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Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Estimating Population Mean with Unknown Standard Deviation01:22

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 Mean with Known Standard Deviation01:16

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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Distributions to Estimate Population Parameter01:26

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...
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

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.
On...
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Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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ebnm: An R Package for Solving the Empirical Bayes Normal Means Problem Using a Variety of Prior Families.

Jason Willwerscheid1, Peter Carbonetto2, Matthew Stephens2

  • 1Providence College.

Journal of Statistical Software
|June 29, 2026
PubMed
Summary

The R package ebnm offers a unified interface for empirical Bayes normal means (EBNM) models, simplifying complex statistical analyses across various fields like genetics and data science.

Keywords:
NPMLEempirical Bayesmaximum likelihoodmixture modelsnormal meansshrinkage estimation

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Area of Science:

  • Statistical modeling
  • Computational statistics

Background:

  • Empirical Bayes Normal Means (EBNM) models are crucial in multiple testing, wavelet denoising, and gene expression analysis.
  • Existing software packages for EBNM models have disparate interfaces and lack implementations for certain prior assumptions.

Purpose of the Study:

  • To develop a unified R package, ebnm, for efficiently fitting EBNM models.
  • To provide a versatile interface supporting diverse prior assumptions, including nonparametric methods.

Main Methods:

  • The ebnm R package integrates existing implementations and introduces new, efficient fitting procedures.
  • Emphasis on speed, numerical stability, and a unified interface for various EBNM models.

Main Results:

  • The ebnm package offers a consistent interface for fitting EBNM models with various priors.
  • Demonstrated utility through an analysis of baseball statistics and integration with the flashier package for matrix factorization.

Conclusions:

  • The ebnm package facilitates the development and application of EBNM methods in statistics and related fields.
  • Provides a foundation for advanced statistical techniques, such as flexible matrix factorization.