Publications by xi'an
optimal leap year
A riddle about leap years: a solar year consists of approximately 365.24217 mean solar days, which is why there is a leap year approximately every four years. Approximately because the Gregorian calendar plans 97 and not 100 leap years over 400 years. Is this the optimal solution? No, since the Gregorian difference is 3.3 10⁻⁴ day per year, o...
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Bayes Factors for Forensic Decision Analyses with R [book review]
My friend EJ Wagenmaker pointed me towards an entire book on the BF by Bozza (from Ca’Foscari, Venezia), Taroni and Biederman. It is providing a sort of blueprint for using Bayes factors in forensics for both investigative and evaluative purposes. With R code and free access. I am of course unable to judge of the relevance of the approach for f...
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shelled and riddled
Consider a shell game with three shells and a ball where only the location of the shell with the ball is exchanged with the location of an empty shell, randomly chosen. If one starts with the ball as rightmost, what is the distribution of the location of the ball after N steps? Running an exploratory R code like o=rep(0,3) for(n in 1:1e6){ b=...
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optimal Gaussian zorbing
A zorbing puzzle from the Riddler: cover the plane with four non-intersecting disks of radius one towards getting the highest probability (under the standard bivariate Normal distribution). As I could not see a simple connection between the disks and the standard Normal, beyond the probability of a disk being given by a non-central chi-square cdf...
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fast track & slow lane
A riddle from the Riddler where N cars going at random (iid) speeds drive a road with a slow and a fast lane, each car choosing the fast lane iff any of the cars ahead in the slow lane is slowerthan them. With the question of the average number of car convoys. If there were one single lane, the problem would be to determine how many times a small...
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why is this algorithm simulating a Normal variate?
A backward question from X validated as to why the above is a valid Normal generator based on exponential generations. Which can be found in most textbooks (if not ours). And in The Bible, albeit as an exercise. The validation proceeds from the (standard) Exponential density dominating the (standard) Normal density and, according to Devroye, may ...
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riddle of the week
The Riddler of April 1 offered this simple question: start with the number 1 and then try to reach a target number through a series of steps. For each step, you can always choose to double the number you currently have. However, if the number happens to be one (1) more than an odd multiple of 3, you can choose to “reduce” — that is, subtrac...
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null recurrent = zero utility?
The stability result that the ratio converges holds for a Harris π-null-recurrent Markov chain for all functions f,g in L¹(π) [Meyn & Tweedie, 1993, Theorem 17.3.2] is rather fascinating. However, it is unclear it can be useful in simulation environments, as for the integral priors we have been studying over the years with Juan Antonio Cano a...
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truncated mixtures
A question on X validated about EM steps for a truncated Normal mixture led me to ponder whether or not a more ambitious completion [more ambitious than the standard component allocation] was appropriate. Namely, if the mixture is truncated to the interval (a,b), with an observed sample x of size n, this sample could be augmented into an untrucat...
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sum of Paretos
A rather curious question on X validated about the evolution of when $M$ increases. Actually, this expectation is asymptotically equivalent to or again where the average is made of Pareto (1,1), since one can invoke Slutsky many times. (And the above comparison of the integrated rv’s does not show a major difference.) Comparing several Monte...
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