poisson process help

I need some help with a patient of mine... Not really help that I will use with her specifically, but more so that I can better understand things from a mathematical perspective.

This patient has just been in her 4th crash in the last 2 years. 3 as a passenger, 1 as a driver (the first one was as a driver). None were her fault and actually none of them were very common ones that could have been avoided even by a fast-thinking driver.

One of the first things we do as exposure therapists is explain to people that crashes causing physical injury are very rare and unlikely to happen in the first place, let alone multiple times. When people develop anxiety related to largely non-threatening things (like driving for instance) we try to make that seem less dangerous so we can collect counter-evidence via exposure. This normal goes off without a hitch as negative events are actually quite rare. But I'm just reading a book on violence by Pinker and learning about poisson shit and realizing that there may be a whole world of stuff on likelihoods of things that I'm not aware of.

I need some sort of help understanding poisson processes as well as what sort of information I'd need to determine likelihoods of crashes.

I think I need help also trying to understand what I want help with. Anybody know of any very basic theory books. These books should be aimed at non-math people lol.

at first i thought you meant poison, then i thought you meant some french cuisine prep advice, now i have no idea what you are talking about but it has me very interested.

  On 5/12/2012 at 5:37 AM, Franklin said:

I need some help with a patient of mine... Not really help that I will use with her specifically, but more so that I can better understand things from a mathematical perspective.

 

This patient has just been in her 4th crash in the last 2 years. 3 as a passenger, 1 as a driver (the first one was as a driver). None were her fault and actually none of them were very common ones that could have been avoided even by a fast-thinking driver.

 

One of the first things we do as exposure therapists is explain to people that crashes causing physical injury are very rare and unlikely to happen in the first place, let alone multiple times. When people develop anxiety related to largely non-threatening things (like driving for instance) we try to make that seem less dangerous so we can collect counter-evidence via exposure. This normal goes off without a hitch as negative events are actually quite rare. But I'm just reading a book on violence by Pinker and learning about poisson shit and realizing that there may be a whole world of stuff on likelihoods of things that I'm not aware of.

 

I need some sort of help understanding poisson processes as well as what sort of information I'd need to determine likelihoods of crashes.

 

I think I need help also trying to understand what I want help with. Anybody know of any very basic theory books. These books should be aimed at non-math people lol.

I'd recommend first starting from here:http://en.wikipedia.org/wiki/Binomial_distribution, http://en.wikipedia....on_distribution

Then I'd recommend this book: http://www.amazon.co...36812615&sr=1-2

I personally haven't used it for my studies, but have used other titles from Schaum and can tell you they truly are fantastically well written and useful.

Generally, first you need to understand the concept of a binomial distribution. Let's say you make an experiment, for example, flip a coin. You have a probability p that the one event, let's say event A will happen, and you have the probability q that opposite event (not A) will happen, event B. Obviously q+p=1, because something must happen (the sum of probabilites of any possible event must be 1). So q=1-p. Binomial distribution tells you what is the probabiliy the the event A will happen exactly x times in n repetitions of an experiments. These experiments are generally also called Bernoulli's independent experiments. The most important thing about them is that you don't know what will happen. The exact formula for this distribution you can see in the wikipedia link I gave you above. The question now arises: What will happen if you let the number of repetitions of an experiment go to infinity, but assume that the probability p is small? You can also say that p=m/n, where m is the number of wanted events (subevents of A) and n number of events. This is the general definition of probability - the number of wanted events divided with the number of total events. If you for example throw a dice, and event A is (odd number will fall), then obviously m=3, because there're three odd numbers on a dice - 1, 3 and 5, while the total number of numbers on dice is n=6. So p=1/2, in this simple example.

Anyway, if you let n go to infinity, while keeping p small, it can be shown that you get Poisson distribution - it is called a distribution of a rare events (Law of small numbers). So, Poisson distribution is a limiting case of a binomial distribution when n goes to infinity, but p is assumed small. If you don't assume that p is small, you'll get normal or Gauss distribution.

The question that appears is when will you get this distribution? The answer is obviously with events with a small probability of happening, such as a suicides ( ) for example, or a telephone calls. Obviously the crashes causing physical injury are quite rare and therefore can be described with Poisson distribution.

Now, what you need here to determine the probability is of course p which is generally known, and n. From this you can get m because m=np, and with m being known you can use Poisson distribution to get what you want. Again, exact formula for Poisson distribution you can see in the wikipedia link I gave you above. Using Poisson distribution you can get the probability that the event A will appear x times, with n and p, and therefore m, being known.

When we say that n goes to infinity, we mean that n is very large of course. Never forget that the Poisson distribution is only a very good approximation.

I hope I was at least somewhat clear. I'm a physics student so this stuff is normal for me.

Ignore my upper post. I added some more in this one, hopefully to be more clear:

  On 5/12/2012 at 5:37 AM, Franklin said:

I need some help with a patient of mine... Not really help that I will use with her specifically, but more so that I can better understand things from a mathematical perspective.

 

This patient has just been in her 4th crash in the last 2 years. 3 as a passenger, 1 as a driver (the first one was as a driver). None were her fault and actually none of them were very common ones that could have been avoided even by a fast-thinking driver.

 

One of the first things we do as exposure therapists is explain to people that crashes causing physical injury are very rare and unlikely to happen in the first place, let alone multiple times. When people develop anxiety related to largely non-threatening things (like driving for instance) we try to make that seem less dangerous so we can collect counter-evidence via exposure. This normal goes off without a hitch as negative events are actually quite rare. But I'm just reading a book on violence by Pinker and learning about poisson shit and realizing that there may be a whole world of stuff on likelihoods of things that I'm not aware of.

 

I need some sort of help understanding poisson processes as well as what sort of information I'd need to determine likelihoods of crashes.

 

I think I need help also trying to understand what I want help with. Anybody know of any very basic theory books. These books should be aimed at non-math people lol.

I'd recommend first starting from here:http://en.wikipedia.org/wiki/Binomial_distribution

http://en.wikipedia....on_distribution

Then I'd recommend this book: http://www.amazon.co...36812615&sr=1-2

I personally haven't used it for my studies, but have used other titles from Schaum and can tell you they truly are fantastically well written and useful.

Generally, first you need to understand the concept of a binomial distribution. Let's say you make an experiment, for example, flip a coin. You have a probability p that the one event, let's say event A will happen, and you have the probability q that opposite event (not A) will happen, event B. Obviously q+p=1, because something must happen (the sum of probabilites of any possible event must be 1). So q=1-p. Binomial distribution tells you what is the probabiliy the the event A will happen exactly x times in n repetitions of an experiments. These experiments are generally also called Bernoulli's independent experiments. The most important thing about them is that you don't know what will happen. The exact formula for this distribution you can see in the wikipedia link I gave you above. The question now arises: What will happen if you let the number of repetitions of an experiment go to infinity, but assume that the probability p is small? You can also say that p=m/n, where m is the number of wanted events (subevents of A) and n number of events. This is the general definition of probability - the number of wanted events divided with the number of total events. If you for example throw a dice, and event A is (odd number will fall), then obviously m=3, because there're three odd numbers on a dice - 1, 3 and 5, while the total number of numbers on dice is n=6. So p=1/2, in this simple example.

Anyway, if you let n go to infinity, while keeping p small, it can be shown that you get Poisson distribution - it is called a distribution of a rare events (Law of small numbers). So, Poisson distribution is a limiting case of a binomial distribution when n goes to infinity, but p is assumed small. If you don't assume that p is small, you'll get normal or Gauss distribution.

The question that appears is when will you get this distribution? The answer is obviously with events with a small probability of happening, such as a suicides ( ) for example, or a telephone calls. Obviously the crashes causing physical injury are quite rare and therefore can be described with Poisson distribution.

Now, what you need here to determine the probability is of course p which is generally known, and n. From this you can get m because m=np, and with m being known you can use Poisson distribution to get what you want. Again, exact formula for Poisson distribution you can see in the wikipedia link I gave you above. Using Poisson distribution you can get the probability that the event A will appear x times, with n and p, and therefore m, being known. In your case, n would be the number of car crashes, and p the probability that a person involved in a crash was physically injured. Therefore, you can find out what is the probability that x persons will be physically injured in crashes, if you know m. Of course, it is desirable that n is as great as possible. For example, you could also check how many crashes were within a certain period/area (n), and how many of those included physical injuries (m). Also, it is desirable to take into account only those events that happened under almost identical/very similar circumstances so that you get more accurate numbers. I would say those circumstances would for example be the intoxication levels of a drivers, the fact whether the seat belts were used or not, how fast were the vehicles driving, how big were the vehicles, weather conditions etc. I think you get the picture. But generally I assume that there's already plenty of statistics done for this kind of events, so you might want to Google around somewhat, for starters, as usual.

Not to forget, when we say that n goes to infinity, we mean that n is very large of course. Never forget that the Poisson distribution is "only" a very good approximation.

I hope I was at least somewhat clear. I'm a physics student so this stuff is normal for me.

would the low general probability of car crashes really matter for someone who's had 4 ? i'm probably oversimplifying your tactic but still..

  On 5/12/2012 at 11:41 AM, eugene said:

would the low general probability of car crashes really matter for someone who's had 4 ? i'm probably oversimplifying your tactic but still..

First of all, I was trying to give the mathematical description of the problem. Second of all, I would put an emphasis on the conditions which I mentioned above - intoxication levels of a drivers, the fact whether the seat belts were used or not, how fast were the vehicles driving, how big were the vehicles, weather conditions etc. And as always we're talking about probability and statistics which is based on some models. From those models it appears that some events have a small probability of happening. There can also be larger deviations in circumstances that led to an event. Whole statistics, which there's plenty of, is based on a certain models which must take as many things in consideration to be as accurate as possible. There're, as I said already, always some greater deviations. We're always talking about probability, after all.

But yes, this may not help toomuch somebody who had a traumatic event, unfortunately. Still, I think this is the best that can be done.

some videos explaining the poisson distribution available here

http://www.khanacademy.org/math/probability

I think you should recommend she becomes a stunt driver.

i believe "poisson process" is the technical term for males undergoing gender reassignment surgery

freak of the week: thank you SO much. That was incredibly helpful and I have bought the 3rd edition of that book. I've sent out an email to an area professor to help find the kinds of statistics I want.

Flurobox: hard high five as well.

BCM and Lump: both of you got a lol out of me.

I understand that the numbers are going to be really small but my interest is so great because this girl is hardly ever in a vehicle. I had another patient several years ago that was in 7 crashes over a 4 year period. both of them are outliers for sure.

one of the more interesting avenues I'd like to look at as well is whether or not, and how much if yes, my patient (sitting as a passenger) was influencing crashes because of her very high anxiety levels. There is some pretty cool research on "chemosignals" produced when people are afraid that negatively influence others. This may have a very slight effect on her drivers and it would be cool to test that somehow.

fuck I wish I knew how to do statistics!

  On 5/12/2012 at 6:13 PM, Franklin said:

freak of the week: thank you SO much. That was incredibly helpful and I have bought the 3rd edition of that book. I've sent out an email to an area professor to help find the kinds of statistics I want.

No problem. Glad I could be helpful.

  On 5/12/2012 at 12:42 PM, BCM said:

I think you should recommend she becomes a stunt driver.

lol

  On 5/12/2012 at 6:20 PM, Franklin said:

one of the more interesting avenues I'd like to look at as well is whether or not, and how much if yes, my patient (sitting as a passenger) was influencing crashes because of her very high anxiety levels. There is some pretty cool research on "chemosignals" produced when people are afraid that negatively influence others. This may have a very slight effect on her drivers and it would be cool to test that somehow.

Interesting. I am afraid I can't really help you there, but this definitely made me interested. To be honest, I never truly considered this kind of phenomenon, although it from a certain point of view makes sense. Something I would for example assume is that the people are being nervous because they're afraid of crashes/accidents, their nervousness affects their concentration and it therefore diminishes their ability to control the vehicle properly, although this is only one-person based. The transfer from one person to other is not something I've yet truly considered in a scientific light. One interesting example of how being nervous can cause you troubles is hyperhydrosis, where in some cases people simply sweat more because they're nervous and afraid of becoming sweaty, and this same nervousness and fear stimulates perspiration.

I don't think statistics are relevant here for one individual.

So many factors go into this that you can't accurately make any statistical assertions or predictions

  On 5/12/2012 at 11:41 AM, eugene said:

would the low general probability of car crashes really matter for someone who's had 4 ? i'm probably oversimplifying your tactic but still..

"look, you've had 4 in the last two years, you filled your statistical quota and are now invincible"

btw my previous post was directed at franklin, not you freak of the week.

  On 5/12/2012 at 6:45 PM, Freak of the week said:

  On 5/12/2012 at 6:20 PM, Franklin said:

one of the more interesting avenues I'd like to look at as well is whether or not, and how much if yes, my patient (sitting as a passenger) was influencing crashes because of her very high anxiety levels. There is some pretty cool research on "chemosignals" produced when people are afraid that negatively influence others. This may have a very slight effect on her drivers and it would be cool to test that somehow.

 

Interesting. I am afraid I can't really help you there, but this definitely made me interested. To be honest, I never truly considered this kind of phenomenon, although it from a certain point of view makes sense. Something I would for example assume is that the people are being nervous because they're afraid of crashes/accidents, their nervousness affects their concentration and it therefore diminishes their ability to control the vehicle properly, although this is only one-person based. The transfer from one person to other is not something I've yet truly considered in a scientific light. One interesting example of how being nervous can cause you troubles is hyperhydrosis, where in some cases people simply sweat more because they're nervous and afraid of becoming sweaty, and this same nervousness and fear stimulates perspiration.

there are some really cool studies on this stuff. I did a paper on it myself a bunch of years ago. Basically you can take sweat from individuals who've watched anxiety or fear-inducing stimuli (scary movies etc) and apply that sweat to other individuals watching happy movies and significantly alter their perceptions of the movie. They've now done it with lots of perceptual-based stuff as well like how quickly you would respond to other danger signals like the speed of reading danger-related words, noticing danger-related cues in pictures etc.

"apply that sweat to other individuals" hahaha gross

  On 5/12/2012 at 8:14 PM, Zeffolia said:

I don't think statistics are relevant here for one individual.

 

So many factors go into this that you can't accurately make any statistical assertions or predictions

Statistical approach is needed when there are toomany factors that define the outcome of one event, and you can't take them all in consideration. If you could, there would be no need for probability and statistics, and everything would be perfectly deterministic. Still, what's important is that you do your best to make sure that the experiments you're performing are as similar to each other as possible. For example, if you repeat experiment of throwing a dice 20 cm above the table and note each time which number fall, and of course each time try to have the hand in the same position as in the previous throwing, and use the same moves etc., you still won't be able to say for sure what'll happen the next time, because there're little things like really really small movements of your hands which you can't control or the imperfections of a dice that lead to, combined with an air resistance for example, and the bouncing off the table before finally ending in a state of rest, different outcome. You make as many experiments as possible, trying to have the same conditions each time, and then you can say that the probability that for example even number will fall will be very close to 0.5. However, if you were to apply this probability in predicting the outcome of a dice being thrown from like 15 m building, you won't really get (that) good results, because air resistance now has a much greater effect then before, and the bouncing off the ground will be quite more intense.

Back to the subject of this topic - if there already is a plenty of statistics being made about the physical injuries received during crashes, the question would be - as franklin mentioned these chemosignals, what causes them and were they present before, or are they an exclusive result of a particularly stressful lifestyle in 21st century? Assuming that they were always present (that is, present during the modern cars era), it means that the statistics made before included them aswell, although maybe scientists weren't aware of them. If however this phenomenon is either a result of a new lifestyle, or is simply drastically magnified as a result of the same, that means that the new statistics must be made to avoid errors in predicting the outcome of some crash. There's analogy somewhat between that and that dice example I described above.

Of course, it's not about chemosignals only, but a general psychological state of people in 21st century, which we all know is quite stressful and of course must affect also people's ability to be able to control the vehicle they're driving properly.

Also, you mention "one individual" but then again before we can say that this is an isolated case, we must know what's really causing this kind of psychological condition etc., and are the factors causing in it general known/common or not. If we're ever dealing with a unique case, then obviously of course, statistics we have can't be useful for us, and we need to develop a new one. But then again I am not really sure that this is a unique case.

  On 5/12/2012 at 11:33 PM, eugene said:

 

btw my previous post was directed at franklin, not you freak of the week.

No problem. I realized toolate that it may not be directed at me.

  On 5/12/2012 at 11:34 PM, Franklin said:

  On 5/12/2012 at 6:45 PM, Freak of the week said:

  On 5/12/2012 at 6:20 PM, Franklin said:

one of the more interesting avenues I'd like to look at as well is whether or not, and how much if yes, my patient (sitting as a passenger) was influencing crashes because of her very high anxiety levels. There is some pretty cool research on "chemosignals" produced when people are afraid that negatively influence others. This may have a very slight effect on her drivers and it would be cool to test that somehow.

 

Interesting. I am afraid I can't really help you there, but this definitely made me interested. To be honest, I never truly considered this kind of phenomenon, although it from a certain point of view makes sense. Something I would for example assume is that the people are being nervous because they're afraid of crashes/accidents, their nervousness affects their concentration and it therefore diminishes their ability to control the vehicle properly, although this is only one-person based. The transfer from one person to other is not something I've yet truly considered in a scientific light. One interesting example of how being nervous can cause you troubles is hyperhydrosis, where in some cases people simply sweat more because they're nervous and afraid of becoming sweaty, and this same nervousness and fear stimulates perspiration.

 

there are some really cool studies on this stuff. I did a paper on it myself a bunch of years ago. Basically you can take sweat from individuals who've watched anxiety or fear-inducing stimuli (scary movies etc) and apply that sweat to other individuals watching happy movies and significantly alter their perceptions of the movie. They've now done it with lots of perceptual-based stuff as well like how quickly you would respond to other danger signals like the speed of reading danger-related words, noticing danger-related cues in pictures etc.

Cool.

i think you should recommend she joins the foreign legion

dunno if I can tell you anything about it that's insightful to you, all I can think of is this book "adventures in stochastic processes" by Sidney Resnick, while it is intended for students in mathematics it is also filled with funny examples and stories. I can send you a pdf if you want.

Also, I'd like to point out that from a mathematical point of view, streaks WILL always happen even for low probability events.

  On 5/13/2012 at 2:49 AM, GORDO said:

Also, I'd like to point out that from a mathematical point of view, streaks WILL always happen even for low probability events.

Exactly, this thread is a tad baffling, are you searching for some sort of modern proof of Jung's "meaningful coincidences" (aka synchronicity)? Don't think yer gonna find it...

I'M OK, YOU'RE OK.

  On 5/13/2012 at 2:49 AM, GORDO said:

dunno if I can tell you anything about it that's insightful to you, all I can think of is this book "adventures in stochastic processes" by Sidney Resnick, while it is intended for students in mathematics it is also filled with funny examples and stories. I can send you a pdf if you want.

 

Also, I'd like to point out that from a mathematical point of view, streaks WILL always happen even for low probability events.

hey thanks Gordo I would love you to send that pdf!

The one thing that I do understand is that random events DO tend to cluster. I'm reading a book on violence by Pinker right now and he's discussed that at length with lots of interesting examples.