Bayesian Demographic Estimation and Forecasting

John Bryant is a senior researcher at Statistics New Zealand. He has previously worked at the New Zealand Treasury, and at universities in New Zealand and Thailand. He has consulted for many international organizations, including UNICEF, the FAO, and the World Bank. His research interests include applied demography, data science, and Bayesian statistics. Junni L. Zhang is an associate professor of statistics at Guanghua School of Management, Peking University. Her research interests include Bayesian statistics, text mining, and causal inference. She has extensive experience teaching undergraduate, graduate, MBA and executive courses, and is the author of Data Mining and Its Applications (in Chinese).

Introduction
Example: Mortality Rates for Maori

Our Approach to Demographic Estimation and Forecasting

Outline of the Rest of the Book

References and Further Reading




Demographic Foundations
Demographic Foundations

References and Further Reading

Demographic Individuals

Attributes

Events

The Lexis Diagram

Twelve Fictitious Individuals

References and Further Reading

Demographic Arrays

Population Counts

Death Counts

Movements

Alternative Representations of Changing Statuses

Non-Demographic Events

Exposure

Age, Period, and Cohort

Rates, Proportions, Means, and Ratios

Super-Population and Finite-Population Quantities

Collapsing Dimensions

References and Further Reading

Demographic Accounts

Demographic Systems

Demographic Accounts

An Account with No Region and No Age

An Account with Region but Not Age

An Account with Age But Not Region

Movements Accounts and Transitions Accounts*

Mathematical Description of the Demographic Accounting Identities*

References and Further Reading

Demographic Data

Traditional Data Sources

New Data Sources

Data Quality and Model Choice

References and Further Reading

3. Bayesian Foundations

Bayesian Foundations

Bayesian Statistics

The Features of a Bayesian Data Analysis

References and Further Reading

Bayesian Model Specification

Using Probability Distributions to Quantify Uncertainty

Posterior as Compromise Between Likelihood and Prior

Standard Probability Distributions

Poisson Distribution

Binomial Distribution

Normal Distribution

Half-t Distribution

Exchangeability

Partial Exchangeability

Exchangeability within Groups

Exchangeable Residuals

Exchangeable Increments

Pooling Information

Hierarchy

Incorporating External Information

Priors

Covariates

Embedding the Model in a Larger Model

References and Further Reading

Bayesian Inference and Model Checking

Computation

Summarizing the Posterior Distribution

Summary Measures

Calculating Posterior Summaries

Derived Distributions

Posterior Distribution for Derived Quantities

Posterior Predictive Distribution

Missing Data

Forecasting

Model Checking

Responsible Modellers Check and Revise their Models

Held back Data

Replicate Data

*Simulation and Calibration

References and Further Reading




Inferring Arrays from Reliable Data
Inferring Demographic Arrays from Reliable Data

Summary of the Framework of Part III

Applications

References and Further Reading

Infant Mortality in Sweden

The Infant Mortality Rate

Modelling Infant Mortality Rates in Swedish Counties

Model

Likelihood

Model for Underlying Infant Mortality Rates

Prior for the Region Effect

Prior for Time Effect

Prior for Intercept

Prior for Standard Deviation

Summary

Results

Infant Mortality Rates

Intercept, Region Effects, and Time Effects

Prior for Time Effect

Standard Deviations

Model Checking

Model Predictions versus Direct Estimates

Regional Variation in Slopes

Summarizing Results via Probabilities

Forecasting

Constructing the Forecasts

Results: Exploding Credible Intervals for Forecasting

A Partial Solution

References and Further Reading

Life Expectancy in Portugal

Mortality Rates

The Log Function

Life Expectancy

Age, Sex, and Time Effects

Interactions

Models

Likelihood

Model for Mortality Rates

Prior for Age Effect

Prior for Time Effect

Prior for Age-Time Interaction

Prior for Sex-Time Interaction

Priors for Other Terms

Summary

Model Choice Using Heldback Data

Estimating and Forecasting with the Baseline and Alternative

Models

Comparing the Forecasts with the Heldback Data

Results

Forecasting of Life Expectancy for -

*Obtaining Forecasts of Life Expectancy

References and Further Reading

Health Expenditure in the Netherlands

A Simple Expenditure Projection

Expenditure Projections for the Netherlands

A Statistical Model for Per Capita Expenditures

Model Checking via Replicate Data

Revised Expenditure Projections

Forecasting Policy Outcomes

References and Further Reading




Inferring Arrays from Unreliable Data
Inferring Demographic Arrays from Unreliable Data

Summary of the Framework

Data Models

Applications

References and Further Reading

Internal Migration in Iceland

Internal Migration in Iceland

Continentalization by Random Rounding to Base Three

Overview of Model

System Model

Data Model

Estimation

Results for Unconfidentialized Migration Counts

Results for Migration Rates

Forecasting

References and Further Reading

Fertility in Cambodia

Data

Overview of Model

System Model

Data Models

Census

Demographic and Health Survey

Results

Revised Model

Final Model

References and Further Reading




Inferring Accounts

Inferring Demographic Accounts

Summary of Our Approach

Applications

The Role of Demographic Accounts in Official Statistical Systems

References and Further Reading

Population in New Zealand

Input Data for the National Demographic Account

Model for National Demographic Account

Overview

Account

System Models

Data Models

Estimation

Results for the National Demographic Account

Sensitivity Tests for the National Demographic Account

Input Data for the Regional Demographic Account

Model for the Regional Demographic Account

System Models

xii Contents

Data Models

Results for the Regional Demographic Account

References and Further Reading

Population in China

Input Data

Model

Overview

Account

System Models

Data Models

Estimation and Forecasting

Results

References and Further Reading

Conclusion