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Estimation of the Physical Quantities

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...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

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Parameter estimation and uncertainty quantification using information geometry.

Jesse A Sharp^1,2, Alexander P Browning^1,2, Kevin Burrage^1,2,3

¹School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia.

Journal of the Royal Society, Interface

|April 26, 2022

Summary

This summary is machine-generated.

This study enhances parameter estimation and uncertainty quantification by integrating information geometry techniques with traditional methods. These novel approaches offer data-independent insights into model identifiability and uncertainty.

Keywords:

epidemic models inference likelihood logistic growth population models

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Area of Science:

Statistics
Information Theory
Computational Science

Background:

Likelihood-based inference is a standard for parameter estimation and confidence region construction.
Uncertainty quantification typically relies on Bayesian methods, profile likelihood, asymptotic analysis, and bootstrapping.
Existing methods may not fully capture inherent data-independent properties of models.

Purpose of the Study:

To review and integrate likelihood-based inference with information geometry for enhanced parameter estimation.
To explore information geometry techniques for supplementing traditional uncertainty quantification methods.
To provide data-independent insights into model uncertainty and identifiability.

Main Methods:

Review of likelihood-based inference for parameter estimation and confidence regions.
Application of information geometry concepts like geodesic curves and Riemann scalar curvature.
Comparison with standard uncertainty quantification techniques (Bayesian, profile likelihood, bootstrapping).

Main Results:

Information geometry offers complementary, data-independent perspectives on uncertainty and identifiability.
Geodesic curves and Riemann scalar curvature can supplement existing uncertainty quantification frameworks.
These techniques can guide optimal data collection strategies.

Conclusions:

Integrating information geometry with likelihood-based inference provides a more comprehensive understanding of parameter uncertainty.
Information geometry offers valuable, model-intrinsic insights beyond data-driven analyses.
The developed methods and code are available to advance statistical modeling and experimental design.