The principle of including only the actual data in the analysis and excluding consideration of all other sample-space possibilities is known as the "likelihood principle", and is at the basis of Bayesian inference. Hence, the concepts of significance level and test power play no role in Bayesian statistics.

The likelihood for a Binomial random variable can be calculated as:

L(x|q) = [n!/k!(n-k)!]p(x)^k(1-p(x))^n-k

The information brought by an observation x about a parameter q is entirely contained in the likelihood function L(x|q), and thus there are 2 key elements in the Bayesian approach to statistics:

1. One is the quantification of prior beliefs about a parameter in the form of a probability distribution and the incorporation of those beliefs into the data analysis.
2. Second is the acceptance of the likelihood principle and the concomitant rejection of all sample-space probabilities from inferential conclusions about the parameter.

(The battle lines between Bayesians and Frequentists are drawn around these 2 elements: because it involves a sample-space probability, the use by the latter of P-values to draw conclusions violates the likelihood principle.)

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