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Related Concept Videos

Expected Value01:15

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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...
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 Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...

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Related Experiment Video

Updated: Jul 12, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Calculating partial expected value of perfect information via Monte Carlo sampling algorithms.

Alan Brennan1, Samer Kharroubi, Anthony O'hagan

  • 1School of Health and Related Research, The University of Sheffield, Sheffield, England. a.brennan@sheffield.ac.uk

Medical Decision Making : an International Journal of the Society for Medical Decision Making
|September 1, 2007
PubMed
Summary

Calculating the value of information in decision models using partial expected value of perfect information (EVPI) requires careful Monte Carlo sampling. Biased estimates can occur with shortcut algorithms, especially with correlated variables or nonlinearities.

Related Experiment Videos

Last Updated: Jul 12, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Area of Science:

  • Decision analysis
  • Health economics
  • Computational statistics

Background:

  • Partial expected value of perfect information (EVPI) quantifies the value of information in decision models.
  • Existing computational approaches for partial EVPI vary.
  • Accurate estimation is crucial for research prioritization.

Purpose of the Study:

  • Examine computation of partial EVPI estimates using Monte Carlo sampling algorithms.
  • Investigate potential biases and inaccuracies in estimation methods.
  • Provide guidance on efficient sampling strategies.

Main Methods:

  • Utilized a generalized Monte Carlo sampling algorithm with nested simulation.
  • Outer loop samples parameters of interest; inner loop samples remaining uncertainties.
  • Analyzed alternative computation methods, including shortcut algorithms.
  • Considered mathematical conditions for shortcut algorithm validity.

Main Results:

  • Nested Monte Carlo simulation is required due to nested expectations and maximization.
  • Maxima of Monte Carlo estimates are upwardly biased.
  • Small sample sizes lead to biased EVPI estimates.
  • Shortcut algorithms are inaccurate with correlated variables or nonlinearities.

Conclusions:

  • Partial EVPI calculations necessitate careful computational approaches to avoid bias.
  • Nested Monte Carlo simulation is a robust method, but efficiency can be improved.
  • Further methodological development is needed for wider application of partial EVPI.