← All workshopsRead Combining Measurements With Different Reliability

Probabilistic Models and Uncertainty

Combine thermometer readings

Equal uncertainty changes the weighting

The thermometers disagree, and their known error variances say they are not equally reliable. Botie needs a combined temperature estimate.

BOTIE

Both thermometers now have the same error variance. How should their contributions compare?
The inputs we are comparing

Temperature readings

Unequal reliability

  1. 020
  2. 124

Equal reliability

  1. 010
  2. 114

Positive error variances

Unequal reliability

  1. 01
  2. 14

Equal reliability

  1. 02
  2. 12
Result for unequal reliability
20.8
Choose an explanation to test
A hot reading from an imprecise thermometer

This check uses the pieces from “Give precise thermometers more influence”.

BOTIE

Three thermometers read the same temperature in degrees Celsius. Assume independent unbiased Gaussian errors with the supplied variances in degrees Celsius squared. Return their precision-weighted estimate.
Temperature readings
  1. 018
  2. 122
  3. 230
Positive error variances
  1. 01
  2. 14
  3. 2100

Use a number, text, or an array matching the requested result. For a matrix, put each row in brackets. Saving your prediction runs your current construction on these inputs and checks the earlier examples too.

Build a construction in the workspace above first. This case will test those pieces.

Why would two thermometers sharing the same calibration error violate the story behind this weighting?

Repeated evidence is less informative when its errors are correlated.

Requires common units, positive known variances, unbiased readings, and independent errors.

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