Fluctuation analysis with cell deaths

The classical Luria-Delbr\"uck model for fluctuation analysis is extended to the case where cells can either divide or die at the end of their generation time. This leads to a family of probability distributions generalizing the Luria-Delbr\"uck family, and depending on three parameters: the expected number of mutations, the relative fitness of normal cells compared to mutants, and the death probability of mutants. The probabilistic treatment is similar to that of the classical case; simulation and computing algorithms are provided. The estimation problem is discussed: if the death probability is known, the two other parameters can be reliably estimated. If the death probability is unknown, the model can be identified only for large samples

Letter counting: a stem cell for Cryptology, Quantitative Linguistics, and Statistics

Counting letters in written texts is a very ancient practice. It has accompanied the development of Cryptology, Quantitative Linguistics, and Statistics. In Cryptology, counting frequencies of the different characters in an encrypted message is the basis of the so called frequency analysis method. In Quantitative Linguistics, the proportion of vowels to consonants in different languages was studied long before authorship attribution. In Statistics, the alternation vowel-consonants was the only example that Markov ever gave of his theory of chained events. A short history of letter counting is presented. The three domains, Cryptology, Quantitative Linguistics, and Statistics, are then examined, focusing on the interactions with the other two fields through letter counting. As a conclusion, the eclectism of past centuries scholars, their background in humanities, and their familiarity with cryptograms, are identified as contributing factors to the mutual enrichment process which is described here

Fluctuation analysis: can estimates be trusted?

The estimation of mutation probabilities and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbr\"{u}ck distribution outside its modelling hypotheses induces an important bias on the estimation of the relative fitness. The model is extended here to any division time distribution. Mutant counts follow a generalization of the Luria-Delbr\"{u}ck distribution, which depends on the mean number of mutations, the relative fitness of normal cells compared to mutants, and the division time distribution of mutant cells. Empirical probability generating function techniques yield precise estimates both of the mean number of mutations and the relative fitness of normal cells compared to mutants. In the case where no information is available on the division time distribution, it is shown that the estimation procedure using constant division times yields more reliable results. Numerical results both on observed and simulated data are reported

Bounds for left and right window cutoffs

The location and width of the time window in which a sequence of processes converges to equilibrum are given under conditions of exponential convergence. The location depends on the side: the left-window and right window cutoffs may have different locations. Bounds on the distance to equilibrium are given for both sides. Examples prove that the bounds are tight

Statistics for the Luria-Delbr\"uck distribution

The Luria-Delbr\"uck distribution is a classical model of mutations in cell kinetics. It is obtained as a limit when the probability of mutation tends to zero and the number of divisions to infinity. It can be interpreted as a compound Poisson distribution (for the number of mutations) of exponential mixtures (for the developing time of mutant clones) of geometric distributions (for the number of cells produced by a mutant clone in a given time). The probabilistic interpretation, and a rigourous proof of convergence in the general case, are deduced from classical results on Bellman-Harris branching processes. The two parameters of the Luria-Delbr\"uck distribution are the expected number of mutations, which is the parameter of interest, and the relative fitness of normal cells compared to mutants, which is the heavy tail exponent. Both can be simultaneously estimated by the maximum likehood method. However, the computation becomes numerically unstable as soon as the maximal value of the sample is large, which occurs frequently due to the heavy tail property. Based on the empirical generating function, robust estimators are proposed and their asymptotic variance is given. They are comparable in precision to maximum likelihood estimators, with a much broader range of calculability, a better numerical stability, and a negligible computing time

1827 : la mode de la statistique en France; origine, extension, personnages

International audienceIndependent to a great extent from the scientific development of the discipline, a trend for statistics has developed in France, from 1827 on. It was probably sparked by Charles Dupin's 'Carte figurative de l'instruction populaire', with its famous Saint-Malo Geneva line, supposed to separate the educated North from the ignorant South. It became attractive to produce, under the name 'statistics', more or less quantitative descriptions on any subject. Beyond literary records, the phenomenon can be measured by its semantic penetration in the press. Even if the ambition of most of these amateurs has remained strictly descriptive, some of them did raise the issue of proving through numbers. This is particularly remarkable, since within institutional science, the techniques of statistical proving, that had been introduced by Laplace at the end of the 18th century, have remained largely ignored for a very long time

Jakob Bielfeld (1717–1770) and the diffusion of statistical concepts in eighteenth century Europe

International audiencePublished between 1760 and 1770, Bielfeld's writings prove that scholars of the time were acquainted with the concepts of both political arithmetic and German statistik, long before they merged into a new discipline at the beginning the following century. It is argued here that these works may have been an important source of diffusion of statistical concepts at the end of the eighteenth century. Bielfeld is now almost completely forgotten, and the reasons for his lack of fame in posterity are examined