← All workshopsRead Tracking a State We Cannot Observe Directly

Probabilistic Models and Uncertainty

Update the hidden pump condition

BOTIE

Apply the transposed row-stochastic transition matrix to the previous belief.
Ready to test
0 passed · 0 failed · 2 not run

An empty floor. Start with the information your machine needs.

Received result

Your answer will arrive here.

Examples, experiments and workspace controls
Live values

Connect a tool's inputs to see what it produces. You can try a branch before connecting it to Result.

Try your own inputs

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.

Start at an output arrow, then click or drag to an input. Drag empty space to pan. Delete removes a selection. Ctrl/Cmd+Z undoes a change.
Context for this challenge

Apply the transposed row-stochastic transition matrix to the previous belief.

Botie has yesterday’s belief, a transition model, and likelihoods for today’s reading.

Inspect the component calculation
Matrix times vector(
  Rows of coefficients: Swap rows and columns(
    Matrix: Check transition rows(
      Transition table: Transition matrix
    )
  )
  Input vector: Check a probability distribution(
    Probabilities: Previous state probabilities
  )
)
Examples and results
Transition matrix
0.90.1
0.20.8
Previous state probabilities
  1. 00.8
  2. 10.2
Required result
  1. 00.76
  2. 10.24
Transition matrix
10
01
Previous state probabilities
  1. 01
  2. 10
Required result
  1. 01
  2. 10
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

This filters supplied models. It does not learn transitions or decode the most likely full path. 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.

A previously faulty pump may have recovered

This check uses the pieces from “Predict the pump state, then condition on its reading”.

BOTIE

Yesterday the pump was certainly faulty. State order is working, faulty; each transition row describes the next state from its corresponding old state. Today's reading favours a working pump. Return the updated state probabilities.
Previous state probabilities
  1. 00
  2. 11
Transition matrix
0.80.2
0.250.75
Reading likelihoods
  1. 00.9
  2. 10.1

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.

Which part of the construction would be missing if you merely multiplied yesterday's belief by today's likelihoods?

Keep temporal prediction and measurement correction as separate operations.

This filters supplied models. It does not learn transitions or decode the most likely full path.

Work through the Python challenges →
Continue the coursePredicting Between Measurements With Uncertainty →
← Combining Measurements With Different Reliability