Maybe there’s a distinction between the two I’m missing but reading about MC, it sounds like the kind of polling which is commonly done for elections, public opinion and marketing but applied to finance/science/computers. Are there differences?
I used to do Monte Carlo simulations for fun and profit (well lack of pain and gas money actually).
In our little world a Montel Carlo simulation went like this:
Lets say you have two functions. You can describe the distribtution of A mathematically exactly. And you have distribution B, for which you can do the same.
Now, let us say C is a result of A and B. But in some complex mathematical way. And this “way” is the problem. When you try to EXACTLY solve for the distribution of C using the math of A AND B it turns out that is an equation for which you don’t have a mathmatical solution.
What to do?
You take a random number generator. You use that to generate discrete values of A and B. You plug those results into the equation of A AND B and calculate C. You do this as many times as your computer/computer time will allow.
Now you have the distribution for C.
Not sure what that has to do with polling. Maybe the question is poorly worded. Maybe I just read poorly?
PS. We weren’t dealing with actual equations…but engineering curves…some simulated themselves and some measured, but the basic idea is the same.
They’re same in the sense that apples and oranges are both fruit and have some similarities, but many differences as well. They involve taking small samples and using them to generalize to a larger population. But polls are conducted once, don’t necessarily involve a model, and generate a margin of error. MC is done say 10,000 times with the assumption that some of those runs (say 500 on average for one type of error) will provide wildly incorrect results just by chance. Running MC on a human population would be prohibitively expensive and probably introduce some new confounds (say when a person gets called with the same survey and refuses to pick up the phone after the second).
The Monte Carlo method is a way of doing integrals, when they can’t be done by any exact or even plausible approximate method. A typical case is where the boundary for the integration is extremely complicated, for example because it is in many dimensions, has a weird shape, holes, et cetera. The requirement is that you have to be able to evaluate the integrand and you have to be able to know whether the point you select is inside or out of the boundary.
What you do is randomly select points that at least cover the region of integration, then check that they are in or out of the region of integration. If they’re inside, you evaluate the integrand and add it to your running sum. When you’re all done, you divide the running sum by the number of points you generated. (There are some complications if your volume element isn’t Cartesian.)
For example, suppose you wanted to evaluate the volume of 100 spheres, some or all of which may overlap. There are analytical ways to do this, but they are complicated and require complex programming. A simple way is to find the size of the cube that contains them all. Then you randomly generate a lot of {x,y,z} points inside that cube. For each, you decide whether the point lies within any sphere (an easy calculation). If it does, you add 1 to the running sum. When you’re all done, you divide the sum by the number of points you generate. That’s the (approximate) volume of the 100 spheres.
The main drawback of the Monte Carlo method is that it converges to the correct answer very slowly. You need a huge number of random points to get reasonable precision.
There is no “the Monte Carlo method”. Monte Carlo is just the name for an extremely broad category of methods for solving an extremely broad set of problems. Any method which involves randomness is a Monte Carlo method. So yes, polling is one example of a Monte Carlo technique, but there are many, many other examples, some of which don’t look much like polling at all.
Quantitative Finance engineer who uses monte carlo simulations in my professional work here, so I know what I’m talking about. A lot of the previous replies are not correct.
Polling and Monte Carlo simulations are completly unrelated. The reason you’re probably asking the question is that Nate Silver’s five thirty eight blog famously uses polls as an input to its monte carlo model, and that has been reported a lot in popular magazines. But polling and monte carlo are still completely different things, Nate is just combining them together.
Polling – exactly what you think it is, you ask a bunch of people who they’re going to vote for. The only hard part is you obviously can’t ask literally every person in the country, so you have to pick a handful of people at random and hope that those randomly selected people think more-or-less the same way as the rest of the nation. (Sometimes by chance, your randomly selected people just happen to all be democrats, for instance, which skews that poll.) So you may have multiple polls that disagree.
Monte Carlo simulation – this just means simulate it over and over again. Useful when you have statistics like “70% of Trump supporters didn’t vote last year, so we don’t know whether they’ll actually show up to the polls this year or not” and “Historically if it rains on election day, people are less likely to vote”, “These two polls contradict each other, but the first one is from a well-known company that historically was right X% of the time in the past”, etc. It’s too many different factors to just write an equation for. What if the percent of people who show up to the polls is slightly higher than expected, but the percent of voters who change their mind at the last minute is lower than expected? It’s too hard to make an equation for, since there’s too many factors you don’t know. So you have your computer pick random numbers for all unknowns (% chance of rain, % of trump supporters who will show up, % of undecided votes who may change their mind to Ted Cruz, % chance that this poll just happened to pick only democrats in their random sample of people, etc), run in thousands of times with different random numbers, and see who wins the majority of the simulations. Then your simulations show that “in X% of our simulations, Trump won; but in Y% of our simulations, Cruz won, etc”. Therefore Trump has an X% chance of winning.
So polling and monte carlo are completely different things, no connection at all between them.
The reason you’re probably asking about the difference between the two – fivethirtyeight.com has a model which uses both of those things. They start with the polls, but the polls may contradict each other. So they use a monte carlo model were they take all the polls which contradict each other, and assume there’s an X% change that this poll is right, a Y% chance that this other poll is right, etc. So you may see polling and monte carlo mentioned in the same sentence then. But that just means they’re using polls as data that is input to the monte carlo simulation.
Most of your post deleted to save space.
Now that all makes sense. I was wondering how polling and Monte Carlo simulations would even be mentioned in the same sentence.
As input for a simulation? Now its all clear!
Thanks for that informative post.
And again, Monte Carlo simulations are not the entirety of Monte Carlo methods. The Monte Carlo method of integration, for instance, is almost exactly like polling: You choose a bunch of points at random, and ask each one of them “Are you less than the integrand?”. The only reason that political polling is not itself called a Monte Carlo method is just an accident of history-- It has just as much right to the title as any other MC method.
Completely disagree.
Polling is choosing a single sample from the actual observed world.
Monte Carlo simulation is a process by which you randomly generate many simulated samples, using statistics of what you think that data probably looks like.
And another difference is that to do a Monte Carlo, you need to already have some idea of what the data looks like (“a median value of X and a variance of Y”) whereas a poll requires no such advance knowledge.
I suppose you could try to claim that polling is a special case of Monte Carlo with N=1, and I suppose you could hand-waive away the difference between “observe an actual sample in the world” vs “Estimate a sample by assuming a median value of X and a variance of Y”. But you’d be really stretching to redefine the terms with a definition different than they are commonly understood.
I’m with doubled on this. Calling actual polling Monte Carlo is a stretch. Like the fabric of space time around a black hole stretch.
Chronos is correct. A Monte Carlo method is one that takes a random subsample of a set to estimate quantities over the entire set. And that is exactly what political polling does. By asking a subset of the population how they would vote, they estimate how the entire population would vote.
What 538 does is takes the output of multiple Monte Carlo measurements as input for a Monte Carlo simulation to predict a future outcome. The fact the output of one Monte Carlo can be used input for another, doesn’t mean the first is not one.
doubled is correct. Any Monte Carlo technique will use random or pseudorandom variables. If you ask a bunch of people whether they will vote for Trump, that’s called polling. If you run a simulation (of, say, an upcoming caucus) based upon polling data and probability distributions, you are probably using a Monte Carlo method.
How do you think they determine which people to poll? They use RNG of some type.
I’m going to say the common feature of both polling and MC is that you’re sampling a larger space.
After that they’re two utterly divergent techniques. As **doubled **said in #10.
IOW, sampling is a *necessary condition *for each technique, but the mere existence of sampling isn’t a *sufficient condition *to label a technique as MC.
It’s also the case that MC is a fairly broad tent, whereas polling is a fairly narrow specific technique. They’re not that far apart, but IMO polling, at least one-time polling, isn’t quite inside the tent.
Using random numbers to collect data not equal using data and random numbers to make a calculation.
OK, so just what is the difference between political polling and the Monte Carlo method of integration? In both cases, you start with some easily-enumerated space. You pick n points at random from within that space, and ask of each a single yes-or-no question. You then count up the number of “yes” answers you get, and compare to the number of points sampled, and say that the yeses are that proportion of the total space, to within a margin of error determined by the number of points sampled. The process works exactly the same way whether the initial space is “All Americans” or “a rectangle completely containing the integrand”, and whether the question is “Do you support Trump?” or “Are you less than the integrand?”.
I just took part in a poll where I was specifically selected, and my answers are going to be used as representative of an entire class of citizens. The pollers already knew what my answers would be and this serves the answers they want to generate; all single peoples do not want to [insert controversial public program], therefore [controversial public program] should be eliminated.
Seems unlikely ABC News would report poll results that condemn one of their most important corporate sponsors.
So, how would one use MC to approximate how light bounces within a room in a way that is computationally cheap?
Question: What fraction f of squares on a starting chess board contain pawns?
Method of answering: Draw two random integers m and n uniformly from 1 to 8. Look at board position (m, n) and increment A (initially zero) if there is a pawn in that board position and increment B (initially zero) if there is not. Repeat a large number of times. A/(A+B) is an ever-improving estimate of f.
I would call that a Monte Carlo method for determining f. I’d be interested if doubled or others disagree. Any distinguishing features between this example and a fair election phone poll seem to be implementation details, not fundamental differences.
I agree that folks doing election polling needn’t (and typically don’t) use the phrase “Monte Carlo method” for their work, but if they wanted to I wouldn’t argue against it. That’s just a question of whether the broader term is linguistically useful to them or not.