{'fraction_non_alphanumeric': 0.025096525096525095, 'fraction_numerical': 0.0019305019305019305, 'mean_word_length': 5.003861003861004, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Response to Reviewers

Three thoughtful responses by Prof. Thomas Louis, Dr. Lorenz Rhomberg, and Profs. Dale Hattis and Rob Goble testify to the importance of uncertainty characterization and the willingness of top researchers to apply themselves to the task. I greatly appreciate this opportunity afforded by Risk Analysis to nudge the discussion forward. Rhomberg succinctly captures the main point “that simply taking an existing formula and imposing distributions on each of its variables to ‘probabilitize’ it is not necessarily a good way to model uncertainty.” The covariance singularity is the most telling symptom. Goble and Hattis render this intuitive by saying that two ways of extrapolating from SP to CR, via SR and via CP, must introduce a dependence. That is basically right, but it is a bit more complicated because these are random variables and not simple numbers. The demonstration requires identifying assumptions and working out the covariance matrix. Simply blocking this singularity would not solve the problems, however. Assuming that a ratio of two random variables is independent of one of its terms, which is entailed in the first step of a probabilized UF method, already raises questions. My article showed that this leads to consequences at variance with our intuitions. A simple example involving height, weight, and body mass index (BMI = weight [kg]/height[m2]) is illustrative. Distributions for all three quantities for U.S. females older than 20 years from the National Health Statistics Report are summarized below.