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Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...

Estimating Population Mean with Unknown Standard Deviation

Estimating Population Mean with Unknown Standard Deviation

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.
William S. Gosset (1876–1937) of the Guinness...

Estimating Population Standard Deviation

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...

Estimating Population Mean with Known Standard Deviation

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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Statistical Methods for Analyzing Epidemiological Data

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Mechanistic Models: Compartment Models in Individual and Population Analysis

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Related Experiment Video

Updated: Jun 18, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Composite likelihood estimation of demographic parameters.

Daniel Garrigan¹

¹Department of Biology, University of Rochester, Rochester, New York, USA. daniel.garrigan@rochester.edu

|November 14, 2009

Summary

This study introduces a flexible and efficient Bayesian method using composite and approximate likelihoods for analyzing whole-genome data. The method accurately estimates demographic parameters, including X chromosome to autosome size ratios, but finds no strong evidence for a non-African founder event.

Related Experiment Videos

Last Updated: Jun 18, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Population Genetics
Genomics
Computational Biology

Background:

Existing likelihood-based methods struggle to scale for whole-genome data analysis.
Composite and approximate likelihood methods offer computational advantages for large datasets and complex models.
This study focuses on a demographic model of allopatric divergence with a founder event or bottleneck.

Purpose of the Study:

To develop and apply a Bayesian Metropolis-coupled Markov chain Monte Carlo (MCMCMC) method for demographic parameter estimation.
To utilize composite and approximate likelihood methods for analyzing whole-genome polymorphism data.
To test the method's accuracy on simulated data and apply it to human population resequencing data.

Main Methods:

A Bayesian MCMCMC approach incorporating composite and approximate likelihoods was developed.
The joint frequency spectrum from human resequencing data was used to summarize genomic information.
The method was validated using simulated datasets with known demographic parameters.

Main Results:

The method accurately estimated demographic parameters, including the effective population size ratio between X chromosomes and autosomes, from simulated data.
Analysis of human population data did not provide strong support for a non-African founder event.
Estimates suggested an X chromosome to autosome effective population size ratio greater than one, though intervals included expected values for equal sex ratios.

Conclusions:

The implemented MCMCMC framework with composite and approximate likelihoods is promising for whole-genome analysis, offering flexibility and computational efficiency.
Further research is needed to understand the impact of the linkage equilibrium assumption on composite likelihood validity.
The developed method shows potential for analyzing complex demographic histories in large-scale genomic datasets.