# Big I in Logarithm Regression Notation

#### bubbafisk

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

[HR][/HR]
3.2. .Prediction Markets for Logistic Regression

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

. . . . .$$\displaystyle \phi_m^1(\mbox{x},\, 1\, -\, c)\, =\, (1\, -\, c)\left(x_m^+\, -\, \dfrac{1}{B}\ln(1\, -\, c)\right)$$

. . . . .$$\displaystyle \phi_m^2(\mbox{x},\, c)\, =\, c\left(-x_m^-\ -\, \dfrac{1}{B}\ln(c)\right)$$

where $$\displaystyle x^+\, =\, xI(x\, >\, 0),\, x^-\, =\, xI(x\, <\, 0),\,$$ and $$\displaystyle B\, =\, \sum_m \beta_m.$$

[HR][/HR]
I can't for the life of me figure it out, and can't find a prior reference in the article. Thanks.

#### Attachments

• 14.8 KB Views: 6
Last edited by a moderator:

#### stapel

##### Super Moderator
Staff member
Does anyone have any idea what the big I in this equation is?

[HR][/HR]
3.2. .Prediction Markets for Logistic Regression

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

. . . . .$$\displaystyle \phi_m^1(\mbox{x},\, 1\, -\, c)\, =\, (1\, -\, c)\left(x_m^+\, -\, \dfrac{1}{B}\ln(1\, -\, c)\right)$$

. . . . .$$\displaystyle \phi_m^2(\mbox{x},\, c)\, =\, c\left(-x_m^-\ -\, \dfrac{1}{B}\ln(c)\right)$$

where $$\displaystyle x^+\, =\, xI(x\, >\, 0),\, x^-\, =\, xI(x\, <\, 0),\,$$ and $$\displaystyle B\, =\, \sum_m \beta_m.$$

[HR][/HR]
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.

#### bubbafisk

##### New member
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!