This note tries to find commonalities and clarify differences between the Bayesian and classical schools of thought on probabilities. An outline is presented for a methodology that keeps different types of uncertainties separate through a risk assessment process. The following controversial theses are discussed and defended: 1. (1) Classical statistical techniques do not require large amounts of data, as is often claimed. 2. (2) Classical frequentist statisticians can consider the parameter being estimated as a random variable; this is not the privilege of Bayesians only. 3. (3) Classical statistical techniques define distributions for parameters, they are not limited to point estimators. 4. (4) Two favourable features of the classical fiducial estimation are: (a) there is no need to assume any prior distribution, either conceptually or numerically; (b) the resulting probability distributions always have the fractional frequency meaning of probability. 5. (5) When the distribution of the source population ('factory') is known and used as a prior distribution, then the classical and Bayesian techniques coincide, and the posterior density also has the fractional frequency meaning. 6. (6) When subjectivistic prior distributions are used, the resulting posterior has the 'personal opinion probability' interpretation, not the objective fractional meaning. © 1990.
