Archive for the R Category
max spacing between mass shootings [data graphics]
Posted in Books, R, Statistics with tags beta distribution, data analysis, data graphics, data journalism, Le Monde, Maine, mass shooting, maximum spacing, US politics, USA on January 11, 2024 by xi'an
so long, and thanks for all the quests
Posted in Books, Kids, R with tags 538, ABC News, blogging, FiveThirtyEight, mathematical puzzle, Og, riddle, The Fiddler, The Riddler, Zach Wissner-Gross on October 25, 2023 by xi'an
The Riddler, which I have followed for many years, has been discontinued by FiveThirtyEight, but its producer, Zach Wissner-Gross, has launched a personal website to keep considering a weekly mathematical puzzle. The Fiddler on the Proof! Expect thus more ‘Og entries in this category!
making the next meeting more productive
Posted in Kids, R, Statistics, University life with tags best equivariant estimator, Cauchy distribution, debugging, R, R code, student, summer project on August 25, 2023 by xi'anOne of the students’ requests I almost invariably reject is code debugging (and they are warned about it from the start). Here is an illustration why, with an R code sent by a student working this summer on the standard estimators of a Cauchy location parameter, asking for debugging help in order “to make the next meeting more productive”. While I could have pointed them to at least four coding mistakes, this would not have helped them towards an autonomous resolution of the issue and it would have almost surely led to further requests for debugging. As it happened, this student showed up with running codes at the following meeting which proved most productive!
X = rcauchy(n, location = theta, scale = 1)
delta_function<-function(theta_lb, theta_ub, X){
#1. delta = best equivariant
Numerator_function<-function(theta) theta/prod((X-theta)**2 + 1)
Denominator_function <-function(theta) 1/prod((X-theta)**2 + 1)
M = integrate(Numerator_function, theta_lb, theta_ub)
D = integrate(Denominator_function, theta_lb, theta_ub)
delta_BE = M/D
##2. delta = MLE
#delta_MLE = argMin(prod((X-theta)**2 + 1))
return (delta_BE)
}
delta = delta_function(X)
uniform spacings
Posted in Books, Kids, R with tags queuing network, riddle, spacings, The Riddler, waiting time on June 8, 2023 by xi'an
A riddle on uniform spacings!, namely when considering eight iid Uniform (0,1) variates as visiting times and three further iid Uniform (0,1) variates as server availability times, with unit service time, the question being the probability a server is available for a ninth visiting time, T⁹. Which can be decomposed into four cases:
- at least one server becomes available between the previous visiting time and T⁹
- at least two servers become available between the penultimate visiting time and the previous visiting time
- two servers become available between the antepenultimate visiting time and penultimate visiting time and one server becomes available between the penultimate visiting time and the previous visiting time
- three servers become available between the antepenultimate visiting time and the penultimate visiting time
with respective probabilities (using Devroye’s Theorem 2.1)
1/4, 8 9!3!/12!, 7 8!3!/12!, 7 8!3!/12!,
resulting in a total probability of 0.2934, compatible with a simulation assessment.
Galton and Watson voluntarily skipping some generations
Posted in Books, Kids, R with tags dynamic programming, Francis Galton, Galton-Watson process, optimisation, R, The Riddler on June 2, 2023 by xi'an
A riddle on a form of a Galton-Watson process, starting from a single unit, where no one dies but rather, at each of 100 generations, Dog either opts for a Uniform number υ of additional units or increments a counter γ by this number υ, its goal being to optimise γ. The solution proposed by the Riddler does not establish his solution’s is the optimal strategy and considers anyway average gains. Solution that consists in always producing more units until the antepenultimate hour (ie incrementing only at the 99th and 100th generations), I tried instead various logical (?) rules and compared outputs by bRute foRce, resulting in higher maxima (over numerous repeated calls) for the alternative principle
s<-function(p=.66){
G=0;K=1 for(t in 1:9){
i=sample(1:K,1)
K=K+i*(i>=K*p)
G=G+i*(i<K*p)}
return(c(G+sample(1:K,1),K))}
