I am learning python at the moment and have just been introduced to the concept of Random Walks.
The lesson taught me how to code one and explained that it is used for data modeling in a number of different disciplines, but it didn’t explain how/why.
Can someone help me understand how a Random walk can be used in practice?
Thanks in advance.
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So I dont think random walks are used to predict anything. By definition they are random, so if properly coded, they should never predict anything.
However, that doesnt mean that modelling them is pointless. For instance, in my field, they are a useful way to think about stock prices. Basically, over the long term we think stock prices should be a signal of company value, but on a time scale of minutes or hours, we can think of them as a random walk. At any given time, we dont necessarily know whether they will go up or down.
Then with that theory, we can model a simulated stock, and see how changing certain parameters changes its movement, ultimately getting an idea of what might happen.
hmmm eli5.
Stochastic? Traveling Salesman?
This is a tough one.
If you have a vastly large plinko board. The Price is Right game with the pegs, and you drop the token from the top and try to get it to land in a particular spot;
One of those but with uncountable rows and columns.
And I asked you what would an ideal path look like to get from a particular spot at the top, to a particular spot at the bottom.
How would you figure that out?
Each time it drops to a new row of pins, it’s going to be shuffled either left or right in a pretty random fashion (not random but indeterminable due to being too complex to calculate).
So we cannot just create an algorithm that will find this optimal path by the use of some optimal method. We’d have to emulate a system of random course correction that averages out over time.
If the disk is mostly falling to the left of the pin, it goes left. If it’s mostly falling right, it goes right.
Simple enough system.
Does it represent something close to the actual system of the disk falling? Will it make predictions that can tell us exactly how the physical system will behave?
Nope. Not at all. Because it’s a crude estimation at each step.
The actual game, maybe the disk starts on the left, but bounces around a bit and ends up going right.
What our program will do however is give an answer that is approximate to the physical board, in it’s terms of efficiency. The will both make the same number of choices at each stop. Left or Right for as many rows as you have.
We’ve sacrificed fine detailed accuracy, but the computation of it is manageable and it produces outcomes that are consistent with the physical system if not a perfect simulation of.
This same technique is used to solve problems that are otherwise intractable, too complex to compute. Like the Traveling Salesman.
Random assignment of the next route to take from any given city (node) based on very simple rules.
It will not find the optimal solution. What it will find is a solution that is close to optimal while being computable.
In science, random walks and similar systems can be used to calculate a lot of things that would be super difficult to do analytically
For astrophysics I’ve done it to do things like see how long it takes a photon to escape from the center of the sun and reach earth using different models on how we think the sun behaves internally, I currently use similar techniques to do curve fitting on data to find values for things like how fast the universe expands
Doing one single random walk probably won’t help you, but in doing a bunch of them you can usually skip over some heavy/hardcore/impossible math to get something close enough to the right answer instead of the exact one by seeing how your walker behaves in the environment/model you give it
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