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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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Sampling Distribution01:12

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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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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Sampling Methods: Sample Types01:18

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Sampling materials are classified into three main types: solid, liquid, and gas.
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Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Sampling Methods: Overview01:06

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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Related Experiment Video

Updated: Mar 7, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
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Efficient computation of the joint sample frequency spectra for multiple populations.

John A Kamm1, Jonathan Terhorst1, Yun S Song2

  • 1Department of Statistics, University of California, Berkeley.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|February 28, 2017
PubMed
Summary

We developed new methods for calculating the sample frequency spectrum (SFS) in population genetics. This improves the accuracy and efficiency of demographic inference, especially for large, complex population structures.

Keywords:
coalescentdemographic inferencepopulation geneticssum-product algorithm

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Area of Science:

  • Population Genetics
  • Genomics
  • Computational Biology

Background:

  • The sample frequency spectrum (SFS) is crucial for analyzing population genomic variation.
  • Inferring demographic history from joint SFS data across multiple populations is of significant interest.
  • Current methods face numerical instability and high computational costs with large sample sizes and multiple populations.

Purpose of the Study:

  • To develop accurate and efficient methods for computing the expected joint SFS.
  • To address limitations of existing SFS-based inference techniques.
  • To facilitate complex demographic modeling in population genetics.

Main Methods:

  • Derived new analytic formulas for expected joint SFS computation.
  • Developed algorithms for efficient calculation with large numbers of individuals and populations.
  • Implemented these methods in the novel software package 'momi'.

Main Results:

  • Achieved accurate and efficient computation of the expected joint SFS.
  • Demonstrated improvements in numerical stability and computational complexity.
  • Enabled analysis of complex demographic models with arbitrary population size histories.

Conclusions:

  • The new analytic formulas and algorithms significantly advance SFS-based demographic inference.
  • 'momi' software provides a robust tool for analyzing large-scale population genomic data.
  • These advancements facilitate more precise understanding of population evolutionary histories.