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Related Concept Videos

Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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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...
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Estimating Population Mean with Unknown Standard Deviation01:22

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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.
William S. Gosset (1876–1937) of the...
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What is Population Genetics?01:25

What is Population Genetics?

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A population is composed of members of the same species that simultaneously live and interact in the same area. When individuals in a population breed, they pass down their genes to their offspring. Many of these genes are polymorphic, meaning that they occur in multiple variants. Such variations of a gene are referred to as alleles. The collective set of all the alleles within a population is known as the gene pool.
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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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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.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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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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Hardy-Weinberg Principle01:49

Hardy-Weinberg Principle

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Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.
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Approximate maximum likelihood estimation for population genetic inference.

Johanna Bertl1, Gregory Ewing1, Carolin Kosiol1

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Statistical Applications in Genetics and Molecular Biology
|November 3, 2017
PubMed
Summary

This study introduces a novel stochastic approximation method for population genetics parameter estimation. It offers a faster, more robust alternative to existing techniques, especially for complex, high-dimensional data.

Keywords:
approximate inferenceisolation-migration modelmaximum likelihood estimationorang-utanspopulation geneticsstochastic approximation

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Area of Science:

  • Population Genetics
  • Computational Biology
  • Statistical Inference

Background:

  • Parameter estimation in population genetics is often hindered by complex likelihood functions.
  • Approximate Bayesian Computation (ABC) and particle filters are common but can be inefficient in high-dimensional scenarios.

Purpose of the Study:

  • To develop a novel, efficient parameter estimation method for population genetics.
  • To address the limitations of existing sampling-based and iterative methods in high-dimensional settings.

Main Methods:

  • A new stochastic approximation algorithm is proposed, simulating movement along a gradient.
  • The method converges to maximum likelihood estimates using summary statistics.
  • Tuning guidelines are provided to enhance robustness and performance.

Main Results:

  • The proposed method demonstrates speed and efficiency, even with numerous summary statistics.
  • It effectively handles high-dimensional problems and low signal-to-noise ratios.
  • The approach was successfully applied to estimate demographic history in orang-utan populations.

Conclusions:

  • Stochastic approximation offers a powerful alternative for parameter estimation in population genetics.
  • The developed method provides a robust and computationally efficient solution for complex genetic data.
  • This approach has significant implications for evolutionary and demographic studies.