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  2. Log probability - Wikipedia

    en.wikipedia.org/wiki/Log_probability

    The logarithm function is not defined for zero, so log probabilities can only represent non-zero probabilities. Since the logarithm of a number in (,) interval is negative, often the negative log probabilities are used. In that case the log probabilities in the following formulas would be inverted.

  3. Odds ratio - Wikipedia

    en.wikipedia.org/wiki/Odds_ratio

    The log odds ratio shown here is based on the odds for the event occurring in group B relative to the odds for the event occurring in group A. Thus, when the probability of X occurring in group B is greater than the probability of X occurring in group A, the odds ratio is greater than 1, and the log odds ratio is greater than 0.

  4. Logit - Wikipedia

    en.wikipedia.org/wiki/Logit

    If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: ⁡ = ⁡ = ⁡ ⁡ = ⁡ = ⁡ (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.

  5. Logistic regression - Wikipedia

    en.wikipedia.org/wiki/Logistic_regression

    The above formula shows that once the are fixed, we can easily compute either the log-odds that = for a given observation, or the probability that = for a given observation. The main use-case of a logistic model is to be given an observation x {\displaystyle {\boldsymbol {x}}} , and estimate the probability p ( x ) {\displaystyle p({\boldsymbol ...

  6. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...

  7. Log5 - Wikipedia

    en.wikipedia.org/wiki/Log5

    The name Log5 is due to Bill James [1] but the method of using odds ratios in this way dates back much farther. This is in effect a logistic rating model and is therefore equivalent to the Bradley–Terry model used for paired comparisons , the Elo rating system used in chess and the Rasch model used in the analysis of categorical data.

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  9. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    The natural logarithm of e itself, ln e, is 1, because e 1 = e, while the natural logarithm of 1 is 0, since e 0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many ...