BTW in case you didn’t find a good explanation: a convex set of probability distributions is a set where if you take any two distributions in the set, let’s say P and Q, the set also contains every weighted average of P and Q: so 0.1P + 0.9Q, 0.622P + 0.378Q etc.
Convex cones only really make sense for measures, which are like probabilities if the probabilities didn’t have to add to one. You’re a convex cone of measures if for any two measures P and Q, you contain all positively-weighted sums of P and Q. So stuff like 0.1P + 0.9Q, but also stuff like 38P + 9.6444442Q (but not necessarily −6.8P + 0.4Q, because that includes a negative weight).
BTW in case you didn’t find a good explanation: a convex set of probability distributions is a set where if you take any two distributions in the set, let’s say P and Q, the set also contains every weighted average of P and Q: so 0.1P + 0.9Q, 0.622P + 0.378Q etc.
Convex cones only really make sense for measures, which are like probabilities if the probabilities didn’t have to add to one. You’re a convex cone of measures if for any two measures P and Q, you contain all positively-weighted sums of P and Q. So stuff like 0.1P + 0.9Q, but also stuff like 38P + 9.6444442Q (but not necessarily −6.8P + 0.4Q, because that includes a negative weight).
Thank you. This helps. The explanations I found online required a background in linear algebra, which is well beyond my high school calculus.