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Related Concept Videos

Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
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...
Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
Parametric Survival Analysis: Weibull and Exponential Methods01:14

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
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
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...

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Related Experiment Video

Updated: Jun 13, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Improved estimation of site occupancy using penalized likelihood.

Monica Moreno1, Subhash R Lele

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada. mmoreno@ualberta.ca

Ecology
|April 16, 2010
PubMed
Summary
This summary is machine-generated.

Maximum likelihood estimators (MLE) for site occupancy face bias and instability issues with small sample sizes. A penalized likelihood method offers improved numerical stability and more accurate confidence intervals for occupancy estimation.

Related Experiment Videos

Last Updated: Jun 13, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Ecology
  • Wildlife Biology
  • Conservation Science

Background:

  • Site occupancy models are crucial for estimating species presence across locations.
  • Maximum likelihood estimators (MLE) can exhibit significant bias and instability when detection or occupancy probabilities are low, or when data is sparse (few sites or visits).
  • Inaccurate confidence intervals from MLE can lead to flawed ecological conclusions.

Purpose of the Study:

  • To address the limitations of maximum likelihood estimators (MLE) in site occupancy modeling.
  • To introduce and evaluate a penalized likelihood method as an alternative estimation technique.
  • To improve the accuracy and reliability of site occupancy parameter estimation, especially in data-limited scenarios.

Main Methods:

  • Developing an estimation method based on penalized likelihood.
  • Comparing the performance of penalized likelihood estimators against traditional MLE.
  • Evaluating estimator bias, numerical stability, and confidence interval coverage.

Main Results:

  • Penalized likelihood estimation demonstrates superior numerical stability compared to MLE.
  • Estimators derived from penalized likelihood exhibit a smaller mean squared error than MLE.
  • Confidence intervals generated using the penalized likelihood approach achieve coverage closer to nominal levels.

Conclusions:

  • Penalized likelihood provides a more robust and accurate method for site occupancy estimation, particularly when dealing with small sample sizes or low probabilities.
  • This approach mitigates bias and improves the reliability of confidence intervals, leading to more dependable ecological inferences.
  • The penalized likelihood method offers a valuable alternative for researchers using occupancy models in challenging data conditions.