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Related Concept Videos

Variance01:15

Variance

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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the data....
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Vector Algebra: Method of Components01:08

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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
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Estimating Population Mean with Known Standard Deviation01:16

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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.
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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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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Variational bayesian method of estimating variance components.

Aisaku Arakawa1, Masaaki Taniguchi1, Takeshi Hayashi2

  • 1Animal Genome Research Unit, National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan.

Animal Science Journal = Nihon Chikusan Gakkaiho
|February 16, 2016
PubMed
Summary
This summary is machine-generated.

The variational Bayesian method efficiently estimates variance components but can overestimate genetic variance in small, low-heritability populations. It offers faster computation than Gibbs sampling with comparable real-world accuracy.

Keywords:
Gibbs samplinglinear mixed modelspectral decomposition

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Area of Science:

  • Quantitative genetics
  • Statistical genetics
  • Bioinformatics

Background:

  • Accurate estimation of variance components is crucial for genetic studies.
  • Bayesian methods offer robust frameworks for estimating these components.
  • Variational inference provides an alternative to traditional sampling methods like Gibbs sampling.

Purpose of the Study:

  • To compare a variational Bayesian method with Gibbs sampling for estimating variance components.
  • To evaluate the performance of these methods using simulated and real pig data.
  • To assess computational efficiency and accuracy trade-offs.

Main Methods:

  • Development of a variational Bayesian inference approach.
  • Application of both variational Bayesian and Gibbs sampling methods.
  • Analysis of simulated datasets with varying heritability and population sizes.
  • Validation using a real pig dataset.

Main Results:

  • Variational Bayesian method showed overestimation bias for genetic variance with low heritability and small population sizes in simulated data.
  • Both methods yielded similar variance component estimates for real pig data.
  • Variational Bayesian method produced narrower posterior distributions and shorter computing times.
  • Posterior standard deviations were lower with the variational Bayesian method.

Conclusions:

  • Variational Bayesian inference is a computationally efficient alternative for variance component estimation.
  • Caution is advised when using variational Bayesian methods for low heritability and small population sizes.
  • The method shows promise for large-scale genetic analyses due to its speed.