The key operation of Bayesian inference is integrating information. This can be from the same source (an additional coin flip, for example) or from different sources (coin flips, plus auxiliary knowledge about where the coin came from, or the person's motives).
Calculated frequency is a point-estimate of bias. A Bayesian estimate is a distribution of belief over possible values of the bias, integrating all available information.
Calculated frequency is a point-estimate of bias. A Bayesian estimate is a distribution of belief over possible values of the bias, integrating all available information.