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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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Bayesian Population Forecasting: Extending the Lee-Carter Method.

Arkadiusz Wiśniowski1, Peter W F Smith, Jakub Bijak

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Summary
This summary is machine-generated.

This study introduces a dynamic Bayesian method for population forecasting by age and sex, integrating fertility, mortality, and migration models for accurate predictions and uncertainty assessment.

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Area of Science:

  • Demography
  • Statistical Modeling
  • Bayesian Inference

Background:

  • Accurate population forecasting is crucial for policy and planning.
  • Existing models often lack integrated approaches for multiple demographic components.
  • Quantifying uncertainty in population projections remains a challenge.

Purpose of the Study:

  • To develop a fully integrated and dynamic Bayesian approach for population forecasting by age and sex.
  • To embed Lee-Carter type models within a cohort projection framework.
  • To demonstrate the adaptability of the methodology for diverse data sources.

Main Methods:

  • Utilized a dynamic Bayesian framework.
  • Integrated Lee-Carter type models for fertility, mortality, immigration, and emigration.
  • Employed a cohort component projection model.
  • Analyzed United Kingdom time series data.

Main Results:

  • Successfully forecasted population components by age and sex to 2024.
  • Quantified uncertainty associated with demographic forecasts.
  • Compared various forecast models for age-specific fertility, mortality, and migration.

Conclusions:

  • The Bayesian approach offers flexibility and advantages for population forecasting.
  • The integrated methodology provides robust and reliable demographic projections.
  • Highlights potential extensions for future research in population modeling.