forecasting//scenario mixture

A scenario mixture combines alternative descriptions of how the world may go by weighting each with its probability instead of averaging them, and it is used when sources disagree because they assume different regimes, not because they measure one quantity with different errors. The probability of an event is then

A scenario mixture combines alternative descriptions of how the world may go by weighting each with its probability instead of averaging them, and it is used when sources disagree because they assume different regimes, not because they measure one quantity with different errors. The probability of an event is then

P(E)=p P(E∣A)+(1−p) P(E∣B)P(E) = p\,P(E \mid A) + (1-p)\,P(E \mid B)P(E)=pP(E∣A)+(1−p)P(E∣B)

where AAA and BBB are the scenarios and ppp is the probability of AAA. The weight ppp is a judgement and is written down as one, so it can be argued with.

The intuition is a fork in a road. If AI spending keeps growing about 70% a year when lab revenue keeps compounding, and about 25% a year when it does not, the average (near 47%) describes neither world: it is a road nobody will drive. A mixture keeps both outcomes and their weights, and its distribution can have two peaks where an average has one.

A mixture is the right tool when the disagreement is about which world holds; random-effects pooling is the right one when the sources measure the same world with different errors.

A useful property of a forecast is to depend little on the weight. A conclusion that holds in both scenarios is robust to the question nobody can settle.