|
Through reading some of the college/class related threads in General occasionally I've noticed quite a good number of high-caliber mathematically-inclined posters on TL! So I've come to prompt some discussion that may lead my research group in a direction that we've been unable to find for a few weeks.
I'm currently doing undergraduate research (Physics) at my university and we (myself, my partner, and my advisor) have had a dilemma over the past few weeks on how to quantify something statistically. Rather than talk about the research in detail, in order to avoid subtleties and unnecessarily dense description, I'll use a fun (and hopefully understandable) example that is essentially counterpart to our data.
It's going to be a rough example, but bear with me. Let's imagine the traffic of Teamliquid. Each time someone visits TL, we'll tag that exact moment in time as "a visitor", and this is how we'll track these events. Over the course of each day or week (long time spans) we'd expect some pretty regular patterns (background) depending on the time of day for the most part, where a large majority of the same people check on a daily or weekly basis. Ignoring smaller subtle fluctuations (noise), there would be presumably some general trend on a daily/weekly/monthly scale we could see and account for as background.
Now, larger events such as showmatches or the final rounds of some tournaments (a much shorter time scale than the background) could cause an increase in flux of visitors, posting in LR threads and viewing the stream(s) and what not. Assuming we subtract the daily background, these events would show up in a graph of visitors over time, and we could attribute this "burst" of visitors to the larger event in question.
With these "bursts" in mind (with a source we can associate with good certainty) we come to my actual dilemma. Let's say there is a showmatch between Idra and Tyler. This would generate a burst of visitors previously discussed, in both posters and viewers. In Game 3, Idra 6 pools, and some TL notables tweet about it as it happens live and there is a spike of people that read it and immediately go to TL and tune in. So not only is there a general increase in visitor flux due to the showmatch as a whole, but this momentary SPIKE in arrival times (remember, we're tagging these events exactly as the time people join, not "how many people currently viewing") that are presumably associated with a specific event (in this case, the 6pool/tweet).
We want to quantify this bunching. The events in question are simply large amounts of arrival times, and we can histogram them to see general trends/flux over long times, or zoom in and look at each time individually to see the small scale structure. After subtracting background, let's say we see exactly 100 events semi-randomly distributed in some time interval. These events are above background and can be associated with a larger-scale event (in the example, the showmatch as a whole). Now, these 100 time-tagged events appear randomly distributed, but upon closer inspection 5 of them come EXTREMELY close together (the tweet-induced visitors). Visually, they are clearly bunched together and hopefully associated with some event, and the goal is to statistically quantify "how bunched they are" in comparison to the overall randomness of the 100 background-subtracted events. Basically, there's a bunch of stuff that should be random or looks random, but there's a clump that is unusually close, and we want to be able to somehow say "in this bunch of random stuff, these are so unusual that they aren't just random".
We've tried most of the basic, "common/acceptable" tests, such as chi-square and something we had high hopes for called a K-S Test. Most tests we've tried either don't capture what we're looking for, in that they don't properly "observe" the closeness in a way that works with small amounts of data (the numbers in the last paragraph are fabricated but basically on the same scale). The basic ratio that we're using "in-house" for our own measurements is a ratio of [events seen in a specific time window / events expected in the same window] where the time window is chosen to be close to the scale of the "bunching" and the expected rate is simply related to the [total events seen times the percentage of the total time our chosen window is]. The larger this ratio is the more significant the clumping in a chosen time window somewhere in the data. However this ratio is, to our knowledge, simply arbitrary. We need a way to actually quantify this in a way that makes sense statistically that others in the field will accept as significant.
Hopefully this doesn't fall into the category of homework help since... it's not?!? No answers to be found here really, just as many possible ways of approaching the problem. We're looking for options that we haven't tried or don't know well enough.
|
so you are basically looking for a high frequency spike in a low frequency background noise? I don't know, but fourier transform came to my mind, but i'm not sure if thats applicable here. But maybe you can steal some techniques from signal analysis, they should have ways to deal with this stuff in continuous spaces, which should be transferable to your discrete space in some way possibly maybe.
|
I'm not a statistician, but what you're describing is a stochastic process. Perhaps you should look up methods for modeling time series.
|
Im sad that this is all the advice you can get 
but alas i cannot help you either.
I'd be interested to know what parallel comes with this example.
|
Who's the grad. statistician at Duke, OneOther or Empyrean? Which ever one it is, it probably wouldn't hurt to ask him
|
I take pride in my blog "PrimeCoverage" for its analytical bend. See if you can find anything useful there~~
Note that I am not a trained statistician (Electrical Engineering), just a hobbyist mathematician.
EDIT: Completely misread the OP, sorry.
Here's the non-self-advertising response. The big question I will have towards this is, how do you propose collecting this "visitor" and traffic data? Simply attempt to scrap the Active and Logged In numbers on the top left of TL?
While doing my own StarCraft analytics, I found that it suffers simultaneously from excess amount of data and insufficient amount of data. It's a brand new industry, so very little statistical analysis was ever done on it, even in BW. Unlike mature sports like baseball, advanced research like Sabermetrics simply does not exist, and no effort have ever been made to properly document data useful to curious amateur statisticians like yours truly (besides the TLPD). Plenty of data is out there - tournament results, matchups, stream numbers - but no one is collecting them.
For example, I once was curious about the NASL viewership, but those data is hard to come by because Justin.tv has horrid (non-existent) site analytic, and I end up using the daily livereport threads views and posts as a rough proxy of "viewership interest". It's imprecise and I don't think the dataset I have properly answered the question, but in the end, it's the best that StarCraft has right now.
Perhaps you can find a better solution, or perhaps somebody is working on resolving this problem in secret. For now, I see no substantial resources where proper statistics can be done, without building those datasets up yourself.
Regarding the non-StarCraft related issue, I think you will care less about the dataset itself but more about its first and perhaps second-derivatives.
|
On July 19 2011 07:23 Primadog wrote:I take pride in my blog "PrimeCoverage" for its analytical bend. See if you can find anything useful there~~ Note that I am not a trained statistician (Electrical Engineering), just a hobbyist mathematician.
EDIT: Completely misread the OP, sorry. Here's the non-self-advertising response. The big question I will have towards this is, how do you propose collecting this "visitor" and traffic data? Simply attempt to scrap the Active and Logged In numbers on the top left of TL? While doing my own StarCraft analytics, I found that it suffers simultaneously from excess amount of data and insufficient amount of data. It's a brand new industry, so very little statistical analysis was ever done on it, even in BW. Unlike mature sports like baseball, advanced research like Sabermetrics simply does not exist, and no effort have ever been made to properly document data useful to curious amateur statisticians like yours truly (besides the TLPD). Plenty of data is out there - tournament results, matchups, stream numbers - but no one is collecting them. For example, I once was curious about the NASL viewership, but those data is hard to come by because Justin.tv has horrid (non-existent) site analytic, and I end up using the daily livereport threads views and posts as a rough proxy of "viewership interest". It's imprecise and I don't think the dataset I have properly answered the question, but in the end, it's the best that StarCraft has right now. Perhaps you can find a better solution, or perhaps somebody is working on resolving this problem in secret. For now, I see no substantial resources where proper statistics can be done, without building those datasets up yourself.
Regarding the non-StarCraft related issue, I think you will care less about the dataset itself but more about its first and perhaps second-derivatives.
He doesn't actually want to do research on TL views, it was just an analogy for his physics research.
|
5003 Posts
So, let me get the situation before I start thinking of a solution.
You are measuring x, and you see how x behaves without any sort of external shocks. So, you know how x moves in an hourly basis without any shocks.
Now, there is a shock, a "major event". Due to this, x starts behaving abnormally -- specifically, it spikes up (does the spiking up matter?). Within this event, there is an additional shock, caused by some element of "major event", and it affects x even more.
Your goal is to prove that these spikes aren't random and that these are something that is caused by the major event? That these shocks *are* abnormal and you want to see how they affect X? Are you looking for causality or just correlation?
Or is it more simple like this: After detrending, 100 people arrive every hour. Out of these, 5 of them are really close to each other, ie: they arrive at a much higher frequency than the other 95. You want to somehow show that these 5 follow a different distribution?
Try fitting the detrended model to a poisson distribution and i think you may be able to show that there is something that causes the mean of the poisson distribution to change at those spikes.
Not sure if this is what you're looking for since there are a lot of ways of studying this (more complicated ways including fitting in some time dependent data) but I think this may do the trick? not sure depending on how sophisicated you want to be with it
|
On July 19 2011 10:54 Milkis wrote:So, let me get the situation before I start thinking of a solution. You are measuring x, and you see how x behaves without any sort of external shocks. So, you know how x moves in an hourly basis without any shocks. Now, there is a shock, a "major event". Due to this, x starts behaving abnormally -- specifically, it spikes up (does the spiking up matter?). Within this event, there is an additional shock, caused by some element of "major event", and it affects x even more. Your goal is to prove that these spikes aren't random and that these are something that is caused by the major event? That these shocks *are* abnormal and you want to see how they affect X? Are you looking for causality or just correlation? Or is it more simple like this: After detrending, 100 people arrive every hour. Out of these, 5 of them are really close to each other, ie: they arrive at a much higher frequency than the other 95. You want to somehow show that these 5 follow a different distribution? Try fitting the detrended model to a poisson distribution and i think you may be able to show that there is something that causes the mean of the poisson distribution to change at those spikes. Not sure if this is what you're looking for since there are a lot of ways of studying this (more complicated ways including fitting in some time dependent data) but I think this may do the trick? not sure depending on how sophisicated you want to be with it
I was thinking about tell him to compare it to a poisson process, but the problem if you do that is that you have to manually choose the endpoints on where the event's influence lies. If there are sensical time endpoints to use that's great, but if it's an event that has a indeterminate influence on the future then you want something more sophisticated I think.
Not knowing very much about time dependent data, I can't give any more than that.
|
On July 19 2011 10:54 Milkis wrote:So, let me get the situation before I start thinking of a solution. You are measuring x, and you see how x behaves without any sort of external shocks. So, you know how x moves in an hourly basis without any shocks. Now, there is a shock, a "major event". Due to this, x starts behaving abnormally -- specifically, it spikes up (does the spiking up matter?). Within this event, there is an additional shock, caused by some element of "major event", and it affects x even more. Your goal is to prove that these spikes aren't random and that these are something that is caused by the major event? That these shocks *are* abnormal and you want to see how they affect X? Are you looking for causality or just correlation? Or is it more simple like this: After detrending, 100 people arrive every hour. Out of these, 5 of them are really close to each other, ie: they arrive at a much higher frequency than the other 95. You want to somehow show that these 5 follow a different distribution? Try fitting the detrended model to a poisson distribution and i think you may be able to show that there is something that causes the mean of the poisson distribution to change at those spikes. Not sure if this is what you're looking for since there are a lot of ways of studying this (more complicated ways including fitting in some time dependent data) but I think this may do the trick? not sure depending on how sophisicated you want to be with it
What you're describing is essentially it yes. There is a "larger" background-subtracted / detrended event (your example's 100 people), and within this broader event there is a short burst of even higher frequency data (times) that we want to say is somehow quantifiably correlated in excess to the rest of the (essentially random) background-subtracted data.
We've been working with Poisson statistics from numerous approaches, especially over the past few days. Any quantitative assessment we arrive at with the Poissonian methods and distributions seem too situationally specific and even TOO low of a probability. Sure lower is better, that's what we'd like! In Physics you have to account for everything and second guess even yourself... we'd like a lower probability to be able to say that the bunching is more significant, but the numbers we were arriving at were TOO absurdly low to even find reasonable haha. Perhaps integrating over some Poissonian distribution or choosing a more general, flexible set of parameters instead of getting so specific. As I said, we've done some with Poisson stats and still are, but we're also looking for more options.
At this point I may just delve into the actuality of what we're doing / working with, but I was trying to avoid that as it's active research blah blah mumbo jumbo. If anyone (Milkis?) is genuinely interested in the specifics if they think it'll help with ideas feel free to PM.
|
|
|
|
|
|
EPT
