Section 6 of 24 · 5 lessons

Probabilistic Models and Uncertainty

A prediction is rarely the only plausible outcome. Botie will keep track of possible outcomes, update an uncertain failure rate, and combine noisy readings. We will distinguish uncertainty about a model from variation in the next observation, then use those ideas to predict between measured locations.

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Describing What We Do Not Know

A single estimate can hide how little evidence supports it. Describe possible outcomes, then update an uncertain failure rate as observations arrive.

  1. 01Planning for More Than One Possible OutcomeA delivery might contain different numbers of damaged sensors. Keep the possible outcomes and their probabilities together before deciding how many replacements to hold.
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  2. 02Updating an Unknown Failure RateA few failed sensors give evidence about a failure rate, but do not determine it exactly. Keep a distribution over plausible rates and update it as results arrive.
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Combining Noisy Evidence

Measurements can disagree without either being useless. Account for their reliability and the way an underlying condition changes before combining them.

  1. 03Combining Measurements With Different ReliabilityTwo thermometers disagree. Their known error variances tell us how strongly each reading should influence a shared estimate.
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  2. 04Tracking a State We Cannot Observe DirectlyAn alarm does not directly reveal whether equipment is healthy. Combine how states change with how each state could produce the observed alarm.
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Predictions as Distributions

An unmeasured location needs both a prediction and an account of what remains uncertain. We will see how a covariance rule lets measured locations inform it.

  1. 05Predicting Between Measurements With UncertaintyBotie has measured temperature at only a few positions. A covariance rule connects nearby locations and describes how uncertain an unmeasured location remains.
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