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Introductory Mathematics

Compare possible germination rules

BOTIE

Calculate one ordered-sequence likelihood per candidate probability.
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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

Calculate one ordered-sequence likelihood per candidate probability.

Botie has observed which seeds germinated. Each candidate rule gives a probability for one seed, but he needs the likelihood of the whole ordered batch.

Inspect the component calculation
Compare Bernoulli sequence likelihoods(
  Candidate success probabilities: Candidate germination probabilities
  Ordered zero-or-one observations: Observed germination outcomes
)
Examples and results
Candidate germination probabilities
  1. 00.25
  2. 10.5
  3. 20.75
Observed germination outcomes
  1. 01
  2. 11
  3. 20
Required result
  1. 00.0469
  2. 10.125
  3. 20.1406
Candidate germination probabilities
  1. 00
  2. 10.5
  3. 21
Observed germination outcomes
  1. 01
  2. 11
Required result
  1. 00
  2. 10.25
  3. 21
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 finite candidate search is not a general estimator. Likelihood does not report uncertainty about the winning parameter. 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 batch with no germination

This check uses the pieces from “Retrieve the candidate that best explains the batch”.

BOTIE

None of four seeds germinated. The candidate list now includes zero. Predict which supplied probability gives this ordered sequence the greatest likelihood.
Candidate germination probabilities
  1. 00
  2. 10.2
  3. 20.8
  4. 31
Observed germination outcomes
  1. 00
  2. 10
  3. 20
  4. 30

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 the final lookup need the candidate list after you have already found the largest likelihood?

An optimiser's winning position, its objective value and its parameter value are different outputs.

This finite candidate search is not a general estimator. Likelihood does not report uncertainty about the winning parameter.

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