Probabilistic Models and Uncertainty
Update a failure probability
BOTIE
Examples, experiments and workspace controls
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.
Context for this challenge
Update alpha and beta independently, then divide updated alpha by their updated total.
New sensor trials should update Botie's belief about a failure rate while retaining the information represented by the prior.
Add failures to alpha and working sensors to beta, then form the updated mean from both parameters.
Examples and results
- Prior alpha
1
- Prior beta
1
- New failures
1
- New working sensors
2
- Required result
0.4
- Prior alpha
1
- Prior beta
1
- New failures
2
- New working sensors
0
- Required result
0.75
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
Use positive prior parameters and non-negative integer counts. Trials assume one stable rate. Numerical tests allow a difference of 0.001. Lists and structures must also have the right shape.
Ten working sensors and no new failures
This check uses the pieces from “Let failures and working sensors update different counts”.
BOTIE
- Prior alpha
2
- Prior beta
8
- New failures
0
- New working sensors
10
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 observing only failures still leave the posterior mean below one in the supplied case?
Prior parameters continue to contribute until the observations outweigh them.
Use positive prior parameters and non-negative integer counts. Trials assume one stable rate.
Work through the Python challenges →