Search results
Results from the WOW.Com Content Network
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".
Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Calibration can mean a reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable; [1]
Best linear unbiased predictions" (BLUPs) of random effects are similar to best linear unbiased estimates (BLUEs) (see Gauss–Markov theorem) of fixed effects. The distinction arises because it is conventional to talk about estimating fixed effects but about predicting random effects, but the two terms are otherwise equivalent.
In Bayesian statistics, the model is extended by adding a probability distribution over the parameter space . A statistical model can sometimes distinguish two sets of probability distributions. The first set Q = { F θ : θ ∈ Θ } {\displaystyle {\mathcal {Q}}=\{F_{\theta }:\theta \in \Theta \}} is the set of models considered for inference.
In statistical prediction, the coverage probability is the probability that a prediction interval will include an out-of-sample value of the random variable. The coverage probability can be defined as the proportion of instances where the interval surrounds an out-of-sample value as assessed by long-run frequency. [2]
Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts (such as forecasting that the maximum temperature at a given site on a given day will be 23 degrees Celsius, or that the result in a given football match will be a no-score draw), probabilistic forecasts assign a probability to each of a number of different ...
A theory or explanation is hard to vary if all details play a functional role, i.e., cannot be varied or removed without changing the predictions of the theory. Easy to vary (i.e., bad) explanations, in contrast, can be varied to be reconciled with new observations because they are barely connected to the details of the phenomenon of question.