Frequentist data interpretation

The frequentist interval is often interpreted as if it were the Bayesian interval, but it is fundamentally defined by the probability of the data values given the parameter and not the probability of the parameter given the data. 

Confidence intervals are interpreted differently by frequentists and Bayesians. The 95% confidence interval derived by a frequentist suggests that the true value of some parameter (0) will be contained within the interval 95% of the time in an infinite number of trials. Note that each trial results in a different interval because the data are different. This statement is dependent on the assumed conditions under which the calculations were done, e.g., an infinite number of trials and identical conditions for each trial (O Hagan 2001). Nothing can be said about whether or not the interval contains the true 0. 

Moreover, as a consequence of working with conditional probabilities that force them to change their point of view back and forth fi om data to model, Bayesians are less prone to fall in love with their model, whichhelps to step back, discuss hypotheses and entertain the cycle of statistical analysis (Box, 1980). The possibility to take into account expert knowledge, the more natural way of interpreting probabilities, credibility intervals, statistical tests are other interesting features in practical applications. In spite ofthat, it cannot be denied that Bayesian setting is not very common in the industrial practice, at least less common than the frequentist approach. 

It is important to note that in Bayesian statistics, the Bayesian interpretation of probability is pertained as opposed to the classical/rcfyueufisf interpretation. In the frequentist interpretation, the probability attributed to a random variable is seen as a measure for the long-term fi equency of occurrence of that variable. The Bayesian interpretation is a subjective interpretation where probability reflects a measure of plausibility or degree of belief attributed to a variable, given the current state of informatiOTi. It is clear that only the Bayesian interpretation is meaningful in the context of forming inferences on model parameters using observed data. 

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