First of all, Bayes predates Gauss. It is inaccurate to suggest frequentist statistics predate Bayesian statistics.
Second, neither is a special case of the other.
Third, neither Bayesian methods nor frequentist methods are inherently "more flexible."
Bayesian statistics set up a model and infer model parameters by applying Bayes' rule to the data. Bayes' rule is an indisputable rule of probability.
For any model parameter b, the result of applying a bayesian model is a probability distribution for b given the available data. Criticisms of bayesian models typically center around the fact that you must use a "prior distribution" indicating the modeler's beliefs about b before seeing the data. Bayesian statisticians have a number of responses to this criticism (that some people find compelling, and others do not).
Frequentist methods build models that are justified by their properties in repeated resampling. For instance, a frequentist method is "unbiased" if, given multiple hypothetical samples, it would on average produce the correct parameter b. Frequentist hypothesis testing reports the probability of observing specified data given some assumption about b.
A standard criticism of frequentist methods is that a modeler wants a probability distribution for an unknown parameter given the known data... rather than knowing the probability of observing the realized data given some assumption about the parameter.
First of all, Bayes predates Gauss. It is inaccurate to suggest frequentist statistics predate Bayesian statistics.
Second, neither is a special case of the other.
Third, neither Bayesian methods nor frequentist methods are inherently "more flexible."
Bayesian statistics set up a model and infer model parameters by applying Bayes' rule to the data. Bayes' rule is an indisputable rule of probability.
For any model parameter b, the result of applying a bayesian model is a probability distribution for b given the available data. Criticisms of bayesian models typically center around the fact that you must use a "prior distribution" indicating the modeler's beliefs about b before seeing the data. Bayesian statisticians have a number of responses to this criticism (that some people find compelling, and others do not).
Frequentist methods build models that are justified by their properties in repeated resampling. For instance, a frequentist method is "unbiased" if, given multiple hypothetical samples, it would on average produce the correct parameter b. Frequentist hypothesis testing reports the probability of observing specified data given some assumption about b.
A standard criticism of frequentist methods is that a modeler wants a probability distribution for an unknown parameter given the known data... rather than knowing the probability of observing the realized data given some assumption about the parameter.