Statistical Information and Likelihood

I vividly recall an occasion in late 1955 when Sir Ronald (then visiting the Indian Statistical Institute, Calcutta and giving a series of seminars based on the manuscript of his forthcoming book) got carried away by his own enthusiasm for fiducial probability and tried to put the fiducial argument in the classical form of the Aristotelian syllogism known as Barbara : ‘A is B, C is A, therefore C is B’. The context was : A random variable X is known to he normally distributed with unit variance and unknown mean θ about which the only information that we have is, − ∞ < θ < ∞. The variable X is observed and the observation is 5. Sir Ronald declared that the following constitutes a ‘proof’: Major premise : Probability that the variable X exceeds θ is 1/2.Minor premise : The variable X is observed and the observation is 5.Conclusion : Probability that 5 exceeds θ is 1/2.