In Professor Jaynes’ theory of probability, probability is the degree of plausibility about a thing given some knowledge and not an physical property of that thing.

However, I see people treating the probability of heads in a coin flip as a parameter that needs to be estimated. Even Professor Jaynes gives the impression that he is “estimating the probability” or looking for “the most plausible probability of heads” in page 164 of his book.

How does the idea of ”estimating a probability from data“ or finding the “most probable probability of heads in a coin flip given some data” make sense from this paradigm?

Thank you for your time

That's my take as well. "estimating the probability" really means "calculating the plausibility based on this knowledge".