Markov Chain Monte Carlo Without All the Bullshit (2015)
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Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#2(2015) Popular in:
2022 (233 points, 53 comments) https://news.ycombinator.com/item?id=33332437
2016 (125 points, 20 comments) https://news.ycombinator.com/item?id=12537043
2015 (114 points, 17 comments) https://news.ycombinator.com/item?id=9331808
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#3[deleted]
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#4Unfortunate that the equation rendering doesn't work in the body text.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#5Unfortunate that the equation rendering doesn't work in the body text.
I experienced this issue, but it works on another device, and after a refresh it worked on the original device. Good luck...
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#6Unfortunate that the equation rendering doesn't work in the body text.
Works fine here, Firefox on Android
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#7Feels too long
I only want the python code
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#8Hmm. 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". That is, to estimate the next state you only need to know the state now, not any of the history. It becomes a Markov chain if it is a discrete, rather than continuous process.
There are lots of random walks on graphs that satisfy this definition. Like say you have a graph and you just specify the end points and say "walk 5 nodes at random from this starting node, what is the expectation that you end up at a specific end node". This could be a Markov process. At any point to estimate the state you only need to know the state now.
But lots of random walks on graphs do not have the Markov property. For example, say I did the exact same thing as the previous example, so I have a random graph and a start and target node and I say "Walk n nodes at random from the starting node. What's the expectation that at some point you visit the target node". Now I have introduced a dependency on the history and my process is no longer memoryless. It is a discrete stochastic process and it is a random walk on a graph but is not a Markov chain.
An example of a Markov and non-Markov processes in real life is if I have a European option on a stock I only care about what the stock price is at the expiry date. But if I have a barrier option or my option has some knock-in/knock-out/autocallable features then it has a path dependence because I care about whether at any point in its trajectory the price hit the barrier level, not just the price at the end. So the price process for the barrier option is non-Markov.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#9Hmm. 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…
Your overall point might be correct but your example does not prove your point.
A Makrov chain is just the path taken through the course of a markov process. The terms 'chain' and 'process' are sometimes conflated in this context, but this is the most common distinction I've seen. As such you can run a markov process for some number of steps N times, and then ask how many generated chains contain the property you are interested in. The process is memoryless but the chain is the result of the process and therefor contains memory.
I agree 'Random walk' is a superset of 'a markov process', but IMO when someone says Random walk - they normally make assumptions that qualify it as a markov chain. Therefor it's useful as a teaching to just call it a random walk.
Re: Markov Chain Monte Carlo Without All the Bullshit (2015)
#10Hmm. 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…
Your overall point might be correct but your example does not prove your point. A Makrov chain is just the path taken through the course of a markov process. The terms 'chain' and 'process' are sometimes conflated in this context, but this is the most common distinction I've seen. As such you can run a markov process for some number of steps N times, and then ask how many generated chains contain the property you are…
Interesting. I'd not heard the term Markov Chain used to describe a path so I checked my copy of "All of Statistics" by Larry Wasserman and he (slightly) disagrees with both of us and says
"A Markov chain is a stochastic process for which the distribution of X_t depends only on X_{t-1}."