So let’s say I’m estimating the position of a train on a straight section of track as a single real number and I want to do an update each time I receive a noisy measurement of the train’s position. Under the theory you’re laying out here I might have, say, three Gaussians N(0, 1), N(1, 10), N(4, 6), and rather than updating a single pdf over the position of the train, I’m updating measures associated with each of these three pdf. Is that roughly correct?
(I realize this isn’t exactly a great example of how to use this theory since train positions are perfectly realizable, but I just wanted to start somewhere familiar to me.)
Do you by chance have any worked examples where you go through the update procedure for some concrete prior and observation? If not, do you have any suggestions for what would be a good toy problem where I could work through an update at a very concrete level?
I’m not sure I understood the question, but the infra-Bayesian update is not equivalent to updating every distribution in the convex set of distributions. In fact, updating a crisp infra-distribution (i.e. one that can be described as a convex set of distributions) in general produces an infra-distribution that is not crisp (i.e. you need sa-measures to describe it or use the Legendre dual view).
Ah this is helpful, thank you.
So let’s say I’m estimating the position of a train on a straight section of track as a single real number and I want to do an update each time I receive a noisy measurement of the train’s position. Under the theory you’re laying out here I might have, say, three Gaussians N(0, 1), N(1, 10), N(4, 6), and rather than updating a single pdf over the position of the train, I’m updating measures associated with each of these three pdf. Is that roughly correct?
(I realize this isn’t exactly a great example of how to use this theory since train positions are perfectly realizable, but I just wanted to start somewhere familiar to me.)
Do you by chance have any worked examples where you go through the update procedure for some concrete prior and observation? If not, do you have any suggestions for what would be a good toy problem where I could work through an update at a very concrete level?
I’m not sure I understood the question, but the infra-Bayesian update is not equivalent to updating every distribution in the convex set of distributions. In fact, updating a crisp infra-distribution (i.e. one that can be described as a convex set of distributions) in general produces an infra-distribution that is not crisp (i.e. you need sa-measures to describe it or use the Legendre dual view).