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Ask HN: Best place to start learning about Markov Chains?

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Re: Ask HN: Best place to start learning about Markov Chains?

#41

Post by usgroup »

soVeryTired wrote: post #40
usgroup wrote: post #27

1. Elementary probability theory. 2. Poisson processes. 3. The Markov property. 4. Stochastic processes. 5. Realise that you’re missing a background in analysis, therefore you don’t know sh?t about measure theory but you actually need it to know anything deeper . Wonder to yourself if you really want to spend the next 3 years getting a maths background you don’t have. 6. Convince yourself that it’s all just engineeri…

Poisson processes are continuous time though. If you're interested in Markov chains you only need the discrete-time theory. In discrete time and discrete space, it mostly just reduces to linear algebra.

Unless you’re interested in continuous markov chains, infinite state spaces, renewal theory, excessive functions, and so on.

Re: Ask HN: Best place to start learning about Markov Chains?

#42

Post by usgroup »

larrydag wrote: post #28
usgroup wrote: post #27

1. Elementary probability theory. 2. Poisson processes. 3. The Markov property. 4. Stochastic processes. 5. Realise that you’re missing a background in analysis, therefore you don’t know sh?t about measure theory but you actually need it to know anything deeper . Wonder to yourself if you really want to spend the next 3 years getting a maths background you don’t have. 6. Convince yourself that it’s all just engineeri…

While I agree with the progression of knowledge listed here I don't think it requires 3 years of foundation to math. If you have a basic understanding of math already you should be able to pick up the theory fairly well in a couple of months of research and application.

I think when you get out of the basic linear algebra and calculus prerequisite and into the analysis and measure theory prerequisite nothing takes a few months anymore :)

Re: Ask HN: Best place to start learning about Markov Chains?

#45

Post by usgroup »

exelius wrote: post #30
usgroup wrote: post #27

1. Elementary probability theory. 2. Poisson processes. 3. The Markov property. 4. Stochastic processes. 5. Realise that you’re missing a background in analysis, therefore you don’t know sh?t about measure theory but you actually need it to know anything deeper . Wonder to yourself if you really want to spend the next 3 years getting a maths background you don’t have. 6. Convince yourself that it’s all just engineeri…

That whole math sequence was part of my MBA program that culminated in Markov chains for synthetic options pricing after like, 9 months. And this is for business school students; not engineers :)

Sure, and for any given application it’ll be possible to explain Markov chains as they apply to it. I recently did a financial valuation course where we did an “intuitive derivation of Itos formula” so that we could skip the measure theory prerequisites. We also skipped talking about Reimann integrals and just accepted that sums are integrals at a limit ... we also glossed the separating hyperplane theorem so that we could say “no arb iff risk neutral measure exists”, and so on.

However, if you actually want a background in the theory of Markov chains, I don’t think this approach works.

Re: Ask HN: Best place to start learning about Markov Chains?

#46

Post by kawera »

penagwin wrote: post #36
lallysingh wrote: post #20

Earlier quoted context omitted.

It's a meta joke

It's hilarious because it's also a "semi"-decent method on how to learn knew topics in general.

And goes well with the article[1] we discussed yesterday[2] !

[1] https://billwadge.wordpress.com/2016/01/08/b-before-a/

[2] https://news.ycombinator.com/item?id=19608883

Re: Ask HN: Best place to start learning about Markov Chains?

#47

Post by joker3 »

larrydag wrote: post #28
usgroup wrote: post #27

1. Elementary probability theory. 2. Poisson processes. 3. The Markov property. 4. Stochastic processes. 5. Realise that you’re missing a background in analysis, therefore you don’t know sh?t about measure theory but you actually need it to know anything deeper . Wonder to yourself if you really want to spend the next 3 years getting a maths background you don’t have. 6. Convince yourself that it’s all just engineeri…

While I agree with the progression of knowledge listed here I don't think it requires 3 years of foundation to math. If you have a basic understanding of math already you should be able to pick up the theory fairly well in a couple of months of research and application.

You don't need much math to pick up the very basic theory, but after a certain point you're going to hit a hard wall unless you have a strong background in analysis.

Re: Ask HN: Best place to start learning about Markov Chains?

#50

Post by AlexCoventry »

activatedgeek wrote: post #34

Markov chains in essence are simple. Instead of diverging and reading all the theory, I'd recommend do it on a need basis. Learn as you go. So pick up a problem and move ahead. I don't think it is fruitful to just learn everything about Markov Chains just for the sake of it. Markov Chain Monte Carlo to sample from probability distributions is a good start - https://arxiv.org/abs/1206.1901 if you are into sampling.

Betancourt's survey is at least as good, and more up to date.

https://arxiv.org/pdf/1701.02434.pdf

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