What is the name of the formula used to compute posterior probabilities related to the null hypothesis?

The formula used to compute posterior probabilities related to the null hypothesis is commonly referred to as Bayes' theorem. This theorem provides a way to update the probability of a hypothesis based on new evidence or data. Bayes' theorem establishes a relationship between prior knowledge (the initial belief about a hypothesis before any data is observed) and the likelihood of observing the new data given that hypothesis.

In a statistical context, posterior probabilities reflect how likely a hypothesis is after taking into account evidence from a sample or experiment. By using Bayes' theorem, analysts can calculate these posterior probabilities, which are useful for making informed decisions about null hypotheses in various research settings.

While the term "Bayes' rule" is sometimes used interchangeably with Bayes' theorem, in a formal setting, they refer to the same underlying mathematics of updating beliefs based on evidence. The other terms present in the choices have distinct meanings: the Frequentist approach focuses on long-term frequency of events without incorporating prior beliefs; Maximum likelihood estimation refers to a method for estimating the parameters of a statistical model; and while they may relate to Bayesian statistics, they do not specifically reference the calculation of posterior probabilities in the context of hypothesis testing.