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Markov Chain Monte Carlo Without All the Bullshit (2015)
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Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
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Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#13[dead]
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#14Hmm. 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…
Not all Markov processes have stationary distributions, and of those that do not all correspond to a non-normalized probability function.
It therefore has some merit to think about MCMC as a random walk on a graph rather than Markov processes, because the “graph” needs to have some properties in order for the Markov process to be useful for MCMC. For example every “node” in the “graph” needs to be reachable from every other “node” (ergodicity).
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#15Hmm. 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…
Not all Markov processes have stationary distributions, and of those that do not all correspond to a non-normalized probability function. It therefore has some merit to think about MCMC as a random walk on a graph rather than Markov processes, because the “graph” needs to have some properties in order for the Markov process to be useful for MCMC. For example every “node” in the “graph” needs to be reachable from ever…
Could you explain further please? I agree with what you're saying but I don't' understand how it applies to what I said so there's definitely something I could learn here.
Edit: Thanks.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#16Hmm. 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 they don’t work with it every day. I think it’s a given that any intuitive take on a mathematical concept will always oversimplify things, with the underlying assumption that, if you actually need to know more, you’re going to have to dive deeper somewhere else. The most important thing I think is to help the reader build a rough conceptual understanding of the concept such that they can reason about it, instead of simply memorizing the terms.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#17Interesting! I also make extensive notes of mathematical and computational concepts (and “buzzwords”) with a “no bullshit” title, and it works great. It’s great for quick refreshers once in a while.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#18Feels too long I only want the python code
it's better to understand the theory before putting up some faulty production code.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#19Hmm. 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…
Stochastic process with the Markov property: Past and future are conditionally independent given the present. The general version of conditionally independent is from probability theory based on measure theory and the Radon-Nikodym theorem (with von Neumann's novel proof in Rudin, Real and Complex Analysis), but an easier introduction is in Erhan Çınlar, Introduction to Stochastic Processes.
In a Poisson process the time until the next event has the Poisson distribution and, thus, from a simple calculus manipulation, is a Markov process.
E.g., time from now until a molecule of hydrogen peroxide H2O2 decomposes to water and oxygen is independent of when it was made from water and oxygen. That is the basis of half life, the same distribution until decomposition starting now no matter when the chemical or particle was created.
In WWII, searching at sea, e.g., for enemy submarines, was important, and then was Bernard O. Koopman, Search and Screening, 1946 with an argument that time to an encounter between two ships had a Poisson distribution, i.e., was a Markov process.
In grad school, there was a question about how long US submarines would last in war at sea. Well, take n Red ships and m Blue ships with, for each ship, position, speed, and detection radius and, for each Red-Blue pair, given a detection, probabilities of Red dies, Blue dies, both die, neither die (right, these four have to be non-negative and add to 1). Now have specified a Markov process that can evaluate with a relatively simple Monte-Carlo simulation.
Had written a random number generator in assembler using an Oak Ridge formula, typed quickly, and did the simulation. Had a review by a famous probability prof and passed when explained how the law of large numbers applied. So, some pure and applied math and computing worked, but some politics didn't!
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#20Hmm. 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…
Stochastic process with the Markov property: Past and future are conditionally independent given the present. The general version of conditionally independent is from probability theory based on measure theory and the Radon-Nikodym theorem (with von Neumann's novel proof in Rudin, Real and Complex Analysis ), but an easier introduction is in Erhan Çınlar, Introduction to Stochastic Processes . In a Poisson process th…
I once failed an interview with a hedge fund because they asked me a variant on that red ships/blue ships problem and at the time I knew nothing about probability. They also hadn’t given me lunch which didn’t help.