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Related Concept Videos

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

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 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...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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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Related Experiment Video

Updated: Jul 13, 2026

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
12:39

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

Exact and approximate Bayesian estimation of net counting rates.

P G Groer1

  • 1The University of Tennessee, Department of Nuclear Engineering, Knoxville 37996-2300, USA. groer@utk.edu

Radiation Protection Dosimetry
|November 15, 2002
PubMed
Summary

Estimating net count rates with background noise is a statistical challenge. Bayesian methods using Poisson and normal distributions provide reliable estimates, especially with large observed counts.

Area of Science:

  • Nuclear physics
  • Statistical analysis
  • Bayesian inference

Background:

  • Stochastic fluctuations in radioactive disintegrations present statistical challenges for accurate measurement.
  • Accurate estimation of net count rates requires accounting for background radiation levels.

Purpose of the Study:

  • To derive and compare exact and approximate Bayesian estimates for net count rates.
  • To evaluate the accuracy of Poisson and normal distributions in modeling count data.
  • To assess the impact of background counts on net rate estimation.

Main Methods:

  • Developed exact and approximate Bayesian estimation methods for net count rates.
  • Utilized Poisson and normal distributions to model detected counts over varying intervals.
  • Derived and plotted posterior densities for net count rates with uniform priors.

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Last Updated: Jul 13, 2026

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  • Compared exact, Poisson-based, and normal approximation posterior densities.

    • Main Results:

    • No significant practical differences were observed between methods when the number of observed gross counts was large.
    • Small numerical differences in posterior expectations and standard deviations emerged for small observed counts.
    • A normal approximation to the Poisson distribution is generally satisfactory for large observed counts.

    Conclusions:

    • Bayesian methods offer robust approaches to estimating net count rates in the presence of background radiation.
    • The normal approximation to the Poisson distribution is a valid and practical tool for analyzing counting data with large sample sizes.
    • Caution is advised when applying the normal approximation with small observed counts due to potential numerical discrepancies.