Upper and Lower Bounds for Probability of Guilt Based on Circumstantial Evidence

Comment

“…Fisher, R.A. (1934), "The Effect of Methods of Ascertainment Upon the Estimation of Frequencies," Annuls of Eugenics, 6, 13-25. Kingston, Charles R. (1965), "Applications of Probability Theory in Criminalistics, 11," Journal of the American Statistical Association, Smith, Robert Longworth and Charrow, Robert P. (1975), "Upper and Lower Bounds for the Probability of Guilt Based on Circumstantial Evidence," Journal of the American Statistical Association, 70, 55560.…”

“…This fact is used in Section 4 of Smith and Charrow (1975) to derive an expression for the expected number of individuals with all traits A. Finally, it is not difficult to show that the same two assumptions, for a suitable restriction of the parameter values, give rise to a recursive hypergeometric probability law governing the number X of nonculprit suspects with all traits (see Smith and Charrow (1975, equation 3.2)).…”

“…Finney, in examining the coin-toss experiment, maintains that both Kingston (1965) and Smith and Charrow (1975) were remiss in not defining with greater precision a conditional event I . He then sets forth several logically possible meanings for the event I and proceeds to analyze the experiment in light of each of the possible meanings.…”

“…The point noted in Smith and Charrow (1975) is that the culprit has an identity based on the fact that he committed the crime. Hence, because of him, and not because of the suspect in custody, we may, by removing the culprit from the population, reduce our problem to finding the probability of one or more persons with all traits in the remaining suspect population.…”