Updating probabilities with data and moments
By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter(s)—e.g., by maximum likelihood or maximum a posteriori estimation (MAP)—and then plugging this estimate into the formula for the distribution of a data point.This has the disadvantage that it does not account for any uncertainty in the value of the parameter, and hence will underestimate the variance of the predictive distribution.In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". In the table, the values w, x, y and z give the relative weights of each corresponding condition and case.
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Bayesian theory calls for the use of the posterior predictive distribution to do predictive inference, i.e., to predict the distribution of a new, unobserved data point.
In this case there is almost surely no asymptotic convergence.
Updating probabilities with data and moments comments