Earlier quoted context omitted.
It is memoryless just in a different state space.
In the state space that includes all of the time periods, with infinitesimal granularity since the birth of the universe.
Welcome to a well formulated POMDP.
Markov Chain Monte Carlo Without All the Bullshit (2015)
51–56 of 56 posts
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#52Hmm. I'm not an expert, but some of this seems definitely not to be accurate. Some of the "Bullshit" turns out perhaps to be quite important. Take the statement: > Markov Chain is essentially a fancy name for a random walk on a graph Is that really true? I definitely don't think so. To my understanding, a Markov process is a stochastic process that has the additional (aka "Markov") property that it is "memoryless". T…
I won’t pretend to know the technical details (as the other replies do) but I want to make a point for the “pedagogical” effect here, which I agree with the author. The way I interpret the article, it’s not supposed to be a deep, theoretical treatise on the subject; more of an introductory, “intuitive” take on it. This works for those who need to either learn the concept to begin with, or refresh their memories if th…
>I won’t pretend to know the technical details (as the other replies do) but I want to make a point for the “pedagogical” effect here, which I agree with the author. The way I interpret the article, it’s not supposed to be a deep, theoretical treatise on the subject; more of an introductory, “intuitive” take on it.
There are ways to teach things at a conceptual level without teaching them incorrectly though, especially when writing for an adult audience.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#53Hmm. I'm not an expert, but some of this seems definitely not to be accurate. Some of the "Bullshit" turns out perhaps to be quite important. Take the statement: > Markov Chain is essentially a fancy name for a random walk on a graph Is that really true? I definitely don't think so. To my understanding, a Markov process is a stochastic process that has the additional (aka "Markov") property that it is "memoryless". T…
I won’t pretend to know the technical details (as the other replies do) but I want to make a point for the “pedagogical” effect here, which I agree with the author. The way I interpret the article, it’s not supposed to be a deep, theoretical treatise on the subject; more of an introductory, “intuitive” take on it. This works for those who need to either learn the concept to begin with, or refresh their memories if th…
Yeah, the hard part of MCMC is going from finite state and time spaces to continuous. But the general concepts and intuition for finite state/time get a LOT more complicated, even though they are ultimately fairly intuitive generalizations of the finite case. Maybe this is a hot take, but I did do my PhD on MCMC and to be honest I think most of the details for the more general case are superfluous for a lot of people who just want to use MCMC, since it boils down to "it basically just works algorithmically the same way as the easier to understand case of finite state/time but beware the actual details of proving that get very involved." The conclusion of the theory for MCMC is that it ends up being pretty darn lenient in terms of caveats and edge cases, so in practice as a user there aren't that many gotchas to not being really well versed in the deepest parts of the theory.
A counterpoint is that finding texts and references that do handle the more advanced cases in depth is quite difficult, bordering on impossible if you want something approachable. I recreated the general proofs for at least the continuous state case as a chapter in my dissertation and stringing together an end-to-end proof with the proper references required quite a lot of digging and discussions with my (co-)advisor.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#54Earlier quoted context omitted.
Those notes look interesting thanks. I’ve really never heard of someone saying you have to have uniform probability for a random walk on a graph. In fact the context where I’m most familiar with them (lattice/grid pricers) it’s always specified something like “the probability of branch a is p and b is 1-p” (ie explicitly not uniform) and they aren’t a weighted graph in the normal sense.
It doesn't have to be uniform or memory less. However, in general when people mention random walks without further qualifications they are usually talking about the uniform and memoryless case. That vanilla case can be generalized extensively, on kinds of state spaces, kinds of index sets, kinds of dependence and so on.
That makes sense. THanks.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#55I had to learn Bayesian econometrics mostly on my own[1]. Fortunately, Jeff Miller[2] created a series of fantastic YouTube videos to explain Markov Chain Monte Carlo in detail. Personally, I prefer to learn mathematical concepts with equations and develop the intuition on my own. If you have the same preference, you will find his videos really helpful: https://www.youtube.com/watch?v=12eZWG0Z5gY
[1] I am lucky to know people who are fantastic Bayesian modelers and they helped me polish my concepts.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#56McMc is bullshit to begin with. Too slow…and alternatives are better for many reasons. It should not be the standard method taught to students when it comes to Bayesian Inference.