Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
I don't have an answer per se, but I have some relevant information: Back in the early days of statistics, one could become a pariah in the eyes of the field if it became suspected one had surreptitiously used Bayes' Theorem in a proof. This was because the early statisticians believed future events were probable. They really, deeply believed it. They were defining a new world view, to be contrasted with the deterministic world view. If you smoked, there was a probability that in the future you might get cancer; it was not certain, nothing was predetermined. In such a context, any talk of backwards-probability is nonsensical. After you have lung cancer, there is not "a probability" that you smoked. Either you did or you did not; it already happened! Thus, at least for the early statisticians, people like Fisher, time was inherent to claims about probability. Now, it is worth noting that one can wager on past events of any kind, given someone willing to take the bet. And in such a context, Bayes' Theorem can be mighty useful. The Theorem is thus quite popular these days, but that is a different matter. Whatever the results of such equations are --- between 1 and 0, having certain properties, etc. --- so long as the results refer to past events, Fisher and many others would have insisted that the result is not "a probability" that said event occurred. Also, from what I can tell, as mathematicians became more prevalent in statistics, as opposed to the grand tradition of scientist-philosophers who happened to be highly proficient in mathematics, such ontological/metaphysical points seem to have become much less important. --- Eric P. Charles, Ph.D. Supervisory Survey Statistician U.S. Marine Corps On Mon, Dec 12, 2016 at 6:47 PM, glen ☣ wrote: > > I have a large stash of nonsense I could write that might be on topic. > But the topic coincides with an argument I had about 2 weeks ago. My > opponent said something generalizing about the use of statistics and I made > a comment (I thought was funny, but apparently not) that I don't really > know what statistics _is_. I also made the mistake of claiming that I _do_ > know what probability theory is. [sigh] Fast forward through lots of > nonsense to the gist: > > My opponent claims that time (the experience of, the passage of, etc.) is > required by probability theory. He seemed to hinge his entire argument on > the vernacular concept of an "event". My argument was that, akin to the > idea that we discover (rather than invent) math theorems, probability > theory was all about counting -- or measurement. So, it's all already > there, including things like power sets. There's no need for time to pass > in order to measure the size of any given subset of the possibility space. > > In any case, I'm a bit of a jerk, obviously. So, I just assumed I was > right and didn't look anything up. But after this conversation here, I > decided to spend lunch doing so. And ran across the idea that probability > is the forward map (given the generator, what phenomena will emerge?) and > statistics is the inverse map (given the phenomena you see, what's the > generator?). And although neither of these really require time, per se, > there is a definite role for [ir]reversibility or at least asymmetry. > > So, does anyone here have an opinion on the ontological status of one or > both probability and/or statistics? Am I demonstrating my ignorance by > suggesting the "events" we study in probability are not (identical to) the > events we experience in space & time? > > > On 12/11/2016 11:31 PM, Nick Thompson wrote: > > Would the following work? > > > > */Imagine you enter a casino that has a thousand roulette tables. The > rumor circulates around the casino that one of the wheels is loaded. So, > you call up a thousand of your friends and you all work together to find > the loaded wheel. Why, because if you use your knowledge to play that > wheel you will make a LOT of money. Now the problem you all face, of > course, is that a run of successes is not an infallible sign of a loaded > wheel. In fact, given randomness, it is assured that with a thousand > players playing a thousand wheels as fast as they can, there will be random > long runs of successes. But the longer a run of success continues, the > greater is the probability that the wheel that produces those successes is > biased. So, your team of players would be paid, on this account, for > beginning to focus its play on those wheels with the longest runs. /* > > > > > > > > FWIW, this, I think, is Peirce’s model of scientific induction. > > -- > ☣ glen > > > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ==
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Excellent! My opponent will be very happy when I make that concession. It's interesting that, for this argument, I've adopted the Platonic perspective despite being a constructivist myself. And it's interesting that my current position (that the math world is extant and static) seems to rely a bit on viewing probability theory as a special subset of math overall. But that perspective seems to encourage me to think about the ontological/metaphysical aspects. Perhaps it's only because I'm not a mathematician. Thanks! On 12/13/2016 05:00 AM, Eric Charles wrote: > I don't have an answer per se, but I have some relevant information: > > Back in the early days of statistics, one could become a pariah in the eyes > of the field if it became suspected one had surreptitiously used Bayes' > Theorem in a proof. This was because the early statisticians believed > future events were probable. They really, deeply believed it. They were > defining a new world view, to be contrasted with the deterministic world > view. If you smoked, there was a probability that in the future you might > get cancer; it was not certain, nothing was predetermined. In such a > context, any talk of backwards-probability is nonsensical. After you have > lung cancer, there is not "a probability" that you smoked. Either you did > or you did not; it already happened! Thus, at least for the early > statisticians, people like Fisher, time was inherent to claims about > probability. > > Now, it is worth noting that one can wager on past events of any kind, > given someone willing to take the bet. And in such a context, Bayes' > Theorem can be mighty useful. The Theorem is thus quite popular these days, > but that is a different matter. Whatever the results of such equations are > --- between 1 and 0, having certain properties, etc. --- so long as the > results refer to past events, Fisher and many others would have insisted > that the result is not "a probability" that said event occurred. > > Also, from what I can tell, as mathematicians became more prevalent in > statistics, as opposed to the grand tradition of scientist-philosophers who > happened to be highly proficient in mathematics, such > ontological/metaphysical points seem to have become much less important. -- ␦glen? FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Glen and Eric, In my role as the Fool Who Rushes In, let me just say that according to an experience monist, past experience, present experience, and future experience are all on the same footing. We come to know them as different because they prove out in different ways. This should fit nicely with your constructivism, Glen, although you may see it as too much of a good thing. We can have expectations about the past, just as well as we can have expectations of the future, and those expectations can prove out or not in subsequent experience. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ -Original Message- From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of ?glen? Sent: Tuesday, December 13, 2016 8:37 AM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] probability vs. statistics (was Re: Model of induction) Excellent! My opponent will be very happy when I make that concession. It's interesting that, for this argument, I've adopted the Platonic perspective despite being a constructivist myself. And it's interesting that my current position (that the math world is extant and static) seems to rely a bit on viewing probability theory as a special subset of math overall. But that perspective seems to encourage me to think about the ontological/metaphysical aspects. Perhaps it's only because I'm not a mathematician. Thanks! On 12/13/2016 05:00 AM, Eric Charles wrote: > I don't have an answer per se, but I have some relevant information: > > Back in the early days of statistics, one could become a pariah in the > eyes of the field if it became suspected one had surreptitiously used Bayes' > Theorem in a proof. This was because the early statisticians believed > future events were probable. They really, deeply believed it. They > were defining a new world view, to be contrasted with the > deterministic world view. If you smoked, there was a probability that > in the future you might get cancer; it was not certain, nothing was > predetermined. In such a context, any talk of backwards-probability is > nonsensical. After you have lung cancer, there is not "a probability" > that you smoked. Either you did or you did not; it already happened! > Thus, at least for the early statisticians, people like Fisher, time > was inherent to claims about probability. > > Now, it is worth noting that one can wager on past events of any kind, > given someone willing to take the bet. And in such a context, Bayes' > Theorem can be mighty useful. The Theorem is thus quite popular these > days, but that is a different matter. Whatever the results of such > equations are > --- between 1 and 0, having certain properties, etc. --- so long as > the results refer to past events, Fisher and many others would have > insisted that the result is not "a probability" that said event occurred. > > Also, from what I can tell, as mathematicians became more prevalent in > statistics, as opposed to the grand tradition of > scientist-philosophers who happened to be highly proficient in > mathematics, such ontological/metaphysical points seem to have become much > less important. -- ␦glen? FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Glenn, This topic was well-developed in the last century. The probabilists argued the issues thoroughly. But I find what the philosophers of science have to say about the subject a little more pertinent to what you are asking, since your discussion seems to be somewhat ontological. In particular I'm thinking of Peirce, Popper and especially Mario Bunge. The latter two had to account for quantum theory, so are a little more pertinent - and interesting. I can give you more specific references if you are interested. Take care, Grant On 12/12/16 4:47 PM, glen ☣ wrote: I have a large stash of nonsense I could write that might be on topic. But the topic coincides with an argument I had about 2 weeks ago. My opponent said something generalizing about the use of statistics and I made a comment (I thought was funny, but apparently not) that I don't really know what statistics _is_. I also made the mistake of claiming that I _do_ know what probability theory is. [sigh] Fast forward through lots of nonsense to the gist: My opponent claims that time (the experience of, the passage of, etc.) is required by probability theory. He seemed to hinge his entire argument on the vernacular concept of an "event". My argument was that, akin to the idea that we discover (rather than invent) math theorems, probability theory was all about counting -- or measurement. So, it's all already there, including things like power sets. There's no need for time to pass in order to measure the size of any given subset of the possibility space. In any case, I'm a bit of a jerk, obviously. So, I just assumed I was right and didn't look anything up. But after this conversation here, I decided to spend lunch doing so. And ran across the idea that probability is the forward map (given the generator, what phenomena will emerge?) and statistics is the inverse map (given the phenomena you see, what's the generator?). And although neither of these really require time, per se, there is a definite role for [ir]reversibility or at least asymmetry. So, does anyone here have an opinion on the ontological status of one or both probability and/or statistics? Am I demonstrating my ignorance by suggesting the "events" we study in probability are not (identical to) the events we experience in space & time? On 12/11/2016 11:31 PM, Nick Thompson wrote: Would the following work? */Imagine you enter a casino that has a thousand roulette tables. The rumor circulates around the casino that one of the wheels is loaded. So, you call up a thousand of your friends and you all work together to find the loaded wheel. Why, because if you use your knowledge to play that wheel you will make a LOT of money. Now the problem you all face, of course, is that a run of successes is not an infallible sign of a loaded wheel. In fact, given randomness, it is assured that with a thousand players playing a thousand wheels as fast as they can, there will be random long runs of successes. But the longer a run of success continues, the greater is the probability that the wheel that produces those successes is biased. So, your team of players would be paid, on this account, for beginning to focus its play on those wheels with the longest runs. /* FWIW, this, I think, is Peirce’s model of scientific induction. FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Yes, definitely. I intend to bring up deterministic stochasticity >8^D the next time I see him. So a discussion of it in the context QM would be helpful. On 12/13/2016 10:54 AM, Grant Holland wrote: > This topic was well-developed in the last century. The probabilists argued > the issues thoroughly. But I find what the philosophers of science have to > say about the subject a little more pertinent to what you are asking, since > your discussion seems to be somewhat ontological. In particular I'm thinking > of Peirce, Popper and especially Mario Bunge. The latter two had to account > for quantum theory, so are a little more pertinent - and interesting. I can > give you more specific references if you are interested. -- ☣ glen FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Glen, On closer reading of the issue you are interested in, and upon re-consulting the sources I was thinking of (Bunge and Popper), I can see that neither of those sources directly address the question of whether time must be involved in order for probability theory to come into play. Nevertheless, I think you may be interested in these two sources anyway. The works that I've been reading from these two folks are: /Causality and Modern Science/ by Mario Bunge and /The Logic of Scientific Discovery/ by Karl Popper. Bunge takes (positive) probability to essentially be the complement of causation. Thus his book ends up being very much about probability. Popper has an eighty page section on probability and is well worth reading from a philosophy of science perspective. I recommend both of these sources. While I'm at it, let me add my two cents worth to the question concerning the difference between probability and statistics. In my view, Probability Theory /should be /defined as "the study of probability spaces". Its not often defined that way - usually something about "random variables" appears in the definition. But the subject of probability spaces is more inclusive, so I prefer it. Secondly, its reasonable to say that a probability space defines "events" (at least in the finite case) as essentially a set of combinations of the sample space (with a few more specifications). Nothing is said in this definition that requires that "the event must occur in the future". But it seems that many people (students) insist that it has to - or else they can't seem to wrap their minds around it. I usually just let them believe that "the event has to be in the future" and let it go at that. But there is nothing in the definition of an event in a probability space that requires anything about time. I regard the discipline of statistics (of the Fisher/Neyman type) as the study of a particular class of problems pertaining to probability distributions and joint distributions: for example, test of hypotheses, analysis of variance, and other problems. Statistics makes some very specific assumptions that probability theory does not always make: such as that there is an underlying theoretical distribution that exhibits "parameters" against which are compared "sample distributions" that exhibit corresponding "statistics". Moreover, the sweet spot of statistics, as I see it, is the moment and central moment functionals that, essentially, measure chance variation of random variables. I admit that some folks would say that probability theory is no more inclusive than I described statistics as being. But I think that it is. Admittedly, what I have just said is more along the lines of "what it is to me" - a statement of preference, rather than an ontic argument that "this is what it is". As long as we're all having a good time... Grant On 12/13/16 12:03 PM, glen ☣ wrote: Yes, definitely. I intend to bring up deterministic stochasticity >8^D the next time I see him. So a discussion of it in the context QM would be helpful. On 12/13/2016 10:54 AM, Grant Holland wrote: This topic was well-developed in the last century. The probabilists argued the issues thoroughly. But I find what the philosophers of science have to say about the subject a little more pertinent to what you are asking, since your discussion seems to be somewhat ontological. In particular I'm thinking of Peirce, Popper and especially Mario Bunge. The latter two had to account for quantum theory, so are a little more pertinent - and interesting. I can give you more specific references if you are interested. FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Hi Glen, I feel a bit like Nick says he feels when immersed in the stream of such erudite responses to each of your seemingly related, but thread-separated questions. As always, though, when reading the posted responses in this forum, I learn a lot from the various and remarkable ways questions can be interpreted based on individual experiences. Perhaps this props up the idea of social constructivism more than Platonism. So, if you can bear with me, my response here is more of a summary of my takeaways from the variety of responses to your two respective questions, with my own interpretations thrown in and based on my own experiences. Taking each question separately ... Imagine a thousand computers, each generating a list of random numbers. > Now imagine that for some small quantity of these computers, the numbers > generated are in n a normal (Poisson?) distribution with mean mu and > standard deviation s. Now, the problem is how to detect these non-random > computers and estimate the values of mu and s. Nick's question seems to be about how to determine non-random event generators from independent streams of reportedly random processes. This is not really difficult to do and doesn't require any assumptions about underlying probability distributions other than that each number in the stream is equally likely as any other number in the stream [i.e., uniformly distributed in probability space] and that the cumulative probability over all possible outcomes sums to unity: the very definition of a random variable ... a non-deterministic event--an observation--mapped to a number line or a categorical bin. A random variable has both mathematical and philosophical properties, as we have heard in this thread. For Nick's question, I think that Roger has provided the most practical answer with Marsaglia's Die Hard battery of tests for randomness. In my professional life, I used these tests to prepare, for example, a QC procedure for ensuring our hashing algorithms remained random allocators after each new build of our software suite. For example, a simple test called the "poker test" using the Chi-squared distribution could be used to satisfy Nick's question with the power of the test (i.e., reducing the probability of rejecting the null hypothesis of randomness when it is true; thus perhaps finding more non-random processes than really exist) increasing with larger sample sizes ... longer runs. So, does anyone here have an opinion on the ontological status of one or > both probability and/or statistics? Am I demonstrating my ignorance by > suggesting the "events" we study in probability are not (identical to) the > events we experience in space & time? At the risk of exposing my own ignorance, I'll also say your question has to do with the ontological status of any random "event" when treated in any estimation experiments or likelihood computation; that is, are proposed probability events or measured statistical events real? For example--examples are always good to help clarify the question--is the likelihood of a lung cancer event given a history of smoking pointing to some reality that will actually occur with a certain amount of uncertainty? In a population of smokers, yes. For an individual smoker, no. In the language of probability and statistics, we say that in a population of smokers we *expect *this reality to be observed with a certain amount of certainty (probability). To be sure, these tests would likely involve several levels of contingencies to tame troublesome confounding variables (e.g., age, length of time, smoking rate). Don't want to get into multi-variate statistics, though. Obviously, time is involved here but doesn't have to be (e.g., the probability of drawing four aces from a trial of five random draws). An event is an observation in, say, a nonparametric Fisher exact test of significance against the null hypothesis of, say, a person that smokes will contract lung cancer, which we can make contingent on, say, the number of years of smoking. Epidemiological studies can be very complex, so maybe not the best of examples ... So, since probability and statistics both deal with the idea of an event--as your "opponent" insists--events are just observations that the event of interest [e.g., four of a kind] occurred; so I would say epistemologically they are real experiences with a potential (probability) based on either controlled randomized experiments of observational experience. But is a potential ontologically real? 🤔 Asking if those events come with ontologically real probabilistic properties is another, perhaps, different question? This gets into worldview notions of determinism and randomness. We tend to say that if a human cannot predict the event in advance, it is random ... enough. If it can be predicted based, say, on known initial conditions, then using probability theory here is misplaced. Still, there are chaotic non-random events that are not practically pred
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Thanks! Everything you say seems to land squarely in my opponent's camp, with the focus on the concept of an action or event, requiring some sort of partially ordered index (like time). But you included the clause "but doesn't have to be". I'd like to hear more about what you conceive probability theory to be without events, actions, time, etc. For the sake of this argument, anyway, my concept is affine to Grant's: "the study of probability spaces". Probability, to me, is just the study of the sizes of sets where all the sizes are normalized to the [0,1] interval. We talk of "selecting" or "choosing" subsets or elements from larger sets. But such "selection" isn't an action in time. Such "selection" is an already extant property of that organization of sets. Likewise, the "events" of probability are merely analogous to the events we experience in subjective time. Those "events" are (various) properties or predicates that hold over whatever set of sets is under consideration. Those "events" don't _happen_. They simply _are_. Since your language seems to depend on the idea that those predicates must _happen_ (i.e. at one point, they are potential or imaginary, and the next they are actual or factual), yet you say they don't have to, I'd like to hear you explain how "they don't have to". What are these "events" absent time (or another such partially ordered index)? p.s. FWIW, I have the same problem with the concept of "function" and asymmetric transformations. I accept the idea of a non-invertible function. But by accepting that, am I forced to admit something like time? Or, asked another way: As all the no-go theorem provers keep telling us (Tarski, Gödel, Wolpert, Arrow, ...), are we doomed to a "turtles all the way down" perspective? On 12/13/2016 05:03 PM, Robert Wall wrote: > At the risk of exposing my own ignorance, I'll also say your question has to > do with the ontological status of any random "event" when treated in any > estimation experiments or likelihood computation; that is, are proposed > probability events or measured statistical events real? > > For example--examples are always good to help clarify the question--is the > likelihood of a lung cancer event given a history of smoking pointing to some > reality that will actually occur with a certain amount of uncertainty? In a > population of smokers, yes. For an individual smoker, no. In the language of > probability and statistics, we say that in a population of smokers we /expect > /this reality to be observed with a certain amount of certainty > (probability). To be sure, these tests would likely involve several levels of > contingencies to tame troublesome confounding variables (e.g., age, length of > time, smoking rate). Don't want to get into multi-variate statistics, though. > > Obviously, time is involved here but doesn't have to be (e.g., the > probability of drawing four aces from a trial of five random draws). An event > is an observation in, say, a nonparametric Fisher exact test of significance > against the null hypothesis of, say, a person that smokes will contract lung > cancer, which we can make contingent on, say, the number of years of smoking. > Epidemiological studies can be very complex, so maybe not the best of > examples ... > > So, since probability and statistics both deal with the idea of an event--as > your "opponent" insists--events are just observations that the event of > interest [e.g., four of a kind] occurred; so I would say epistemologically > they are real experiences with a potential (probability) based on either > controlled randomized experiments of observational experience. But is a > potential ontologically real? 🤔 > > Asking if those events come with ontologically real probabilistic properties > is another, perhaps, different question? This gets into worldview notions of > determinism and randomness. We tend to say that if a human cannot predict the > event in advance, it is random ... enough. If it can be predicted based, say, > on known initial conditions, then using probability theory here is misplaced. > Still, there are chaotic non-random events that are not practically > predictable ... they seem random ... enough. Santa Fe science writer and > book author George Johnson gets into this in his book /Fire in the Mind/. -- ☣ glen FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Ack! Well... I guess now we're in the muck of what the heck probability and statistics are for mathematicians vs. scientists. Of note, my understanding is that statistics was a field for at least a few decades before it was specified in a formal enough way to be invited into the hallows of mathematics departments, and that it is still frequently viewed with suspicion there. Glen states: *We talk of "selecting" or "choosing" subsets or elements from larger sets. But such "selection" isn't an action in time. Such "selection" is an already extant property of that organization of sets.* I find such talk quite baffling. When I talk about selecting or choosing or assigning, I am talking about an action in time. Often I'm talking about an action that I personally performed. "You are in condition A. You are in condition B. You are in condition A." etc. Maybe I flip a coin when you walk into my lab room, maybe I pre-generated some random numbers, maybe I look at the second hand of my watch as soon as you walk in, maybe I write down a number "arbitrarily", etc. At any rate, you are not in a condition before I put you in one, and whatever it is I want to measure about you hasn't happened yet. I fully admit that we can model the system without reference to time, if we want to. Such efforts might yield keen insights. If Glen had said that we can usefully model what we are interested in as an organized set with such-and-such properties, and time no where to be found, that might seem pretty reasonable. But that would be a formal model produced for specific purposes, not the actual phenomenon of interest. Everything interesting that we want to describe as "probable" and all the conclusions we want to come to "statistically" are, for the lab scientist, time dependent phenomena. (I assert.) --- Eric P. Charles, Ph.D. Supervisory Survey Statistician U.S. Marine Corps On Wed, Dec 14, 2016 at 12:16 PM, glen ☣ wrote: > > Thanks! Everything you say seems to land squarely in my opponent's camp, > with the focus on the concept of an action or event, requiring some sort of > partially ordered index (like time). But you included the clause "but > doesn't have to be". I'd like to hear more about what you conceive > probability theory to be without events, actions, time, etc. > > For the sake of this argument, anyway, my concept is affine to Grant's: > "the study of probability spaces". Probability, to me, is just the study > of the sizes of sets where all the sizes are normalized to the [0,1] > interval. We talk of "selecting" or "choosing" subsets or elements from > larger sets. But such "selection" isn't an action in time. Such > "selection" is an already extant property of that organization of sets. > Likewise, the "events" of probability are merely analogous to the events we > experience in subjective time. Those "events" are (various) properties or > predicates that hold over whatever set of sets is under consideration. > Those "events" don't _happen_. They simply _are_. > > Since your language seems to depend on the idea that those predicates must > _happen_ (i.e. at one point, they are potential or imaginary, and the next > they are actual or factual), yet you say they don't have to, I'd like to > hear you explain how "they don't have to". What are these "events" absent > time (or another such partially ordered index)? > > p.s. FWIW, I have the same problem with the concept of "function" and > asymmetric transformations. I accept the idea of a non-invertible > function. But by accepting that, am I forced to admit something like > time? Or, asked another way: As all the no-go theorem provers keep telling > us (Tarski, Gödel, Wolpert, Arrow, ...), are we doomed to a "turtles all > the way down" perspective? > > > On 12/13/2016 05:03 PM, Robert Wall wrote: > > At the risk of exposing my own ignorance, I'll also say your question > has to do with the ontological status of any random "event" when treated in > any estimation experiments or likelihood computation; that is, are proposed > probability events or measured statistical events real? > > > > For example--examples are always good to help clarify the question--is > the likelihood of a lung cancer event given a history of smoking pointing > to some reality that will actually occur with a certain amount of > uncertainty? In a population of smokers, yes. For an individual smoker, > no. In the language of probability and statistics, we say that in a > population of smokers we /expect /this reality to be observed with a > certain amount of certainty (probability). To be sure, these tests would > likely involve several levels of contingencies to tame troublesome > confounding variables (e.g., age, length of time, smoking rate). Don't want > to get into multi-variate statistics, though. > > > > Obviously, time is involved here but doesn't have to be (e.g., the > probability of drawing four aces from a trial of five random draws). An > event is an obs
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Ha! Yay! Yes, now I feel like we're discussing the radicality (radicalness?) of Platonic math ... and how weird mathematicians sound (to me) when they say we're discovering theorems rather than constructing them. 8^) Perhaps it's helpful to think about the "axiom of choice"? Is a "choosable" element somehow distinct from a "chosen" element? Does the act of choosing change the element in some way I'm unaware of? Does choosability require an agent exist and (eventually) _do_ the choosing? On 12/14/2016 10:24 AM, Eric Charles wrote: > Ack! Well... I guess now we're in the muck of what the heck probability and > statistics are for mathematicians vs. scientists. Of note, my understanding > is that statistics was a field for at least a few decades before it was > specified in a formal enough way to be invited into the hallows of > mathematics departments, and that it is still frequently viewed with > suspicion there. > > Glen states: /We talk of "selecting" or "choosing" subsets or elements from > larger sets. But such "selection" isn't an action in time. Such "selection" > is an already extant property of that organization of sets./ > > I find such talk quite baffling. When I talk about selecting or choosing or > assigning, I am talking about an action in time. Often I'm talking about an > action that I personally performed. "You are in condition A. You are in > condition B. You are in condition A." etc. Maybe I flip a coin when you walk > into my lab room, maybe I pre-generated some random numbers, maybe I look at > the second hand of my watch as soon as you walk in, maybe I write down a > number "arbitrarily", etc. At any rate, you are not in a condition before I > put you in one, and whatever it is I want to measure about you hasn't > happened yet. > > I fully admit that we can model the system without reference to time, if we > want to. Such efforts might yield keen insights. If Glen had said that we can > usefully model what we are interested in as an organized set with > such-and-such properties, and time no where to be found, that might seem > pretty reasonable. But that would be a formal model produced for specific > purposes, not the actual phenomenon of interest. Everything interesting that > we want to describe as "probable" and all the conclusions we want to come to > "statistically" are, for the lab scientist, time dependent phenomena. (I > assert.) -- ☣ glen FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
And I completely agree with Eric. But we can language it real simply and intuitively by just looking at what a probability space is. For further simplicity lets keep it to a finite probability space. (Neither a finite nor an infinite one says anything about "time".) A finite probability space has 3 elements: 1) a set of sample points called "the sample space", 2) a set of events, and 3) a set of probabilities /for the events/. (An infinite probability space is strongly similar.) But what is this "set of events"? That's the question that is being discussed on this thread. It turns out that the events for a finite space is nothing more than /the set of all possible combinations of the sample points/. (Formally the event set is something called a "sigma algebra", but no matter.) So, an event scan be thought of simply /all //combination//s of the sample points/. Notice that it is the events that have probabilities - not the sample points. Of course it turns out that each of the sample points happens to be a (trivial) combination of the sample space - therefore it has a probability too! So, the events already /have/ probabilities by virtue of just being in a probability space. They don't have to be "selected", "chosen" or any such thing. They "just sit there" and have probabilities - all of them. The notion of time is never mentioned or required. Admittedly, this formal (mathematical) definition of "event" is not equivalent to the one that you will find in everyday usage. The everyday one /does/ involve time. So you could say that everyday usage of "event" is "an application" of the formal "event" used in probability theory. This confusion between the everyday "event" and the formal "event" may be the root of the issue. Jus' sayin'. Grant On 12/14/16 11:36 AM, glen ☣ wrote: Ha! Yay! Yes, now I feel like we're discussing the radicality (radicalness?) of Platonic math ... and how weird mathematicians sound (to me) when they say we're discovering theorems rather than constructing them. 8^) Perhaps it's helpful to think about the "axiom of choice"? Is a "choosable" element somehow distinct from a "chosen" element? Does the act of choosing change the element in some way I'm unaware of? Does choosability require an agent exist and (eventually) _do_ the choosing? On 12/14/2016 10:24 AM, Eric Charles wrote: Ack! Well... I guess now we're in the muck of what the heck probability and statistics are for mathematicians vs. scientists. Of note, my understanding is that statistics was a field for at least a few decades before it was specified in a formal enough way to be invited into the hallows of mathematics departments, and that it is still frequently viewed with suspicion there. Glen states: /We talk of "selecting" or "choosing" subsets or elements from larger sets. But such "selection" isn't an action in time. Such "selection" is an already extant property of that organization of sets./ I find such talk quite baffling. When I talk about selecting or choosing or assigning, I am talking about an action in time. Often I'm talking about an action that I personally performed. "You are in condition A. You are in condition B. You are in condition A." etc. Maybe I flip a coin when you walk into my lab room, maybe I pre-generated some random numbers, maybe I look at the second hand of my watch as soon as you walk in, maybe I write down a number "arbitrarily", etc. At any rate, you are not in a condition before I put you in one, and whatever it is I want to measure about you hasn't happened yet. I fully admit that we can model the system without reference to time, if we want to. Such efforts might yield keen insights. If Glen had said that we can usefully model what we are interested in as an organized set with such-and-such properties, and time no where to be found, that might seem pretty reasonable. But that would be a formal model produced for specific purposes, not the actual phenomenon of interest. Everything interesting that we want to describe as "probable" and all the conclusions we want to come to "statistically" are, for the lab scientist, time dependent phenomena. (I assert.) FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Don't think about choosing. The axiom of choice says that there is a function from each set (subset) to an element of itself, as I recall. Frank Frank C. Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 wimber...@gmail.com wimbe...@cal.berkeley.edu Phone: (505) 995-8715 Cell: (505) 670-9918 -Original Message- From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of glen ? Sent: Wednesday, December 14, 2016 11:36 AM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] probability vs. statistics (was Re: Model of induction) Ha! Yay! Yes, now I feel like we're discussing the radicality (radicalness?) of Platonic math ... and how weird mathematicians sound (to me) when they say we're discovering theorems rather than constructing them. 8^) Perhaps it's helpful to think about the "axiom of choice"? Is a "choosable" element somehow distinct from a "chosen" element? Does the act of choosing change the element in some way I'm unaware of? Does choosability require an agent exist and (eventually) _do_ the choosing? On 12/14/2016 10:24 AM, Eric Charles wrote: > Ack! Well... I guess now we're in the muck of what the heck probability and > statistics are for mathematicians vs. scientists. Of note, my understanding > is that statistics was a field for at least a few decades before it was > specified in a formal enough way to be invited into the hallows of > mathematics departments, and that it is still frequently viewed with > suspicion there. > > Glen states: /We talk of "selecting" or "choosing" subsets or elements > from larger sets. But such "selection" isn't an action in time. Such > "selection" is an already extant property of that organization of > sets./ > > I find such talk quite baffling. When I talk about selecting or choosing or > assigning, I am talking about an action in time. Often I'm talking about an > action that I personally performed. "You are in condition A. You are in > condition B. You are in condition A." etc. Maybe I flip a coin when you walk > into my lab room, maybe I pre-generated some random numbers, maybe I look at > the second hand of my watch as soon as you walk in, maybe I write down a > number "arbitrarily", etc. At any rate, you are not in a condition before I > put you in one, and whatever it is I want to measure about you hasn't > happened yet. > > I fully admit that we can model the system without reference to time, > if we want to. Such efforts might yield keen insights. If Glen had > said that we can usefully model what we are interested in as an > organized set with such-and-such properties, and time no where to be > found, that might seem pretty reasonable. But that would be a formal > model produced for specific purposes, not the actual phenomenon of > interest. Everything interesting that we want to describe as > "probable" and all the conclusions we want to come to "statistically" > are, for the lab scientist, time dependent phenomena. (I assert.) -- ☣ glen FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Hi Glen, et al, Thanks for cashing mu $0.02 check. :-) When I wrote that "but it doesn't have to be" I wasn't asserting that probability theory is devoid of events. Events are fundamental to probability theory. They are the outcomes to which probability is assigned. In a nutshell, the practice of probability theory is the mapping of the events--outcomes-- from random processes to numbers, thus making the practice purposefully mathematical. And in this regard, we speak of a mathematical entity dubbed a random variable in order to carry out the calculus of probability and statistics. A random variable is like any other variable in mathematics, but with specific properties concerning the values it can take on. A random variable is considered "discrete" if it can take on only countable, distinct, or separate values [e.g., the sum of the values of a roll of seven die]. Otherwise, a random variable can be considered "continuous" if it can take on any value in an interval [e.g., the mass of an animal]. But, a random variable is a real-valued function--a one-to-one mapping of a random process to a number line. This is arguably as long about way of explaining [muck?!] why I said "but it doesn't have to be ... time." Time doesn't have to be involved such that the random variable does not have to distributed in time but often can be, such as in reliability theory--for, example, the probability that a device will survive for at least T cycles or months. Yes to your and Grant's notion that thinking in terms of probability spaces is a good way of thinking of probability and statistic and this mapping, as mathematically we are doing convolutions of distributions [spaces?] when modeling independent, usually identically distributed random trials [activities]. But, let's not confuse the mathematical modeling with the selection process of, say picking four of a kind from a deck of 52 cards. All we are interested in doing is mapping the outcomes--events-- to possibilities over which the probabilities all sum or integrate to no more than unity. The activity gets mapped in the treatment of the random variable in the mapping [e..g., the number of trials]. So, for example, rolling 6s six times in a row is not a function of time, but of six discrete, independent and identically distributed trials. For the computed probability, in this case, it doesn't matter how long it took to roll the dice six times. I am thinking that this is the way your "opponent" is thinking about the problem and suspect that he has been formally trained to see it this way. Not the only way but a classical way. When Eric talks about the historic difference between scientists, mathematicians, and statisticians practicing probability theory and statistics, these differences quickly disappeared when the idea of *uncertainty *bubbled up into the models found in the fields of physics, economics, measurement theory, decision theory, etc. No longer could the world be completely described by the classical system dynamic models. Maybe before Gauss even (the late-1700s), who was a polymath to be sure, error terms were starting to be added to their equations and had to be estimated. As to my language of "when" an event occurs with some calculated likelihood, it can be a description or a prediction. The researcher may be asking like Nick is [kind of?] asking in the other thread, what is the likelihood of my getting this many 1s in a row if the process is supposedly generating discrete random numbers between, say, one and five? In this case, a *psychologically *unexpected event has happened. Or in planning his experiment in advance, he may just want to set a halting threshold for determining that any machine that gives him the same N consecutive numbers in a row to be suspect. In that case, the event hasn't happened but has a finite potential for happening and we want to detect that if it happens ... too much. Those "events" don't _happen_. They simply _are_ This bit seems more philosophical than something a statistician would likely [no pun intended] worry about. Admittedly, my choice of words--throughout my post--could have been more precise, but I would not have said that "events simply are." When discussing the nature of time in a "block universe," maybe that could be said, but I would have been in Henri Bergson's corner [to my peril, of course] in the 1922 debate between Bergson and Albert Einstein on the subject of time. :-) Curiously, Bergson's idea of time is coming back--see *Time Reborn* (2013) by Lee Smolin. But this is likely not what you meant. However, you are an out-of-the-closet Platonist by your own admission. No worries; I have friends who are Platonists, most of them being mathematicians or philosophers or believe the brain to be a computer, but not typically computational scientists and certainly not cognitive scientists. :-) No such thing as computational philosophy ... yet. Hmmm. BTW, a Random Variable--continuous or discrete-
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
ld. So I don't think this is helpful to your cause. But I would be more than curious to see how you think it might be. I am more an applied mathematician|statistician than anything like a theoretical mathematician; though, I have happily worked with many of the latter ... and hopefully the reverse was true. :-) Okay, back to your observation: the fact that it is possible to choose a particular event from the set of all possible events in the event space is a trivial requirement. I cannot, for example, pick a black ball--an impossible event--from the previous urn of only red and white balls. So being able to choose three red balls from that urn makes the event "choosable." Is that event then distinct from that same event that has been "chosen?" At the classical level--as opposed to the quantum level--I cannot see any meaningful distinction EXCEPT to say that the former event is a possibility and the second event is a realization ... and that the way such events get discussed in practical probability and statistics. There is no spooky agent that needs to get factored into the calculus, IMHO. Somehow, I still feel I am missing something. Maybe you can figure it out, but it may not be all that important, and your question may have already been addressed satisfactorily by the other responses posted to the thread. Cheers On Wed, Dec 14, 2016 at 2:41 PM, Frank Wimberly wrote: > Don't think about choosing. The axiom of choice says that there is a > function from each set (subset) to an element of itself, as I recall. > > Frank > > > Frank C. Wimberly > 140 Calle Ojo Feliz > Santa Fe, NM 87505 > > wimber...@gmail.com wimbe...@cal.berkeley.edu > Phone: (505) 995-8715 Cell: (505) 670-9918 > > -Original Message----- > From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of glen ? > Sent: Wednesday, December 14, 2016 11:36 AM > To: The Friday Morning Applied Complexity Coffee Group > Subject: Re: [FRIAM] probability vs. statistics (was Re: Model of > induction) > > > Ha! Yay! Yes, now I feel like we're discussing the radicality > (radicalness?) of Platonic math ... and how weird mathematicians sound (to > me) when they say we're discovering theorems rather than constructing them. > 8^) > > Perhaps it's helpful to think about the "axiom of choice"? Is a > "choosable" element somehow distinct from a "chosen" element? Does the act > of choosing change the element in some way I'm unaware of? Does > choosability require an agent exist and (eventually) _do_ the choosing? > > > > On 12/14/2016 10:24 AM, Eric Charles wrote: > > Ack! Well... I guess now we're in the muck of what the heck probability > and statistics are for mathematicians vs. scientists. Of note, my > understanding is that statistics was a field for at least a few decades > before it was specified in a formal enough way to be invited into the > hallows of mathematics departments, and that it is still frequently viewed > with suspicion there. > > > > Glen states: /We talk of "selecting" or "choosing" subsets or elements > > from larger sets. But such "selection" isn't an action in time. Such > > "selection" is an already extant property of that organization of > > sets./ > > > > I find such talk quite baffling. When I talk about selecting or choosing > or assigning, I am talking about an action in time. Often I'm talking about > an action that I personally performed. "You are in condition A. You are in > condition B. You are in condition A." etc. Maybe I flip a coin when you > walk into my lab room, maybe I pre-generated some random numbers, maybe I > look at the second hand of my watch as soon as you walk in, maybe I write > down a number "arbitrarily", etc. At any rate, you are not in a condition > before I put you in one, and whatever it is I want to measure about you > hasn't happened yet. > > > > I fully admit that we can model the system without reference to time, > > if we want to. Such efforts might yield keen insights. If Glen had > > said that we can usefully model what we are interested in as an > > organized set with such-and-such properties, and time no where to be > > found, that might seem pretty reasonable. But that would be a formal > > model produced for specific purposes, not the actual phenomenon of > > interest. Everything interesting that we want to describe as > > "probable" and all the conclusions we want to come to "statistically" > > are, for the lab scientist, time dependent phenomena. (I assert.) > > -- > ☣ glen > >
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Well, sure. But the point is that the axiom of choice asserts, merely, the existence of the ability to choose a subset. They call them "choice functions", as if there exists some "chooser". But there's no sense of time (before the choice function is applied versus after it's applied). The name "choice" is a misleading misnomer. And that's my point. Probability theory is a special case of measure theory. Calling the set measures "probabilities" is an antiquated, misleading, and unfortunate name. On 12/14/2016 01:41 PM, Frank Wimberly wrote: > Don't think about choosing. The axiom of choice says that there is a > function from each set (subset) to an element of itself, as I recall. -- ☣ glen FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Well, my question hasn't been addressed satisfactorily. But I sincerely appreciate all the different ways everyone has tried to talk about it. My question is about language, not math or statistics. I'm adept enough at those. What I'm having trouble with in the argument (the guy's name is Steve, btw) is my inability to communicate the measure theory conception of probability theory in plain English. (He's not a mathematician, either.) I'm especially appreciative of what you, Eric, and Grant have laid out from the practical "just get 'er done" perspective. The reason my initial (failed) joke about not understanding what statistics _is_, but claiming to understand what probability theory _is_, was a joke, is because both are so heavily applied and so lightly ontological. Were I able to tell the joke so that Steve saw the Platonic vs. constructivist, noun vs. verb, (false) dichotomy implied, then I wouldn't find myself having to explain it. I would have avoided the need to make the Platonic view explicit ... which would have been good because I'm not a Platonist. On 12/14/2016 05:05 PM, Robert Wall wrote: > Somehow, I still feel I am missing something. Maybe you can figure it out, > but it may not be all that important, and your question may have already been > addressed satisfactorily by the other responses posted to the thread. -- ☣ glen FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Hey Glen, Yes, on the first issue with respect to the Axiom of Choice, I think the word "choice" there does not map one-for-one to the same word used in probability theory. I think the two concepts are mutually exclusive, but this may be beyond my "pay grade" to worry or talk about. 🤐 However, I can most certainly see your point about the beneficial relationship between measurement theory and probability theory. The notion sigma algebra is spot on, especially for the mathematics of theoretical probability. Even though I may be considered an old dog professionally, I can still resonate with Grant's notion of probability spaces as well. It's all good! You know, I can still have fun while simultaneously being lost in the forest. This has been fun! Thanks for letting me play in the sandbox ... 😊 Cheers On Wed, Dec 14, 2016 at 6:50 PM, glen ☣ wrote: > > Well, sure. But the point is that the axiom of choice asserts, merely, > the existence of the ability to choose a subset. They call them "choice > functions", as if there exists some "chooser". But there's no sense of > time (before the choice function is applied versus after it's applied). > The name "choice" is a misleading misnomer. > > And that's my point. Probability theory is a special case of measure > theory. Calling the set measures "probabilities" is an antiquated, > misleading, and unfortunate name. > > On 12/14/2016 01:41 PM, Frank Wimberly wrote: > > Don't think about choosing. The axiom of choice says that there is a > function from each set (subset) to an element of itself, as I recall. > > -- > ☣ glen > > > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove > FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
