I was doing great following along for the first 20 minutes or so. I’ve paused at 28:19 to learn what a convex probability set is and about closed convex cones. I should’ve paused about five minutes ago but was hoping a convex probability set only sounded intimidating but would be easily explained (the same way you and your guests typically put difficult concepts in understandable terms).
I have never in my life gotten even close to such concepts, to my knowledge, but I was a humanities major.
I’m not complaining! Just feeding back. This is the first time I’ve had to pause AXRP to go get educated.
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).
Gotcha. FWIW, my sense is that for the purposes of this interview it’s fine if you just go on without knowing what a convex set or cone is, and just understand that we’re dealing with sets of things like probability distributions, which is why I didn’t ask for a clarification. But perhaps I should have just said that out loud.
n=1:
I was doing great following along for the first 20 minutes or so. I’ve paused at 28:19 to learn what a convex probability set is and about closed convex cones. I should’ve paused about five minutes ago but was hoping a convex probability set only sounded intimidating but would be easily explained (the same way you and your guests typically put difficult concepts in understandable terms).
I have never in my life gotten even close to such concepts, to my knowledge, but I was a humanities major.
I’m not complaining! Just feeding back. This is the first time I’ve had to pause AXRP to go get educated.
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.
Gotcha. FWIW, my sense is that for the purposes of this interview it’s fine if you just go on without knowing what a convex set or cone is, and just understand that we’re dealing with sets of things like probability distributions, which is why I didn’t ask for a clarification. But perhaps I should have just said that out loud.