(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

Hmm. 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.

I 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.

[2] https://jwmi.github.io/index.html

So he sets up a toy problem (drawing from a baby names distribution), then never explains how to solve this problem.

The intuition is, you set up a graph where the vertices are names, and the edges are based on name similarity. Two names are neighbors if e.g. their edit distance is within some limit. You start at a random name, then at the neighbors, flip a biased coin with the ratio of the P(x) of your current name and the neighbor, if heads you move to the neighbor.

I'm sure this is wrong in many and subtle ways, but when I read an article like this I expect some intuition like this to be imparted.

Science communication is so important. I write scientific papers and I always write a blog post about the paper later, because nobody understands the scientific paper -- not even the scientists. The scientists regularly read my blog instead. The "scientific style" has become so obtuse and useless that even the professionals read the blog instead. True insanity.