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In Bayesian statistics, the posterior predictive distribution is the distribution of possible unobserved values conditional on the observed values. [1] [2]Given a set of N i.i.d. observations = {, …,}, a new value ~ will be drawn from a distribution that depends on a parameter , where is the parameter space.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
Predictive power addresses this issue assuming the parameter has a specific distribution. Predictive power is a Bayesian power. A parameter in Bayesian setting is a random variable. Predictive power is a function of a parameter(s), therefore predictive power is also a variable.
Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true positives and true negatives) among the total number of cases examined. [10]
The prior predictive distribution is the distribution of a new data point, marginalized over the prior: (~) = (~) () 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.
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
Predictive modeling is a statistical technique used to predict future behavior. It utilizes predictive models to analyze a relationship between a specific unit in a given sample and one or more features of the unit. The objective of these models is to assess the possibility that a unit in another sample will display the same pattern.
Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.