"Of course, we know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude, "The Coming of Age of the Cell", Science, 1975)
"We often use the ideas of chance, likelihood, or probability in everyday language. For example, 'It is unlikely to rain today', 'The black horse will probably win the next race', or 'A playing card selected at random from a pack is unlikely to be the ace of spades' . Each of these remarks, if accepted at face value, is likely to reflect the speaker's expectation based on experience gained in the same position, or similar positions, on many previous occasions. In order to be quantitative about probability, we focus on this aspect of repeatable situations." (Peter Lancaster, "Mathematics: Models of the Real World", 1976)
"The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient." (Benoit Mandelbrot, "The Fractal Geometry of Nature", 1977)
"In decision theory, mathematical analysis shows that once the sampling distribution, loss function, and sample are specified, the only remaining basis for a choice among different admissible decisions lies in the prior probabilities. Therefore, the logical foundations of decision theory cannot be put in fully satisfactory form until the old problem of arbitrariness (sometimes called 'subjectiveness') in assigning prior probabilities is resolved." (Edwin T Jaynes, "Prior Probabilities", 1978)
"Another reason for the applied statistician to care about Bayesian inference is that consumers of statistical answers, at least interval estimates, commonly interpret them as probability statements about the possible values of parameters. Consequently, the answers statisticians provide to consumers should be capable of being interpreted as approximate Bayesian statements." (Donald B Rubin, "Bayesianly justifiable and relevant frequency calculations for the applied statistician", Annals of Statistics 12(4), 1984)
"In the path-integral formulation, the essence of quantum physics may be summarized with two fundamental rules: (1). The classical action determines the probability amplitude for a specific chain of events to occur, and (2) the probability that either one or the other chain of events occurs is determined by the probability amplitudes corresponding to the two chains of events. Finding these rules represents a stunning achievement by the founders of quantum physics." (Anthony Zee, "Fearful Symmetry: The Search for Beauty in Modern Physics", 1986)
"In the design of experiments, one has to use some informal prior knowledge. How does one construct blocks in a block design problem for instance? It is stupid to think that use is not made of a prior. But knowing that this prior is utterly casual, it seems ludicrous to go through a lot of integration, etc., to obtain ‘exact’ posterior probabilities resulting from this prior. So, I believe the situation with respect to Bayesian inference and with respect to inference, in general, has not made progress. Well, Bayesian statistics has led to a great deal of theoretical research. But I don’t see any real utilizations in applications, you know. Now no one, as far as I know, has examined the question of whether the inferences that are obtained are, in fact, realized in the predictions that they are used to make." (Oscar Kempthorne, "A conversation with Oscar Kempthorne", Statistical Science vol. 10, 1995)
"Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved." (Brain S Everitt, "Chance Rules", 1999)
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