| conditional_distributions.txt |
in probability theory and statistics, a conditional distribution is the probability distribution of a random variable given that another random variable is fixed (has occurred). more generally, a conditional distribution is the joint probability distribution of two or more random variables, given that some other random variables have already occurred. |
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| conditional_probability.txt |
conditional probability is the measure of the likelihood of an event occurring given that another event has already occurred. the concept is often used in statistical analysis to predict the probability of a certain outcome given a certain set of circumstances. for example, if it is known that someone has a 60% chance of winning a game, the conditional probability of them winning two games in a row can be calculated as 36%. |
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| expectation_and_variance.txt |
given a random variable, we often compute the expectation and variance, two important summary statistics. the expectation describes the average value and the variance describes the spread (amount of variability) around the expectation |
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| maximum_a_posteriori_estimation.txt |
in bayesian statistics, a maximum a posteriori probability (map) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. the map can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. it is closely related to the method of maximum likelihood (ml) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate. map estimation can therefore be seen as a regularization of maximum likelihood estimation. |
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