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In probability theory and computer science, a log probability is simply a logarithm of a probability. [1] The use of log probabilities means representing probabilities on a logarithmic scale ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} , instead of the standard [ 0 , 1 ] {\displaystyle [0,1]} unit interval .
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A.
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.
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 ...
In probability theory and statistics, odds and similar ratios may be more natural or more convenient than probabilities. In some cases the log-odds are used, which is the logit of the probability. Most simply, odds are frequently multiplied or divided, and log converts multiplication to addition and division to subtractions.
A logarithmic unit is a unit that can be used to express a quantity (physical or mathematical) on a logarithmic scale, that is, as being proportional to the value of a logarithm function applied to the ratio of the quantity and a reference quantity of the same type. The choice of unit generally indicates the type of quantity and the base of the ...
The log-likelihood is also particularly useful for exponential families of distributions, which include many of the common parametric probability distributions. The probability distribution function (and thus likelihood function) for exponential families contain products of factors involving exponentiation. The logarithm of such a function is a ...
The pretest odds of a particular diagnosis, multiplied by the likelihood ratio, determines the post-test odds. This calculation is based on Bayes' theorem. (Note that odds can be calculated from, and then converted to, probability.)