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  1. #1

    Default The Fallacy of the Accident --Grrr-- Frequentists vs. Bayesians

    I was prompted by yet another pompous idiot w/ an MBA espousing statistics to argue something in a particular case better handled by contigency planning...This followed yet another incident from last night where a friend made an argument from statistics about a particular chess position.

    So, I am wondering, if I am actually the one off base in these circumstances.

    It goes as follows:
    P1: p% of As are Bs.
    P2: X is an A
    ----------------------------------, Therefore, I believe
    C1: X is a B

    Consider not that there may or may not be another argument that concludes with
    !C1: X is not a B.

    1. At what p does this argument a strong one for you (in that it begins to convince you)?
    2. What forms of arguments that conclude that X is not B, would change your mind in this case?
    3. At what p, would you stop looking for good arguments that X is not B?


    Also as background, and to provide more rich context, consider two popular, and both admittedly flawed, philosophical views of probability:

    Frequentists and Bayesians

    A more in depth article (a pdf).

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  2. #2
    Furry Critter with Claws Kiddo's Avatar
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    There are no accidents, only opportunities to learn.

    There problem solved.
    Quote Originally Posted by Silently Honest View Post
    OMNi: Wisdom at the cost of Sanity.

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    Boring old fossil Night's Avatar
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    Static v. fluid systems - I miss the old days.

    In terms of identifying the probability of occurrence of variable A, relative to frequency of occurrence against frequency of non (or "other") occurrence within the subset of concurrent variables (B; etc.), there are some things to carefully consider before we can conclude that x is necessarily A; B; y...

    - Identifying the empirical distinctions of A, relative to the observed distinctions of B; y
    - Reviewing the system to which A and B are oriented - what stimulates frequency of occurrence of A? B? y?
    - How strong is our margin of certainty in terms of reliably forecasting A; B; y in our given system?
    - To what extent can we be certain that A matches our empirical expectations for A (or "A" as an ideal)?

    In short, our margin of error is a derivative of the system it accents.

    Statistics provide an enumerative vehicle intended to reduce uncertainty (versus increase certainty) of event in a given system. Nothing more.

    Your friend can provide a baseline for previous occurrences, relative to his observed pattern of event with similar conditions.

    He's not necessarily incorrect - he's just got a nasty case of confirmation bias.

  4. #4

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    I am at heart, a Bayesian, because, as you've mentioned, the a-priori distribution makes a big difference on what the a-posteri distributions is.

    However, the tenet that on can expect a particular situation to work like one expects is too much. This is something, that frequentists would basically never assume.

    Also, as you pointed out, Bayesians can get themselves in situations with severe confirmation bias.

    Unfortunately, nobody else want to else wants to play, and we pretty much agree.

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

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    I didn't respond before because I was skimming... and I had no idea what you were saying. So I just reread this more carefully, then followed the conversation. Maybe people are not responding because it's phrased in a way they can't easily understand.

    To put it in English: What percentage of a group's members have to belong the subgroup for you to accept personally that the next member of the group you run across would ALSO fall within the subgroup?

    Or, to borrow from an old maxim and put flesh on the example, what percentage of Cretians would have to be known to be liars for you to accept that the NEXT Cretian you met is also a liar?

    1. What would the percentage need to be?
    2. What argument(s) or situation(s) would make you rethink your idea that perhaps your percentage is too high, or even that Cretians are not really liars at all?
    3. What would the percentage have to be so that you'd draw closure on the idea -- never willing to question again the proposition that a certain % of Cretians are liars?


    * * * *

    Actually, I think it's a wonderful topic simply because of the practical nature of it. We all makes decisions like this every day, we just normally don't realize we're making the calculations.

    Every time we judge someone or evaluate them without knowing all the information, we are making "hunches" based on how much proof we need that our hunch is probably true.

    • The guy selling things out of the booth -- based on my knowledge of booth vendors, his appearance, the things he's selling, and other characteristics I can observe, what are the odds that he is ripping me off.... and probably by how much?
    • The guy taking me out for a date -- based on my knowledge of his appearance, articulateness, occupation, background, topics of conversation, etc, what's the odds he's just out to score and not good LTR material?
    • The woman running for office -- based on my knowledge of elections and politicians, her personality, her presentation, the groups she affiliates with etc., what's the odd's she'll be a good leader?


    I mean, this is what comes up in religious and political discussions ALL the time (usually to support cynicism) -- "Oh, they're a <religion or party affiliation", they're just out to <some nefarious deed>, you can't trust them!"

    What percentage of experiences have to be negative, etc., to result in this sort of blanket judgment, and what sort of proof is needed to change it (if it can be)?
    "Hey Capa -- We're only stardust." ~ "Sunshine"

    “Pleasure to me is wonder—the unexplored, the unexpected, the thing that is hidden and the changeless thing that lurks behind superficial mutability. To trace the remote in the immediate; the eternal in the ephemeral; the past in the present; the infinite in the finite; these are to me the springs of delight and beauty.” ~ H.P. Lovecraft

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    Boring old fossil Night's Avatar
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    I enjoy you both very much, Ygolo and Jennifer.

    Thank you. Truly.

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    Well, I am neither a Bayesian nor a Frequentist, nor do I care about what theories, ideas or statements are probably true. Talk of probability, especially in regard to rational decision-making, is mostly a load of rubbish.
    A criticism that can be brought against everything ought not to be brought against anything.

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    Boring old fossil Night's Avatar
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    Quote Originally Posted by nocturne View Post
    Well, I am neither a Bayesian nor a Frequentist, nor do I care about what theories, ideas or statements are probably true. Talk of probability, especially in regard to rational decision-making, is mostly a load of rubbish.
    Please elaborate.
    While I'm sure you've means for your dissent, empty-handed critique is just that...

    Probability is a fragile creature. Easily toppled, yet interesting to speculate on.

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    Quote Originally Posted by Night View Post
    Please elaborate.
    While I'm sure you've means for your dissent, empty-handed critique is just that...

    Probability is a fragile creature. Easily toppled, yet interesting to speculate on.
    I will write about it someday, and perhaps post something on MBTICentral, but not at the moment. The problem requires a lengthy and difficult treatment.
    A criticism that can be brought against everything ought not to be brought against anything.

  10. #10

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    Quote Originally Posted by Jennifer View Post
    I didn't respond before because I was skimming... and I had no idea what you were saying. So I just reread this more carefully, then followed the conversation. Maybe people are not responding because it's phrased in a way they can't easily understand.
    Funny, it made perfect sense to me.

    Quote Originally Posted by Jennifer View Post
    To put it in English: What percentage of a group's members have to belong the subgroup for you to accept personally that the next member of the group you run across would ALSO fall within the subgroup?
    An interesting idea, English

    Quote Originally Posted by Jennifer View Post
    Or, to borrow from an old maxim and put flesh on the example, what percentage of Cretians would have to be known to be liars for you to accept that the NEXT Cretian you met is also a liar?

    1. What would the percentage need to be?
    2. What argument(s) or situation(s) would make you rethink your idea that perhaps your percentage is too high, or even that Cretians are not really liars at all?
    3. What would the percentage have to be so that you'd draw closure on the idea -- never willing to question again the proposition that a certain &#37; of Cretians are liars?
    To highlight the fallacy of the accident in particular, we can take an example from Wikipedia:

    1. Cutting people with a knife is a crime.
    2. Surgeons cut people with knives.
    [---------------------------------------]
    3. Surgeons are criminals.
    Quote Originally Posted by Jennifer View Post
    * * * *

    Actually, I think it's a wonderful topic simply because of the practical nature of it. We all makes decisions like this every day, we just normally don't realize we're making the calculations.

    Every time we judge someone or evaluate them without knowing all the information, we are making "hunches" based on how much proof we need that our hunch is probably true.

    • The guy selling things out of the booth -- based on my knowledge of booth vendors, his appearance, the things he's selling, and other characteristics I can observe, what are the odds that he is ripping me off.... and probably by how much?
    • The guy taking me out for a date -- based on my knowledge of his appearance, articulateness, occupation, background, topics of conversation, etc, what's the odds he's just out to score and not good LTR material?
    • The woman running for office -- based on my knowledge of elections and politicians, her personality, her presentation, the groups she affiliates with etc., what's the odd's she'll be a good leader?


    I mean, this is what comes up in religious and political discussions ALL the time (usually to support cynicism) -- "Oh, they're a <religion or party affiliation", they're just out to <some nefarious deed>, you can't trust them!"

    What percentage of experiences have to be negative, etc., to result in this sort of blanket judgment, and what sort of proof is needed to change it (if it can be)?
    The thing about this juegement from probability is that most people do it rather poorly. There are whole research programs based on the way most people assign probabilities to events in inconsistent and/or illogical ways.

    Quote Originally Posted by nocturne View Post
    Well, I am neither a Bayesian nor a Frequentist, nor do I care about what theories, ideas or statements are probably true. Talk of probability, especially in regard to rational decision-making, is mostly a load of rubbish.
    In a way, I agree with you. If I have to rely on an argument like the above, it would be because I had no other line of reasoning.

    P:Consider, it rains most of the time in Seattle (assume this is true for now)
    C:Therefore it is likely raining now in Seattle.

    C may or may not be ture. In a sense, the statement is a good conclusion. However, it is immediately overturned by going outside and not finding it to be raining (assuming it is not raining in Seatle at the moment).

    Every branch of science uses statistics to form their conclusions. However, no matter what the statistics of medical symptoms may say, something fundamental about the mechanisms of a particular human is what determines whether or not the diagnosis is correct.

    I am not much of a card player. But, I know, that even if you play by the "odds," you can loose. There is a reason they call it gambling.

    Ther is even a claim that, if you play by the "odds," over the long term, you come out ahead. Again, there is no gaurantee of this either, just an increasing likelyhood that the numbers come out as expected. This is assuming a lot of things about fair play (and sometimes even assumptions about sane play from other players).

    The financial markets are a still more complicated version of the same thing.

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

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