The Inapplicability of the Concept of Subjective Probability

Controversy over the Bayesian approach has diminished and one can't but admire the elegance of the definition of subjective probability. But it is still a hard sell in practice. This is a fact gathered through engineering experience. When the effect of the prior washes off quickly, the issue is irrelevant and one enjoys the probabilistic updating algorithm. When there is little data, one seriously questions the validity of the Bayesian approach. Very little has been achieved in developing means to support the existence of a prior, assess it and calibrate the person providing the opinion. We review the theory and show a case in bridge maintenance where the likelihood of the expert can be assessed. We state the reason for its inapplicability, take a step back to the days of Kolmogorov and reflect on Bayesian theory.