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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Confidence Coefficient01:24

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

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Confidence intervals for population projections based on Monte Carlo methods.

P Pflaumer

    International Journal of Forecasting
    |January 1, 1988
    PubMed
    Summary

    This study uses Monte Carlo simulation to create confidence intervals for population forecasts. It accounts for uncertainty in fertility and immigration rates, projecting U.S. population between 255-355 million by 2082 with 90% probability.

    Keywords:
    AmericasDeveloped CountriesDeveloping CountriesEstimation TechnicsFertilityInternational MigrationMethodological StudiesMigrationModels, TheoreticalNorth AmericaNorthern AmericaPopulation ProjectionProbabilityResearch MethodologyStatistical StudiesStudiesUnited States

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    Area of Science:

    • Demography
    • Statistical modeling
    • Population studies

    Background:

    • Population forecasting relies on predicting future fertility and net immigration rates.
    • These demographic variables are highly volatile, introducing significant uncertainty into projections.
    • Accurate population projections are crucial for policy and resource planning.

    Purpose of the Study:

    • To develop a method for constructing confidence intervals in population projections.
    • To incorporate uncertainty from key demographic variables (fertility and net immigration) into forecasting models.
    • To provide a probabilistic range for future population sizes.

    Main Methods:

    • Utilizing Monte Carlo simulation to model population dynamics.
    • Treating fertility and net immigration rates as random variables with specified distributions.
    • Generating a distribution of possible population outcomes to establish confidence intervals.

    Main Results:

    • The Monte Carlo simulation approach successfully generates confidence intervals for population forecasts.
    • For the U.S. in 2082, the model estimates a population range of 255 million to 355 million with 90% probability.
    • This range reflects the inherent uncertainty in projecting volatile demographic factors.

    Conclusions:

    • Monte Carlo simulation is a viable technique for quantifying uncertainty in population projections.
    • Careful specification of subjective distributions for fertility and migration is key to reliable forecasts.
    • The method provides a more realistic and informative outlook on future population sizes compared to single-point estimates.