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Thread: Big I in Logarithm Regression Notation

  1. #1

    Big I in Logarithm Regression Notation

    Does anyone have any idea what the big I in this equation is?



    3.2. .Prediction Markets for Logistic Regression

    A variant of logistic regression can also be modeled using prediction markets, with the following betting functions:

    . . . . .[tex]\phi_m^1(\mbox{x},\, 1\, -\, c)\, =\, (1\, -\, c)\left(x_m^+\, -\, \dfrac{1}{B}\ln(1\, -\, c)\right)[/tex]

    . . . . .[tex]\phi_m^2(\mbox{x},\, c)\, =\, c\left(-x_m^-\ -\, \dfrac{1}{B}\ln(c)\right)[/tex]

    where [tex]x^+\, =\, xI(x\, >\, 0),\, x^-\, =\, xI(x\, <\, 0),\, [/tex] and [tex]B\, =\, \sum_m \beta_m.[/tex]



    I can't for the life of me figure it out, and can't find a prior reference in the article. Thanks.
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    Last edited by stapel; 01-31-2018 at 03:37 PM. Reason: Typing out the text in the graphic.

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by bubbafisk View Post
    Does anyone have any idea what the big I in this equation is?



    3.2. .Prediction Markets for Logistic Regression

    A variant of logistic regression can also be modeled using prediction markets, with the following betting functions:

    . . . . .[tex]\phi_m^1(\mbox{x},\, 1\, -\, c)\, =\, (1\, -\, c)\left(x_m^+\, -\, \dfrac{1}{B}\ln(1\, -\, c)\right)[/tex]

    . . . . .[tex]\phi_m^2(\mbox{x},\, c)\, =\, c\left(-x_m^-\ -\, \dfrac{1}{B}\ln(c)\right)[/tex]

    where [tex]x^+\, =\, xI(x\, >\, 0),\, x^-\, =\, xI(x\, <\, 0),\, [/tex] and [tex]B\, =\, \sum_m \beta_m.[/tex]



    I can't for the life of me figure it out, and can't find a prior reference in the article. Thanks.
    I think you're referring to this document, which contains this notation on pages 4 and 9. The notation is nowhere defined, that I can see. My guess is that the author means to say that x^+ means "x, when x is on the interval I = (0, infinity)" (in other words, where x is positive) and x^- means "x, when x in on the interval I = (-infinity, 0)" (in other words, where x is negative).

    But that's just my guess.

  3. #3
    Quote Originally Posted by stapel View Post
    I think you're referring to this document, which contains this notation on pages 4 and 9. The notation is nowhere defined, that I can see. My guess is that the author means to say that x^+ means "x, when x is on the interval I = (0, infinity)" (in other words, where x is positive) and x^- means "x, when x in on the interval I = (-infinity, 0)" (in other words, where x is negative).

    But that's just my guess.
    Yeah, I think you're right. Thanks a lot!

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