Bayesian Demographic Estimation and Forecasting

John Bryant, Junni L. Zhang

• Verlag: Chapman and Hall/CRC
• Jahr: 2018
• ISBN:
  9780429841330
• Auflage: 1
• Thema: Matemáticas
• Thema: Probabilidad y estadística

Bayesian Demographic Estimation and Forecasting presents three statistical frameworks for modern demographic estimation and forecasting. The frameworks draw on recent advances in statistical methodology to provide new tools for tackling challenges such as disaggregation, measurement error, missing data, and combining multiple data sources. The methods apply to single demographic series, or to entire demographic systems. The methods unify estimation and forecasting, and yield detailed measures of uncertainty.

The book assumes minimal knowledge of statistics, and no previous knowledge of demography. The authors have developed a set of R packages implementing the methods. Data and code for all applications in the book are available on www.bdef-book.com.

"This book will be welcome for the scientific community of forecasters…as it presents a new approach which has already given important results and which, in my opinion, will increase its importance in the future." ~Daniel Courgeau, Institut national d'études démographiques

Contents

Preface

1 Introduction

1.1 Example: Mortality Rates for Maori

1.2 Our Approach to Demographic Estimation and Forecasting

1.3 Outline of the Rest of the Book

1.4 References and Further Reading

PART I Demographic Foundations

2 Demographic Foundations

2.1 References and Further Reading

3 Demographic Individuals

3.1 Attributes

3.2 Events

3.3 Lexis Diagram

3.4 Twelve Fictitious Individuals

3.5 References and Further Reading

4 Demographic Arrays

4.1 Population Counts

4.2 Death Counts

4.3 Movements

4.4 Alternative Representations of Changing Statuses

4.5 Non-Demographic Events

4.6 Exposure

4.7 Age, Period, and Cohort

4.8 Rates, Proportions, Means, and Ratios

4.9 Super-Population and Finite-Population Quantities

4.10 Collapsing Dimensions

4.11 References and Further Reading

5 Demographic Accounts

5.1 Demographic Systems

5.2 Demographic Accounts

5.3 Account with No Region and No Age

5.4 Account with Region and No Age

5.5 Account with Age and No Region

5.6 Movements Accounts and Transitions Accounts*

5.7 Mathematical Description of Accounting Identities*

5.8 References and Further Reading

6 Demographic Data

6.1 Traditional Data Sources

6.2 New Data Sources

6.3 Data Quality and Model Choice

6.4 References and Further Reading

PART II Bayesian Foundations

7 Bayesian Foundations

7.1 Bayesian Statistics

7.2 Features of a Bayesian Data Analysis

7.3 References and Further Reading

8 Bayesian Model Specification

8.1 Using Probability Distributions to Quantify Uncertainty

8.2 Posterior as a Compromise between Likelihood and Prior

8.3 Standard Probability Distributions

8.3.1 Poisson Distribution

8.3.2 Binomial Distribution

8.3.3 Normal Distribution

8.3.4 Half-t Distribution

8.4 Exchangeability

8.5 Partial Exchangeability

8.5.1 Exchangeability within Groups

8.5.2 Exchangeable Residuals

8.5.3 Exchangeable Increments

8.6 Pooling Information

8.7 Hierarchy

8.8 Incorporating External Information

8.8.1 Priors

8.8.2 Covariates

8.8.3 Embedding the Model in a Larger Model

8.9 References and Further Reading

9 Bayesian Inference and Model Checking

9.1 Computation

9.2 Summarizing the Posterior Distribution

9.2.1 Summary Measures

9.2.2 Calculating Posterior Summaries

9.3 Derived Distributions

9.3.1 Posterior Distribution for Derived Quantities

9.3.2 Posterior Predictive Distribution

9.4 Missing Data

9.5 Forecasting

9.6 Model Checking

9.6.1 Responsible Modelers Check and Revise their Models

9.6.2 Heldback Data

9.6.3 Replicate Data

9.7 Simulation and Calibration*

9.8 References and Further Reading

PART III Inferring Demographic Arrays from Reliable Data

10 Inferring Demographic Arrays from Reliable Data

10.1 Summary of the Framework of Part

10.2 Applications

10.3 References and Further Reading

11 Infant Mortality in Sweden

11.1 Infant Mortality Rate

11.2 Infant Mortality Rates in Swedish Counties

11.3 Model

11.3.1 Likelihood

11.3.2 Model for Underlying Infant Mortality Rates

11.3.3 Prior for Region Effect

11.3.4 Prior for Time Effect

11.3.5 Prior for Intercept

11.3.6 Prior for Standard Deviation

11.3.7 Summary

11.4 Results

11.4.1 Infant Mortality Rates

11.4.2 Intercept, Region Effects, and Time Effects

11.4.3 Prior for Time Effect

11.4.4 Standard Deviations

11.5 Model Checking

11.5.1 Model Predictions versus Direct Estimates

11.5.2 Regional Variation in Slopes

11.6 Summarizing Results via Probabilities

11.7 Forecasting

11.7.1 Constructing the Forecasts

11.7.2 Results: Exploding Credible Intervals for Forecasting

11.7.3 A Partial Solution

11.8 References and Further Reading

12 Life Expectancy in Portugal

12.1 Mortality Rates

12.2 Log Function

12.3 Life Expectancy

12.4 Age, Sex, and Time Effects

12.5 Interactions

12.6 Models

12.6.1 Likelihood

12.6.2 Model for Mortality Rates

12.6.3 Prior for Age Effect

12.6.4 Prior for Time Effect

12.6.5 Prior for Age-Time Interaction

12.6.6 Prior for Sex-Time Interaction

12.6.7 Priors for Other Terms

12.6.8 Summary

12.7 Model Choice Using Heldback Data

12.8 Estimating and Forecasting

12.9 Comparing the Forecasts with the Heldback Data

12.10 Results

12.11 Forecasting of Life Expectancy for 2016-2035

12.12 Obtaining Forecasts of Life Expectancy*

12.13 References and Further Reading

13 Health Expenditure in the Netherlands

13.1 A Simple Expenditure Projection

13.2 Expenditure Projections for the Netherlands

13.3 A Statistical Model for Per Capita Expenditures

13.4 Model Checking via Replicate Data

13.5 Revised Expenditure Projections

13.6 Forecasting Policy Outcomes

13.7 References and Further Reading

PART IV Inferring Demographic Arrays from Unreliable Data

14 Inferring Demographic Arrays from Unreliable Data

14.1 Summary of the Framework

14.2 Data Models

14.3 Applications

14.4 References and Further Reading

15 Internal Migration in Iceland

15.1 Internal Migration in Iceland

15.2 Confidentialization by Random Rounding to Base Three

15.3 Overview of Model

15.4 System Model

15.5 Data Model

15.6 Estimation

15.7 Results for Unconfidentialized Migration Counts

15.8 Results for Migration Rates

15.9 Forecasting

15.10 References and Further Reading

16 Fertility in Cambodia

16.1 Data

16.2 Overview of Model

16.3 System Model

16.4 D...