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Calling all Stats Nerds

BuckGup
By BuckGup
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I haven't had my stats class yet so I am having trouble answering this. So if something has a 90% chance of not happening in a year and a completely different thing has an 80% chance of not happening. When these two are used in tandem do their probabilities add so it's close to 100% or is it only as effective as the largest percent? Same thing goes for likely hood of something happening every time. If there is an 88% it is going to happen and doesn't happen does the fact it didn't happen influence the next time statistically even though it's only measures for a single event?

▓ƆԀ▓ S▓₱▓Ɇ▓c▓s▓: i7 6ʇɥפᴉƎ00K (4.4ghz), Asus DeLuxe X99A II, GT҉X҉1҉0҉8҉0 Zotac Amp ExTrꍟꎭe),Si6F4Gb D???????r PlatinUm, EVGA G2 Sǝʌǝᘉ5ᙣᙍᖇᓎᙎᗅᖶt, Phanteks Enthoo Primo, 3TB WD Black, 500gb 850 Evo, H100iGeeTeeX, Windows 10, K70 R̸̢̡̭͍͕̱̭̟̩̀̀̃́̃͒̈́̈́͑̑́̆͘͜ͅG̶̦̬͊́B̸͈̝̖͗̈́, G502, HyperX Cloud 2s, Asus MX34. פN∩SW∀S 960 EVO

Just keeping this here as a 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This covers the first half since I'm too lazy write that out https://www.statisticshowto.datasciencecentral.com/probability-of-a-and-b/

 

If a reoccurring event's probability is impacted by the event occurring, then yes the probability could increase (or decrease). It depends on the event itself and cannot be said about every event, it's something you'd need to identify.

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13 minutes ago, 2FA said:

This covers the first half since I'm too lazy write that out https://www.statisticshowto.datasciencecentral.com/probability-of-a-and-b/

 

If a reoccurring event's probability is impacted by the event occurring, then yes the probability could increase (or decrease). It depends on the event itself and cannot be said about every event, it's something you'd need to identify.

I guess on more of an abstract scale looking at the universe of the problem. Does the fact that event happened influence future events? Not necessarily a butterfly effect but the event itself happening

▓ƆԀ▓ S▓₱▓Ɇ▓c▓s▓: i7 6ʇɥפᴉƎ00K (4.4ghz), Asus DeLuxe X99A II, GT҉X҉1҉0҉8҉0 Zotac Amp ExTrꍟꎭe),Si6F4Gb D???????r PlatinUm, EVGA G2 Sǝʌǝᘉ5ᙣᙍᖇᓎᙎᗅᖶt, Phanteks Enthoo Primo, 3TB WD Black, 500gb 850 Evo, H100iGeeTeeX, Windows 10, K70 R̸̢̡̭͍͕̱̭̟̩̀̀̃́̃͒̈́̈́͑̑́̆͘͜ͅG̶̦̬͊́B̸͈̝̖͗̈́, G502, HyperX Cloud 2s, Asus MX34. פN∩SW∀S 960 EVO

Just keeping this here as a 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4 minutes ago, BuckGup said:

I guess on more of an abstract scale looking at the universe of the problem. Does the fact that event happened influence future events? Not necessarily a butterfly effect but the event itself happening

Every event is considered individual until you identify a relationship with other events.

 

Also, that's exactly the butterfly effect. You're treading into philosophy now instead of stats.

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Posted

Basically what 2FA said.

To maybe add an example to make it more clear regarding point two.

If you have a situation where an event has say a 1% chance of occurring say each unit of time(or event), and that event is based on a random set of conditions, then no, the chance doesn't increase if it hasn't happened the previous event.

For example, imagine a spinning wheel in a carnival, or roulette table(same idea), then each time that wheel is spun, every chance is effectively reset.  Just because say it didn't land on red 22 last spin, then the next spin has exactly the same chance of landing on red 22 as it did on the last spin.  Same as with that carnival wheel.  This is a pretty common misconception, that it changes, many people assume it must change the odds, it doesn't.

However if you have a system where the probability is based on a set of events which are not random.  Like say there is a 0.0001% chance of your car tire blowing while driving 1km. Then the next 1km, if you keep driving that car over time, the chance of that tire blowing will change because there is a sort of wear that happens that changes the conditions for the next time.  Another example is say the chance of an earthquake each year.  Because with each year the pressure being build up increases if that pressure is not released. So in that case, every year that stored energy along that fault line is not released by a seismic event, then the next year the chance increases.  

So people think that because their numbers in a lottery haven't come up yet, that means there is more chance it will. The way the lotto machines work, that is not true.  Same with so many areas people think like that.  Also with computers, most randomness on a computer is based on a combination of some state the computer can read in that particular moment(reading the exact clock tick at that moment it is called, or the last keystroke, or better sometimes is the moment some radioactive element decays) and then using that number in a algorithm that relies on ideas from cryptography(primes, keys, etc) to generate a new value from that 'random event' that theoretically makes it nearly impossible to deduce the original random event's value.   Or even better relying on an algorithm that uses several 'random' states together.  Hackers used to be able to exploit 'pseudo-random' number generators in old machine operating systems, but random number generators in programming has since come a very long way.  

Regarding the first question, it depends again on the relationship between those probabilities.  If they are again both completely random, then it is just a matter of multiplying the probabilities against each other.  So say one event 1A has a 10% chance of occurring(90% of not occurring (we can call 1B)) and in a different unrelated system, another event(2A has a 20% chance of occurring(and 80% chance of not occurring 2B).  Then the chances would play out like...

Chance of 1A and 2A  is 0.1 * 0.2 = 0.02  = 2 %
Chance of 1A and 2B  is 0.1 * 0.8 = 0.08  = 8 %
Chance of 1B and 2A  is 0.9 * 0.2 = 0.18   = 18%
Chance of 1B and 2B is 0.9 * 0.8 =  0.72  = 72%
Total                                                           = 100%

Again as 2FA said, that all changes if there is some other relationship between those events you are speaking of. For instance, if that propability represent the chance of two different people winning in a fantasy pool.  Person A has 90% chance, and person B has 80%, then if you know that say person say didn't win, that does have an effect on the probability of person B willing, since his chances can now go up or down.  If you knew nothing of their 'picks' then the default would be to assume that person B now has a better chance of winning since there are effectively less people in the pool now. But if you know more information, and know say that person B has many of the same picks as person A's team, then it is likely than that person B is also doing crappy in the fantasy pool, and so his chances will go down most likely.

Again so it depends very much on what the relationship is between those two events.

(Ok this is a post edit note, just ignore the rest unless you are actually also interested in deep learning concepts around probability as well...)

And incidentally, that is effectively what deep learning is all about, pulling out the probability of every possible combination of events you can feed into the matrix, a giant sparse matrix, and once you solve it, what happens is the computer is essentially combining all these probabilities together to find patterns so complex that humans would not be able to keep track of all the variables.  Like face recognition, is largely about identifying the probability associated with each pixel in an image(a huge matrix of probabilities associated with colors) For instance in a real basic kind of sense, a person with dark black hair will have way more pixels having dark black in them then vs someone who has bright blue hair for instance. And so when you combine not just the color of each pixel, but the combination of colors beside each pixel on an image.  You get a giant bloody matrix of probabilities, and out of that you can deduce what the probability is that the image is the same as some set of images of a person the computer build a probability matrix model of in a training stage. Basically, run through a bunch of images of a person, build the probabilities out of that around what color each pixel will be against all the other pixels in the image, and then compare that against a new image to deduce if it the same person. 


In that case, in the case of deep learning, you assume you mostly don't have any clue what the underlying structures are, and rely purely on historic data say to form the best guess.  And in doing so computers find out crazy relationships, like the computers that pick stock, they use any information they can find they think might have some correlation with stocks going up or down. This includes sometimes millions of internet pages, that the computer just might pull out some crazy correlation, that says that every time Trump comes on tv, and this particular blog writes an article about it, this other stock, that most people might think has no correlation between those events, might go up or down. And a human would ignore that because they can't understand the correlation, but a deep learning machine says, I don't really care why it happens, only that there is a strong probability between those events, and so it 'guesses' better effectively because it isnt' prejudice, and it also is using millions upon millions of small correlations that sometimes can all add up to a very strong ability to predict events...

Sorry I rambled endlessly there.  Cleary I need to be doing something else. 

I hope there was something in there that perhaps helped... ;)
 

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19 hours ago, comander said:




I'm a stats nerd (multiple degrees in relevant fields and relevant professional experience). 
I will point out that your question could be phrased better so I'm going to make educated guesses. 

At a high level, your question touches on correlation and causation in the realm of probability. These issues aren't really statistics though. 

TLDR: It depends on the type of event and how they're linked. 0% correlation and 100% correlation DO occur and there are cases where the correlation changes with time. "What's the probability that the sun will raise tomorrow?" is basically 100% and you can see it as being "granger causal" from the previous days' data points. In 5 billion years the answer will be different (the sun will have exploded). At some point the sun will go nova and there will be a shift. 

     if something has a 90% chance of not happening in a year
P(A) = .10 = 10%
     completely different thing has an 80% chance of not happening.
P(B) = .20 = 20%
     When these two are used in tandem do their probabilities add so it's close to 100% or is it only as effective as the largest percent?
If you have a bunch of events will the probability of at least one occurring get near 100%?

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so unpacking the above... "it depends". If the events are uncorrelated then the probability will eventually converge towards 100% as your number of trials increases. 
If you have a series of independent and identically distributed (iid) events then it'll work like this
Prob(any occurrences in n events) = 100% - (prob(no-occurence))n

using dummy numbers(10% and 3 trials): 100% - 90%3 = 100% - .729 = 27.1%
using dummy numbers(10% and 20 trials): 100% - 90%20 = 87.84%
using dummy numbers(50% and 3 trials): 100% - 50%20 = 87.5%
using dummy numbers(50% and 20 trials): 100% - 50%20 = 99.9999%

note that this assumes 0 relationship. If the events are PERFECTLY correlated then it'll be the probability of the most likely event. Think of it this way - you have 20 different widgets you're making from different parts. The probability of any one unit working will be a mix of the probability of the parts going into it being good and the probability of no screw ups during assembly. If one part going into it is made in batches and the batch is 100% bad then all 20 of your parts will have a shared fate. 

https://en.wikipedia.org/wiki/Joint_probability_distribution

-----

Same thing goes for likely hood of something happening every time. If there is an 88% it is going to happen and doesn't happen does the fact it didn't happen influence the next time statistically even though it's only measures for a single event?


You can look at this as an inverse of the above. "What's the probability of an event NOT happening at least once" is analogous. The concept then reduces to the above. 

In terms of "if it didn't happen once does it impact the next?" - this depends on how closely the events are causally linked. 

If you can clarify your questions a bit I can try to address it a bit more.

It depends. For coin flips, nope. For "is this person's hair a certain length" you can think of it changing throughout their life with jumps whenever someone gets a haircut, goes bald, etc.
Another example would be "20% of the widgets a factory with 3 assembly lines produces are defective, if one assembly line has one defect, the next item will likely be defective, what's the probability of picking 5 items out of a bin and having 2 or more be defective?" <- in this case you'd find "clustering". 


For the record, I SUCK at probability. I'm lazy so I just run simulations using statistical programming languages. It's computationally inefficient but it's "close enough" and WAY faster than doing the closed form, analytical formula. Half the time, after having the approximate answer I can even reason backwards to the analytical formula for the exact answer. 


-------

Some things to look at - 
https://en.wikipedia.org/wiki/Negative_binomial_distribution
https://en.wikipedia.org/wiki/Multinomial_distribution
https://en.wikipedia.org/wiki/Conditional_probability


As a rule of thumb, the more "conditions" you can properly control for (this is hard and requires A TON of data in any non-trivial case), the more outcomes will look like completely random, disjoint events relative to the expected baseline. 

Alright you seem fairly well verse in this so I guess I should just ask the question I had originally. I censored it as I thought it wasn't beneficial and would turn some away but I think it matter now.

So my question is in regards to contraceptive effectiveness. I asked my local health counselor school and used WHO for some info but they all said to ask a statistician. The way they get the effectiveness for say 99% is they take out of 100 couples in one year 1 couple will get pregnant. It's sort of bogus as they go off self reporting so the average time the couple make love could vary wildly. But say they use a contraceptive that is 97% effective and use one that is 88% effective at the same time. Would it only be as effective as 97%? Or since the effectiveness is calculated by year out of 100 would the effectiveness compensate for one another where one may lack and become additive in some way? Say where the one lacks in 3% the 88% takes care of it or is this not how percentages work at all and they are strictly bottom up where that 3% remains no matter how many lower percentages you add? I know  it may be a weird question but I have yet to find an answer anywhere on the internet and in person.

▓ƆԀ▓ S▓₱▓Ɇ▓c▓s▓: i7 6ʇɥפᴉƎ00K (4.4ghz), Asus DeLuxe X99A II, GT҉X҉1҉0҉8҉0 Zotac Amp ExTrꍟꎭe),Si6F4Gb D???????r PlatinUm, EVGA G2 Sǝʌǝᘉ5ᙣᙍᖇᓎᙎᗅᖶt, Phanteks Enthoo Primo, 3TB WD Black, 500gb 850 Evo, H100iGeeTeeX, Windows 10, K70 R̸̢̡̭͍͕̱̭̟̩̀̀̃́̃͒̈́̈́͑̑́̆͘͜ͅG̶̦̬͊́B̸͈̝̖͗̈́, G502, HyperX Cloud 2s, Asus MX34. פN∩SW∀S 960 EVO

Just keeping this here as a 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On 5/10/2019 at 1:31 AM, BuckGup said:

I guess on more of an abstract scale looking at the universe of the problem. Does the fact that event happened influence future events? Not necessarily a butterfly effect but the event itself happening

I haven't read the rest of the thread so apologies if this has been mentioned.  But this reminded me of the reason most people get tripped in stats, that is because we tend to try and bridge the gap between probability and causality. We're in reality probability has nothing to do with causality, it simply seeks to describe it't likelihood.

 

If two events are are separate, then the outcome of the previous event has no effect on the following.  however over the course of enough events the results will eventually change which defines the probability rather than occurs because of it.

Grammar and spelling is not indicative of intelligence/knowledge.  Not having the same opinion does not always mean lack of understanding.  

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1 minute ago, comander said:

To add to this - Ice cream sales and pool drownings are strongly correlated. If you know that there's a lot of ice cream sales you can expect pool drownings to be high. 

This isn't because ice cream causes drownings or vice versa - it's because hot weather pushes both to occur. This is referred to as a lurking variable or a confounding variable. 

Even for single events, like flipping 100 coins.  the number of times you have to flip all the coins before you get a perfect run of heads or tails is presented as a probability, but each flipping of all the coins has no effect on the outcome of the next flip.

 

even if the the odds were 1 in a thousand, and you flipped them 999 times already, the odds of the next flip being a perfect run is still 1 in a thousand.  

Grammar and spelling is not indicative of intelligence/knowledge.  Not having the same opinion does not always mean lack of understanding.  

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2 hours ago, comander said:

Full disclosure, I'm not a biostatistician and my knowledge of healthcare is limited. I'm also trying to "infer" what you mean because your wording is a bit different from what I'd find in a "stats 101" textbook - let me know if I failed to touch on what you actually wanted to know. 

My understanding is that one (97%) is "perfect use" and the other (88%) is "what happens in the real world" after one year.
Loosely speaking, if you picked out 100 people involved in a clinical study who only had sex in clinical conditions and did everything right and never did anything stupid, you'd expect 97% non-pregnancy rates after a year. Keep in mind that people who participate in these studies (commonly college students) might also be a bit different than "normal" people even beyond their actions. 
In the other case, if you picked out 100 people at random at the start of the year, you'd expect around 88% who used the contraceptive to be pregnancy-free in one year. 

Also be aware that both of these figures are "biased" with respect to predicting your individual situation as they don't take into account the nuances of your situation. Affluent and well educated individuals generally have lower risk rates. The poor and uneducated have higher risk rates. If you skew towards one group you should be considering THAT figure as your baseline and not the overall population statistic. 

If you're trying to look at things from a multi-year perspective, you'd probably want to look at it as a series of multiple sub-populations. 

For 5 years it might be roughly .95^5 vs .70^5 with the overall population being roughly .88^5. This of course is an oversimplification of a number of reasons - a couples' risk level can change with time for example. Be aware that .95 and .70 were pulled out of my rear. 

All in all, if your concern is to know "what are my odds over N years", I would look for longer term (e.g. 5 year) figures than trying to "hack" together .88%^5 as your baseline if you want to know your own risk profile. The more data and the more relevant data you have the better when it comes to making a model. I'd also probably be looking at something like this: https://en.wikipedia.org/wiki/Kaplan–Meier_estimator to get a feel for what your "survival" rate would be for something like non-pregnancy. Full disclosure, I have only  personally used KM estimators when estimating the lifespan of high power signal amplifiers, NOT the time until pregnancy. I also couldn't find anything on it on my phone and I'm afraid to google "condom success rate" at work. Be aware that "lots of data + sophisticated model" is a lot harder to communicate than "88% effective"... which is why you hear "88% effective" instead of "X% effective between years 1-2 then Y% effective... but only if you're green-skinned, 6'8" and have a Harvard MBA... with a +/- 5% points margin of error"

Also if you're personally worried about pregnancy... IUDs work VERY well and are pretty much idiot proof. 

Alright you sorta answered my question but the 97% and 88% are two different contraceptives being used not the same in ideal and real world. This is why I raise the question of if their percent effectiveness are compounding or additive or something like that. Mainly what I have collected so far is it's really a shot in the dark for every individual and to make a blanket statement like that is misleading

▓ƆԀ▓ S▓₱▓Ɇ▓c▓s▓: i7 6ʇɥפᴉƎ00K (4.4ghz), Asus DeLuxe X99A II, GT҉X҉1҉0҉8҉0 Zotac Amp ExTrꍟꎭe),Si6F4Gb D???????r PlatinUm, EVGA G2 Sǝʌǝᘉ5ᙣᙍᖇᓎᙎᗅᖶt, Phanteks Enthoo Primo, 3TB WD Black, 500gb 850 Evo, H100iGeeTeeX, Windows 10, K70 R̸̢̡̭͍͕̱̭̟̩̀̀̃́̃͒̈́̈́͑̑́̆͘͜ͅG̶̦̬͊́B̸͈̝̖͗̈́, G502, HyperX Cloud 2s, Asus MX34. פN∩SW∀S 960 EVO

Just keeping this here as a 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