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Probabilistic Models and Uncertainty

Predict a residual temperature

BOTIE

Solve the linear system whose right-hand side contains observed residuals.
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0 passed · 0 failed · 2 not run

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Use a copy of the example to try your own data. Keep the problem's assumptions in mind, and predict the effect of a change before checking the output. You can also add another branch to compare two ways of doing the calculation.

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Context for this challenge

Solve the linear system whose right-hand side contains observed residuals.

Botie is given a valid noisy training covariance, observed residuals, and query covariances.

Inspect the component calculation
Solve a linear system(
  Square coefficient matrix A: Noisy training covariance
  Right-hand vector b: Observed residuals
)
Examples and results
Noisy training covariance
1.25
Observed residuals
  1. 02
Required result
  1. 01.6
Noisy training covariance
20
02
Observed residuals
  1. 02
  2. 14
Required result
  1. 01
  2. 12
Try a fresh construction

This clears this draft, including its undo history. Earlier successful attempts stay recorded. Build again without opening hints to record an independent attempt.

Stuck? Inspect a worked construction

The tools below form one possible solution. You can assemble it, follow its signals, and undo that change to return to your own construction.

Assumptions and test precision

The supplied covariance must be valid and nonsingular. This construction returns a mean, not a full uncertainty interval. Numerical tests allow a difference of 0.001. Lists and structures must also have the right shape.

Your last tested pieces can start the full construction. An existing draft there keeps its own pieces.

Two correlated temperature observations

This check uses the pieces from “Use covariance to predict the query residual”.

BOTIE

These residual observations have nonzero covariance with each other. Use their full noisy covariance matrix and the query covariances to return the query's conditional mean residual.
Noisy training covariance
21
12
Observed residuals
  1. 03
  2. 10
Query-to-training covariance
  1. 01
  2. 10.5

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 does a zero residual mean here say nothing by itself about certainty?

A conditional mean and a predictive variance are different outputs; this construction returns only the mean.

The supplied covariance must be valid and nonsingular. This construction returns a mean, not a full uncertainty interval.

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