
Demographic Forecasting
Description
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By showing how to include more information in statistical models, Demographic Forecasting carries broad statistical implications for social scientists, statisticians, demographers, public-health experts, policymakers, and industry analysts.
- Introduces methods to improve forecasts of mortality rates and similar variables
- Provides innovative tools for more effective statistical modeling
- Makes available free open-source software and replication data
- Includes full-color graphics, a complete glossary of symbols, a self-contained math refresher, and more
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Content
- Cover
- Title Page
- Copyright Page
- Contents
- List of Figures
- List of Tables
- Preface
- Acknowledgments
- 1 Qualitative Overview
- 1.1 Introduction
- 1.2 Forecasting Mortality
- 1.2.1 The Data
- 1.2.2 The Patterns
- 1.2.3 Scientific versus Optimistic Forecasting Goals
- 1.3 Statistical Modeling
- 1.4 Implications for the Bayesian Modeling Literature
- 1.5 Incorporating Area Studies in Cross-National Comparative Research
- 1.6 Summary
- Part I: Existing Methods for Forecasting Mortality
- 2 Methods without Covariates
- 2.1 Patterns in Mortality Age Profiles
- 2.2 A United Statistical Framework
- 2.3 Population Extrapolation Approaches
- 2.4 Parametric Approaches
- 2.5 A Nonparametric Approach: Principal Components
- 2.5.1 Introduction
- 2.5.2 Estimation
- 2.6 The Lee-Carter Approach
- 2.6.1 The Model
- 2.6.2 Estimation
- 2.6.3 Forecasting
- 2.6.4 Properties
- 2.7 Summary
- 3 Methods with Covariates
- 3.1 Equation-by-Equation Maximum Likelihood
- 3.1.1 Poisson Regression
- 3.1.2 Least Squares
- 3.1.3 Computing Forecasts
- 3.1.4 Summary Evaluation
- 3.2 Time-Series, Cross-Sectional Pooling
- 3.2.1 The Model
- 3.2.2 Postestimation Intercept Correction
- 3.2.3 Summary Evaluation
- 3.3 Partially Pooling Cross Sections via Disturbance Correlations
- 3.4 Cause-Specific Methods with Microlevel Information
- 3.4.1 Direct Decomposition Methods Modeling
- 3.4.2 Microsimulation Methods
- 3.4.3 Interpretation
- 3.5 Summary
- Part II: Statistical Modeling
- 4 The Model
- 4.1 Overview
- 4.2 Priors on Coefficients
- 4.3 Problems with Priors on Coeffcients
- 4.3.1 Little Direct Prior Knowledge Exists about Coefficients
- 4.3.2 Normalization Factors Cannot Be Estimated
- 4.3.3 We Know about the Dependent Variable, Not the Coefficients
- 4.3.4 Difficulties with Incomparable Covariates
- 4.4 Priors on the Expected Value of the Dependent Variable
- 4.4.1 Step 1: Specify a Prior for the Dependent Variable
- 4.4.2 Step 2: Translate to a Prior on the Coefficients
- 4.4.3 Interpretation
- 4.5 A Basic Prior for Smoothing over Age Groups
- 4.5.1 Step 1: A Prior for µ
- 4.5.2 Step 2: From the Prior on µ to the Prior on ß
- 4.5.3 Interpretation
- 4.6 Concluding Remark
- 5 Priors over Grouped Continuous Variables
- 5.1 Definition and Analysis of Prior Indifference
- 5.1.1 A Simple Special Case
- 5.1.2 General Expressions for Prior Indifference
- 5.1.3 Interpretation
- 5.2 Step 1: A Prior for µ
- 5.2.1 Measuring Smoothness
- 5.2.2 Varying the Degree of Smoothness over Age Groups
- 5.2.3 Null Space and Prior Indifference
- 5.2.4 Nonzero Mean Smoothness Functional
- 5.2.5 Discretizing: From Age to Age Groups
- 5.2.6 Interpretation
- 5.3 Step 2: From the Prior on µ to the Prior on ß
- 5.3.1 Analysis
- 5.3.2 Interpretation
- 6 Model Selection
- 6.1 Choosing the Smoothness Functional
- 6.2 Choosing a Prior for the Smoothing Parameter
- 6.2.1 Smoothness Parameter for a Nonparametric Prior
- 6.2.2 Smoothness Parameter for the Prior over the Coefficients
- 6.3 Choosing Where to Smooth
- 6.4 Choosing Covariates
- 6.4.1 Size of the Null Space
- 6.4.2 Content of the Null Space
- 6.5 Choosing a Likelihood and Variance Function
- 6.5.1 Deriving the Normal Specification
- 6.5.2 Accuracy of the Log-Normal Approximation to the Poisson
- 6.5.3 Variance Specification
- 7 Adding Priors over Time and Space
- 7.1 Smoothing over Time
- 7.1.1 Prior Indifference and the Null Space
- 7.2 Smoothing over Countries
- 7.2.1 Null Space and Prior Indifference
- 7.2.2 Interpretation
- 7.3 Smoothing Simultaneously over Age, Country, and Time
- 7.4 Smoothing Time Trend Interactions
- 7.4.1 Smoothing Trends over Age Groups
- 7.4.2 Smoothing Trends over Countries
- 7.5 Smoothing with General Interactions
- 7.6 Choosing a Prior for Multiple Smoothing Parameters
- 7.6.1 Example
- 7.6.2 Estimating the Expected Value of the Summary Measures
- 7.7 Summary
- 8 Comparisons and Extensions
- 8.1 Priors on Coefficients versus Dependent Variables
- 8.1.1 Defining Distances
- 8.1.2 Conditional Densities
- 8.1.3 Connections to "Virtual Examples" in Pattern Recognition
- 8.2 Extensions to Hierarchical Models and Empirical Bayes
- 8.2.1 The Advantages of Empirical Bayes without Empirical Bayes
- 8.2.2 Hierarchical Models as Special Cases of Spatial Models
- 8.3 Smoothing Data without Forecasting
- 8.4 Priors When the Dependent Variable Changes Meaning
- Part III: Estimation
- 9 Markov Chain Monte Carlo Estimation
- 9.1 Complete Model Summary
- 9.1.1 Likelihood
- 9.1.2 Prior for ß
- 9.1.3 Prior for s[sub(i)]
- 9.1.4 Prior for ?
- 9.1.5 The Posterior Density
- 9.2 The Gibbs Sampling Algorithm
- 9.2.1 Sampling s
- The Conditional Density
- Interpretation
- 9.2.2 Sampling ?
- The Conditional Density
- Interpretation
- 9.2.3 Sampling ß
- The Conditional Density
- Interpretation
- 9.2.4 Uncertainty Estimates
- 9.3 Summary
- 10 Fast Estimation without Markov Chains
- 10.1 Maximum A Posteriori Estimator
- 10.2 Marginal Maximum A Posteriori Estimator
- 10.3 Conditional Maximum A Posteriori Estimator
- 10.4 Summary
- Part IV: Empirical Evidence
- 11 Illustrative Analyses
- 11.1 Forecasts without Covariates: Linear Trends
- 11.1.1 Smoothing over Age Groups Only
- 11.1.2 Smoothing over Age and Time
- 11.2 Forecasts without Covariates: Nonlinear Trends
- 11.3 Forecasts with Covariates: Smoothing over Age and Time
- 11.4 Smoothing over Countries
- 12 Comparative Analyses
- 12.1 All Causes in Males
- 12.2 Lung Disease in Males
- 12.2.1 Comparison withLeast Squares
- 12.2.2 Country-by-Country Analysis
- 12.3 Breast Cancer in Females
- 12.3.1 Comparison with Least Squares
- 12.3.2 Country-by-country Analysis
- 12.4 Comparison on OECD Countries
- 12.4.1 Transportation Accidents in Males
- 12.4.2 Cardiovascular Disease in Males
- 13 Concluding Remarks
- Appendixes
- A Notation
- A.1 Principles
- A.2 Glossary
- B Mathematical Refresher
- B.1 Real Analysis
- B.1.1 Vector Space
- B.1.2 Metric Space
- B.1.3 Normed Space
- B.1.4 Scalar Product Space
- B.1.5 Functions, Mappings, and Operators
- B.1.6 Functional
- B.1.7 Span
- B.1.8 Basis and Dimension
- B.1.9 Orthonormality
- B.1.10 Subspace
- B.1.11 Orthogonal Complement
- B.1.12 Direct Sum
- B.1.13 Projection Operators
- B.2 Linear Algebra
- B.2.1 Range, Null Space, Rank, and Nullity
- B.2.2 Eigenvalues and Eigenvectors for Symmetric Matrices
- B.2.3 Definiteness
- B.2.4 Singular Values Decomposition
- Definition
- For Approximation
- B.2.5 Generalized Inverse
- B.2.6 Quadratic Form Identity
- B.3 Probability Densities
- B.3.1 The Normal Distribution
- B.3.2 The Gamma Distribution
- B.3.3 The Log-Normal Distribution
- C Improper Normal Priors
- C.1 Definitions
- C.2 An Intuitive Special Case
- C.3 The General Case
- C.4 Drawing Random Samples
- D Discretization of the Derivative Operator
- E Smoothness over Graphs
- Bibliography
- Index
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