Bayesien statistics is a large domain in the field of statistics that differs due to an axiomatization of the statistics that gives it a certain internal coherence.
The basic idea is to interpret the probability of an event as it is commonly used; in other words as the uncertainty that is related to it. In contrast, the classical approach considers the probability of an event to be the limit of the relative frequency (see probability for a more formal approach).
The most well-known aspect of Bayesian inference is the probability of calculating the joint probability distribution (or density function) \( { f (\boldsymbol\theta, X = x_1, \ldots, X=x_n) } \) of one or many parameters \( { \boldsymbol\theta } \) (one parameter or a vector of parameters) having observed the data \( { x_1, \ldots, x_n } \) sampled independently from a random variable X on which \( { \boldsymbol\theta } \)depends. (It is worth noting that it also allows us to calculate the probability distribution for a new...
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(2008). Bayesian Statistics. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_23
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