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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.

Instrument Calibration

Instrument Calibration

Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
Analytical Balance Calibration
An analytical balance measures mass and requires regular calibration to...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Estimating Population Mean with Unknown Standard Deviation

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...

Estimating Population Mean with Known Standard Deviation

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 +...

Calibration Curves: Linear Least Squares

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...

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Calibrating machine learning approaches for probability estimation: A comprehensive comparison.

Francisco M Ojeda^1,2, Max L Jansen³, Alexandre Thiéry³

¹Department of Cardiology, University Heart and Vascular Center Hamburg, University Medical Center Hamburg-Eppendorf, Hamburg, Germany.

Statistics in Medicine

|October 18, 2023

Summary

This summary is machine-generated.

Statistical prediction models require calibration for new populations. Regression-based methods, especially logistic and beta calibration on transformed probabilities, offer the best performance for accurate probability estimates.

Keywords:

calibration logistic regression machine learning probability estimation probability machine updating

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Area of Science:

Statistics
Machine Learning
Biostatistics

Background:

Statistical prediction models are increasingly used in research.
Transferring models to new populations presents challenges due to structural differences.
Calibration techniques adapt models to target populations, but many methods exist.

Approach:

Systematic evaluation of popular calibration approaches for two-class probability estimation.
Literature review and comprehensive simulation study comparing methods.
Assessment of empirical properties, generalizability, and software availability.

Key Points:

Logistic and beta calibration demonstrated superior performance in simulations.
Calibration on logit-transformed probabilities generally outperformed non-transformed methods.
Regression-based calibration with transformed probabilities and estimated slopes is recommended.

Conclusions:

Regression-based calibration, particularly using transformed probabilities with estimated slopes, is effective for updating probability estimates in validation studies.
The choice between re-estimating the entire model versus calibration depends on structural differences and validation data sample size.
This study provides practical code for real-world application by researchers.