*Given a typical set, you could add the most probable element and drop the least probable element. This would keep the set the same size and increase its probability, so the proof should still work with this new set. You could repeat this as many times as you wanted, until the typical set contains all the most probable elements.

2021年7月21日 · The typical set is defined as the sequences which have a probability in $[2^{-nH(X) - \epsilon}, 2^{-nH(X) + \epsilon}]$. These are the sequences which give the average informativeness but certainly do not include the most probable sequences.

2020年5月19日 · From there we can speak of the typical set of, e.g., a high-dimensional standard normal distribution. But I've seen people referring to the "typical set" of general high-dimensional distributions (such as in Betancourt’s introduction to Hamiltonian Monte Carlo). Is there any rigorous definition in such cases?

2020年2月5日 · I've been reading a bit about typical sequences (in particular from these notes (pdf alert), pages 3 and 4). Let us focus on the case of binary sequences for simplicity. As far as I understand the idea is to consider those sequences that are typical in the sense that the number of $1$ s and $0$ s in the sequence equals its expected number.

2018年1月3日 · The mode of the density identifies a special point in space around which the density is the largest. Then in order to understand how the typical set behaves we have to consider how volume behaves around this one, special point.

2017年8月15日 · There is this article where the author Michael Betancourt uses this image to convey the concept of the typical set in a distribution. I would like to plot the typical set of a univariate or a bivariate Gaussian distribution.

The paper says: "So long as this condition holds, at every initial point the Markov transition will concen-trate towards the typical set. Consequently, no matter where we begin in parameter space the corresponding Markov chain will eventually drift into, and then across, the typical set". The stationary condition is

2022年3月5日 · I understand that this is essentially the entire point of introducing Hamiltonian dynamics in our MCMC framework, as we would like to sample from the typical set, and, in doing so, utilize symplectic integrators to trace an approximate Hamiltonian trajectory in our augmented parameter space for a set amount of time from which we marginalize out ...

2010年8月14日 · On page 331 of "Elements of Information Theory" (1991), author says that while entropy is related to the volume of the typical set, Fisher information is related to the surface area of the typical ...

2017年4月4日 · Given a set of events and their probability of occuring, where they all add to 1. Edit: the set of events can be of any size, the example below is only A and B with 50/50 probabilities for simplicity of example. Such as A=0.5 and B=0.5.