books.Additional physical formats: Print version:: Empirical Model Building : Data, Models, and RealityDDC classification: 519.5/7 LOC classification: QA279 -- .T49 2011ebOnline resources: Click to View
Contents:
Intro -- Empirical Model Building: Data, Models, and Reality -- Contents -- Preface -- 1. Models of Growth and Decay -- 1.1. A Simple Pension and Annuity Plan -- 1.2. Income Tax Bracket Creep and the Quiet Revolution of 1980 -- 1.3. Retirement of a Mortgage -- 1.4. Some Mathematical Descriptions of the Theory of Malthus -- 1.5. Metastasis and Resistance -- Problems -- References -- 2. Models of Competition, Survival, and Combat -- 2.1. An Analysis of the Demographics of Ancient Israel -- 2.2. The Plague and John Graunt's Life Table -- 2.3. Modular Data-Based Wargaming -- 2.3.1. Herman Kahn and the Winning of the Cold War -- 2.4. Predation and Immune Response Systems -- 2.5. Pyramid Clubs for Fun and Profit -- Problems -- References -- 3. Epidemics -- 3.1. Introduction -- 3.2. John Snow and the London Cholera Epidemic of 1854 -- 3.3. Prelude: The Postwar Polio Epidemic -- 3.4. AIDS: A New Epidemic for America -- 3.5. Why an AIDS Epidemic in America? -- 3.5.1. Political Correctness Can Kill -- 3.6. The Effect of the Gay Bathhouses -- 3.7. A More Detailed Look at the Model -- 3.8. Forays into the Public Policy Arena -- 3.9. Modeling the Mature Epidemic -- 3.10. AIDS as a Facilitator of Other Epidemics -- 3.11. Comparisons with First World Countries -- 3.12. Conclusions: A Modeler's Portfolio -- Problems -- References -- 4. Bootstrapping -- 4.1. Introduction -- 4.2. Bootstrapping Analysis of Darwin's Data -- 4.3. A Bootstrapping Approximation to Fisher's Nonparametric Test -- 4.4. A Resampling Bassed Sign Test -- 4.5. A Bootstrapping Approach for Confidence Intervals -- 4.6. Solving Ill-Structured Problems -- Problems -- References -- 5. Monte Carlo Solutions of Differential Equations -- 5.1. Introduction -- 5.2. Gambler's Ruin -- 5.3. Solution of Simple Differential Equations -- 5.4. Solution of the Fokker-Planck Equation.
5.5. The Dirichlet Problem -- 5.6. Solution of General Elliptic Differential Equations -- 5.7. Conclusions -- Problems -- References -- 6. SIMEST, SIMDAT, and Pseudoreality -- 6.1. Introduction -- 6.2. The Bootstrap: A Dirac-Comb Density Estimator -- 6.3. SIMDAT: A Smooth Resampling Algorithm -- 6.3.1. The SIMDAT Algorithm -- 6.3.2. An Empirical Justification of SIMDAT -- 6.4. SIMEST: An Oncological Example -- 6.4.1. An Exploratory Prelude -- 6.4.2. Models and Algorithms -- Problems -- References -- 7. Exploratory Data Analysis -- 7.1. Introduction -- 7.2. Smoothing -- 7.3. The Stem and Leaf Plot -- 7.4. The Five Figure Summary -- 7.5. Tukey's Box Plot -- Problems -- References -- 8. Noise Killing Chaos -- 8.1. Introduction -- 8.2. The Discrete Logistic Model -- 8.3. A Chaotic Convection Model -- 8.4. Conclusions -- Problems -- References -- 9. A Primer in Bayesian Data Analysis -- 9.1. Introduction -- 9.2. The EM Algorithm -- 9.3. The Data Augmentation Algorithm -- 9.4. The Gibbs Sampler -- 9.5. Conclusions -- Problems -- References -- 10. Multivariate and Robust Procedures in Statistical Process Control -- 10.1. Introduction -- 10.2. A Contamination Model for SPC -- 10.3. A Compound Test for Higher Dimensional SPC Data -- 10.4. Rank Testing with Higher Dimensional SPC Data -- 10.5. A Robust Estimation Procedure for Location in Higher Dimensions -- Problems -- References -- 11. Considerations for Optimization and Estimation in the Real (Noisy) World -- 11.1. Introduction -- 11.2. The Nelder-Mead Algorithm -- 11.3. The Box-Hunter Algorithm -- 11.4. Simulated Annealing -- 11.5. Exploration and Estimation in High Dimensions -- Problems -- References -- 12. Utility and Group Preference -- 12.1. Introduction -- 12.2. The St. Petersburg Paradox -- 12.3. von Neumann-Morgenstern Utility -- 12.4. Creating a St. Petersburg Trust.
12.5. Some Problems with Aggregate Choice Behavior -- 12.6. Jeffersonian Realities -- 12.7. Conclusions -- Problems -- References -- 13 A Primer in Sampling -- 13.1. Introduction -- 13.1.1. Tracking Polls -- 13.2. Stratification -- 13.2.1. A Warehouse Inventory -- 13.3. The Saga of Happy Valley -- 13.3.1. The Problem with Standards -- 13.4. To Annex or Not -- 13.4.1. The Bootstrap: The World in a Drop of Water -- 13.4.2. Resampling and Histograms -- 13.5. Using Sampling to Estimate Total Population Size -- 13.5.1. Capture Recapture -- Problems -- References -- 14 Stock Market: Strategies Based on Data versus Strategies Based on Ideology -- 14.1. Introduction -- 14.2. Markowitz's Efficient Frontier: Portfolio Design as Constrained Optimization -- 14.3. Sharpe's Super Efficient Frontier: The Capital Market Line (CAPM) -- 14.4. The Security Market Line -- 14.5. The Sharpe Diagonal Model -- 14.6. Portfolio Evaluation and the Capital Asset Pricing Model -- 14.7. Views of Risk -- 14.7.1. Diversification -- 14.8. Stock Progression as Geometric Brownian Motion -- 14.8.1. Ito's Lemma -- 14.8.2. A Geometric Brownian Model for Stocks -- 14.9. Estimating μ and σ -- 14.10. The Time Indexed Distribution of Portfolio Value -- 14.11. Negatively Correlated Portfolios -- 14.12. Bear Jumps -- 14.13. "Everyman's" MaxMedian Rule for Portfolio Manangement -- 14.13.1. Investing in a 401k -- 14.14. Derivatives -- 14.14.1. Black-Scholes and the Search for Risk Neutrality -- 14.14.2. A Game Independent of the Odds 3 -- 14.14.3. The Black-Scholes Hedge Using Binomial Trees -- 14.15. The Black-Scholes Derivation Using Differential Equations -- 14.16. Black-Scholes: Some Limiting Cases -- 14.17. Conclusions -- Problems -- References -- Appendix A. A Brief Introduction to Probability and Statistics -- A.1. Craps: An Intuitive Introduction to Probability and Statistics.
A.1.1. Random Variables, Their Means and Variances -- A.2. Combinatorics Basics -- A.3. Bayesian Statistics -- A.3.1. Bayes' Theorem -- A.3.2. A Diagnostic Example -- A.4. The Binomial Distribution -- A.5. The Uniform Distribution -- A.6. Moment Generating Functions -- A.7. The Normal (Gaussian) Distribution -- A.8. The Central Limit Theorem -- A.9. The Gamma Distribution -- A.10. Conditional Density Functions -- A.11. The Weak Law of Large Numbers -- A.12. The Multivariate Normal Distribution -- A.13. The Wiener Process -- A.14. The Poisson Process and the Poisson Distribution -- A.14.1. Simulating Bear Jumps -- A.15. Parametric Simulation -- A.15.1. Simulating a Geometric Brownian Walk -- A.15.2. The Multivariate Case -- A.16. Resampling Simulation -- A.16.1. The Multivariate Case -- A.17. A Portfolio Case Study -- Appendix B. Statistical Tables -- Tables of the Normal Distribution -- Tables of the Chi-Square Distribution -- Index.
Summary: Praise for the First Edition "This...novel and highly stimulating book, which emphasizes solving real problems...should be widely read. It will have a positive and lasting effect on the teaching of modeling and statistics in general." - Short Book Reviews This new edition features developments and real-world examples that showcase essential empirical modeling techniques Successful empirical model building is founded on the relationship between data and approximate representations of the real systems that generated that data. As a result, it is essential for researchers who construct these models to possess the special skills and techniques for producing results that are insightful, reliable, and useful. Empirical Model Building: Data, Models, and Reality, Second Edition presents a hands-on approach to the basic principles of empirical model building through a shrewd mixture of differential equations, computer-intensive methods, and data. The book outlines both classical and new approaches and incorporates numerous real-world statistical problems that illustrate modeling approaches that are applicable to a broad range of audiences, including applied statisticians and practicing engineers and scientists. The book continues to review models of growth and decay, systems where competition and interaction add to the complextiy of the model while discussing both classical and non-classical data analysis methods. This Second Edition now features further coverage of momentum based investing practices and resampling techniques, showcasing their importance and expediency in the real world. The author provides applications of empirical modeling, such as computer modeling of the AIDS epidemic to explain why North America has most of the AIDS cases in the First World and data-based strategies that allow individual investors to build their own investmentSummary: portfolios. Throughout the book, computer-based analysis is emphasized and newly added and updated exercises allow readers to test their comprehension of the presented material. Empirical Model Building, Second Edition is a suitable book for modeling courses at the upper-undergraduate and graduate levels. It is also an excellent reference for applied statisticians and researchers who carry out quantitative modeling in their everyday work.
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Intro -- Empirical Model Building: Data, Models, and Reality -- Contents -- Preface -- 1. Models of Growth and Decay -- 1.1. A Simple Pension and Annuity Plan -- 1.2. Income Tax Bracket Creep and the Quiet Revolution of 1980 -- 1.3. Retirement of a Mortgage -- 1.4. Some Mathematical Descriptions of the Theory of Malthus -- 1.5. Metastasis and Resistance -- Problems -- References -- 2. Models of Competition, Survival, and Combat -- 2.1. An Analysis of the Demographics of Ancient Israel -- 2.2. The Plague and John Graunt's Life Table -- 2.3. Modular Data-Based Wargaming -- 2.3.1. Herman Kahn and the Winning of the Cold War -- 2.4. Predation and Immune Response Systems -- 2.5. Pyramid Clubs for Fun and Profit -- Problems -- References -- 3. Epidemics -- 3.1. Introduction -- 3.2. John Snow and the London Cholera Epidemic of 1854 -- 3.3. Prelude: The Postwar Polio Epidemic -- 3.4. AIDS: A New Epidemic for America -- 3.5. Why an AIDS Epidemic in America? -- 3.5.1. Political Correctness Can Kill -- 3.6. The Effect of the Gay Bathhouses -- 3.7. A More Detailed Look at the Model -- 3.8. Forays into the Public Policy Arena -- 3.9. Modeling the Mature Epidemic -- 3.10. AIDS as a Facilitator of Other Epidemics -- 3.11. Comparisons with First World Countries -- 3.12. Conclusions: A Modeler's Portfolio -- Problems -- References -- 4. Bootstrapping -- 4.1. Introduction -- 4.2. Bootstrapping Analysis of Darwin's Data -- 4.3. A Bootstrapping Approximation to Fisher's Nonparametric Test -- 4.4. A Resampling Bassed Sign Test -- 4.5. A Bootstrapping Approach for Confidence Intervals -- 4.6. Solving Ill-Structured Problems -- Problems -- References -- 5. Monte Carlo Solutions of Differential Equations -- 5.1. Introduction -- 5.2. Gambler's Ruin -- 5.3. Solution of Simple Differential Equations -- 5.4. Solution of the Fokker-Planck Equation.

5.5. The Dirichlet Problem -- 5.6. Solution of General Elliptic Differential Equations -- 5.7. Conclusions -- Problems -- References -- 6. SIMEST, SIMDAT, and Pseudoreality -- 6.1. Introduction -- 6.2. The Bootstrap: A Dirac-Comb Density Estimator -- 6.3. SIMDAT: A Smooth Resampling Algorithm -- 6.3.1. The SIMDAT Algorithm -- 6.3.2. An Empirical Justification of SIMDAT -- 6.4. SIMEST: An Oncological Example -- 6.4.1. An Exploratory Prelude -- 6.4.2. Models and Algorithms -- Problems -- References -- 7. Exploratory Data Analysis -- 7.1. Introduction -- 7.2. Smoothing -- 7.3. The Stem and Leaf Plot -- 7.4. The Five Figure Summary -- 7.5. Tukey's Box Plot -- Problems -- References -- 8. Noise Killing Chaos -- 8.1. Introduction -- 8.2. The Discrete Logistic Model -- 8.3. A Chaotic Convection Model -- 8.4. Conclusions -- Problems -- References -- 9. A Primer in Bayesian Data Analysis -- 9.1. Introduction -- 9.2. The EM Algorithm -- 9.3. The Data Augmentation Algorithm -- 9.4. The Gibbs Sampler -- 9.5. Conclusions -- Problems -- References -- 10. Multivariate and Robust Procedures in Statistical Process Control -- 10.1. Introduction -- 10.2. A Contamination Model for SPC -- 10.3. A Compound Test for Higher Dimensional SPC Data -- 10.4. Rank Testing with Higher Dimensional SPC Data -- 10.5. A Robust Estimation Procedure for Location in Higher Dimensions -- Problems -- References -- 11. Considerations for Optimization and Estimation in the Real (Noisy) World -- 11.1. Introduction -- 11.2. The Nelder-Mead Algorithm -- 11.3. The Box-Hunter Algorithm -- 11.4. Simulated Annealing -- 11.5. Exploration and Estimation in High Dimensions -- Problems -- References -- 12. Utility and Group Preference -- 12.1. Introduction -- 12.2. The St. Petersburg Paradox -- 12.3. von Neumann-Morgenstern Utility -- 12.4. Creating a St. Petersburg Trust.

12.5. Some Problems with Aggregate Choice Behavior -- 12.6. Jeffersonian Realities -- 12.7. Conclusions -- Problems -- References -- 13 A Primer in Sampling -- 13.1. Introduction -- 13.1.1. Tracking Polls -- 13.2. Stratification -- 13.2.1. A Warehouse Inventory -- 13.3. The Saga of Happy Valley -- 13.3.1. The Problem with Standards -- 13.4. To Annex or Not -- 13.4.1. The Bootstrap: The World in a Drop of Water -- 13.4.2. Resampling and Histograms -- 13.5. Using Sampling to Estimate Total Population Size -- 13.5.1. Capture Recapture -- Problems -- References -- 14 Stock Market: Strategies Based on Data versus Strategies Based on Ideology -- 14.1. Introduction -- 14.2. Markowitz's Efficient Frontier: Portfolio Design as Constrained Optimization -- 14.3. Sharpe's Super Efficient Frontier: The Capital Market Line (CAPM) -- 14.4. The Security Market Line -- 14.5. The Sharpe Diagonal Model -- 14.6. Portfolio Evaluation and the Capital Asset Pricing Model -- 14.7. Views of Risk -- 14.7.1. Diversification -- 14.8. Stock Progression as Geometric Brownian Motion -- 14.8.1. Ito's Lemma -- 14.8.2. A Geometric Brownian Model for Stocks -- 14.9. Estimating μ and σ -- 14.10. The Time Indexed Distribution of Portfolio Value -- 14.11. Negatively Correlated Portfolios -- 14.12. Bear Jumps -- 14.13. "Everyman's" MaxMedian Rule for Portfolio Manangement -- 14.13.1. Investing in a 401k -- 14.14. Derivatives -- 14.14.1. Black-Scholes and the Search for Risk Neutrality -- 14.14.2. A Game Independent of the Odds 3 -- 14.14.3. The Black-Scholes Hedge Using Binomial Trees -- 14.15. The Black-Scholes Derivation Using Differential Equations -- 14.16. Black-Scholes: Some Limiting Cases -- 14.17. Conclusions -- Problems -- References -- Appendix A. A Brief Introduction to Probability and Statistics -- A.1. Craps: An Intuitive Introduction to Probability and Statistics.

A.1.1. Random Variables, Their Means and Variances -- A.2. Combinatorics Basics -- A.3. Bayesian Statistics -- A.3.1. Bayes' Theorem -- A.3.2. A Diagnostic Example -- A.4. The Binomial Distribution -- A.5. The Uniform Distribution -- A.6. Moment Generating Functions -- A.7. The Normal (Gaussian) Distribution -- A.8. The Central Limit Theorem -- A.9. The Gamma Distribution -- A.10. Conditional Density Functions -- A.11. The Weak Law of Large Numbers -- A.12. The Multivariate Normal Distribution -- A.13. The Wiener Process -- A.14. The Poisson Process and the Poisson Distribution -- A.14.1. Simulating Bear Jumps -- A.15. Parametric Simulation -- A.15.1. Simulating a Geometric Brownian Walk -- A.15.2. The Multivariate Case -- A.16. Resampling Simulation -- A.16.1. The Multivariate Case -- A.17. A Portfolio Case Study -- Appendix B. Statistical Tables -- Tables of the Normal Distribution -- Tables of the Chi-Square Distribution -- Index.

Praise for the First Edition "This...novel and highly stimulating book, which emphasizes solving real problems...should be widely read. It will have a positive and lasting effect on the teaching of modeling and statistics in general." - Short Book Reviews This new edition features developments and real-world examples that showcase essential empirical modeling techniques Successful empirical model building is founded on the relationship between data and approximate representations of the real systems that generated that data. As a result, it is essential for researchers who construct these models to possess the special skills and techniques for producing results that are insightful, reliable, and useful. Empirical Model Building: Data, Models, and Reality, Second Edition presents a hands-on approach to the basic principles of empirical model building through a shrewd mixture of differential equations, computer-intensive methods, and data. The book outlines both classical and new approaches and incorporates numerous real-world statistical problems that illustrate modeling approaches that are applicable to a broad range of audiences, including applied statisticians and practicing engineers and scientists. The book continues to review models of growth and decay, systems where competition and interaction add to the complextiy of the model while discussing both classical and non-classical data analysis methods. This Second Edition now features further coverage of momentum based investing practices and resampling techniques, showcasing their importance and expediency in the real world. The author provides applications of empirical modeling, such as computer modeling of the AIDS epidemic to explain why North America has most of the AIDS cases in the First World and data-based strategies that allow individual investors to build their own investment

portfolios. Throughout the book, computer-based analysis is emphasized and newly added and updated exercises allow readers to test their comprehension of the presented material. Empirical Model Building, Second Edition is a suitable book for modeling courses at the upper-undergraduate and graduate levels. It is also an excellent reference for applied statisticians and researchers who carry out quantitative modeling in their everyday work.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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