Irénée-Jules Bienaymé

b. 28 August 1796, Paris, France
d. 19 October 1878, Paris

Sometime around 1834, Bienaymé became an active member of the Societé Philomatique de Paris; many of his papers were published in its journal. In all, thirty-six published articles were written by Bienaymé. Those which appeared in L'Institute, Paris were printed first in the Extraits des Procès-Verbaux de la Societé philomatique de Paris. Those papers published by the Philomatic Society typically had little mathematical detail and for this reason they are unsatisfactory. 

The list of publications has been taken from that compiled by Heyde and Seneta: I.J. Bienaymé, Statistical Theory Anticipated, Springer-Verlag 1977. Since Heyde and Seneta fully summarize his researches, there is little annotation below and the reader is directed to that work.

Demography and Social Statistics

• (1829) "Mortalité des nouveaux-nés." Moniteur Universel, 18 April 1829, p. 564.
  
  
• (1835) "Sur les erreurs présumées des documents à l'aide desquels on a calculé, en France, les tables de population." Comptes Rendus Acad. Sci., Paris, 1, p. 364.
  
  
• (1837) "De la durée de la vie en France depuis le commencement du XIX^e siécle." Annales d'hygiéne publique et de médecine légale, 18, pp. 177-218.
  
  
  This particular paper examines the validity of the mortality table of Antoine Deparcieux and that of Emmanuel Etienne Duvillard in his time. The first table may be found in the Essai sur les probabilités de la duree de la vie humaine (1746). The second is in the Analyse et Tableaux de l'influence de la petite vérole sur la mortalité é chaque age ( 1806).  Bienaymé mentions in particular three other works as well. These are  Recherches et considérations sur la population de La France by Moheau (1778), Recherches sur la population (1766) by Messance and especially Poisson's "Mémoire sur la proportion des naissances des filles et des garéons". 
  
   
  The technique is most interesting in that the census counts of 20 year old males made for army recruitment and which reflect births twenty years earlier are used for this validation. 
   
  
• (1837) "Naissances des enfants dans le mariage. Soc. Philomat. Paris Extraits, Ser. 5, 153-155. L'Institut, 223, Vol. 6 (1838), 18.
  
  
• (1838) "Probabilité des jugements et des témoignages" Soc. Philomat. Paris Extraits, Ser. 5, pp. 93-96.  L'Institut, 235, Vol. 6, 207-208.  This is connected to the 1st Supplement to Laplace's Théorie Analytique des Probabilités. It concerns  distinguishing the probability of speaking the truth when affirming a fact from that of speaking truly when denying a fact.
  
  
• (1839) "Effets de l'intérét composé." Soc. Philomat. Paris Extraits, Ser. 5, 60-65. L'Institut, 286, Vol. 7, pp. 208-209.
  
  
  This paper, "The effects of compound interest," makes the observation that an assurance company incurs too much risk if insuring too few persons. We all know that a modest sum can grow to an enormous quantity if interest is compounded. But the forcasting of revenue and expenses depends upon events happening as expected. Companies with a small number of subscribers may have large losses early which cannot be recovered easily.    
  
  
  The following remarks and papers concern the viability of the Benefit Society of Metz. This society sold annuities that were, in the mind of Bienaymé, not fully funded.   We find him engaged in an attempt to get the managers of the fund to make changes to remedy the situation. 
  
  
• (1857) [Untitled remarks on a report by M. Didion concerning the calculation of pensions by the Société de Metz, 1855-1859]. Comptes Rendus Acad. Sci., Paris, 44, 573.
  
• (1862) "Remarques sur les Sociétés de Secours mutuels." Comptes Rendus Acad. Sci., Paris, 54, pp. 536-537.
  
• (1862) [Untitled remarks following the paper Société de Metz, 1862]. Comptes Rendus Acad. Sci., Paris, 54, 796.
  
• (1862) "Remarques sur les Sociétés de Secours mutuels." Comptes Rendus Acad. Sci., Paris, 54, pp. 889-891.
  
  
• (1865) [Untitled remarks in connection with the presentation of a pamphlet entitled "Calcul des pensions dans les Sociétés de prévoyance" by M. Didion] Comptes Rendus Acad. Sci., Paris, 60, p. 415.

Statistical Trends

• (1838) "Mémoire sur la probabilité des résultats moyens des observations; démonstation directe de la régle de Laplace." Mém. pres. Acad. Roy. Sci. Inst. France, 5, 513-558. "Théoréme sur la probabilité des résultats moyens des observations"  Soc. Philomat. Paris Extraits, Ser. 5, 42-49. L'Institut, 284, Vol. 7, pp. 187-189. "Calcul des probabilités"  Soc. Philomat. Paris Extraits, Ser. 5, 18-22. L'Institut, 326, Vol. 8, pp. 111-112.
  
  The problem is this: What is the probability of the deviation of which a mean is able to be affected among any great number of different values of a phenomenon or of an event, given by so many observations, when one is not aware of the law of the probabilities of the partial deviations of each observation?
  
  I have not attempted to correct the work of Bienaymé and it appears as published (subject to my own errors of translation and reproduction, of course).
  
  
• (1839) "Théoréme sur la probabilité des résultats moyens des observations"  Soc. Philomat. Paris Extraits, Ser. 5, 42-49. L'Institut, 284, Vol. 7, pp. 187-189. Here the concern is the situation where probability distribution associated with a sequence of observations will change during the course of collecting data.
   
  
• (1840) "Calcul des probabilités"  Soc. Philomat. Paris Extraits, Ser. 5, 18-22. L'Institut, 327, Vol. 8, pp. 119-120. This is on the understanding of the meaning of the phrase "the constancy of mean results."
  
  
• (1840) "Probabilités. Principe nouveau du calcul des probabilités avec ses applications aux sciences d'observation"  Soc. Philomat. Paris Extraits, Ser. 5, 37-43. L'Institut, 333, Vol. 8, pp. 167-169. A sequence of observations may be partitioned into a sequence of subsequences each of which (under certain circumstances) should behave as the entire sequence.

Miscellaneous papers on statistics

• (1840) "Application à la statistique médicale"  Soc. Philomat. Paris Extraits, Ser. 5, 10-13. L'Institut, 322, Vol. 8, pp. 78-79. This paper discusses in a very superficial way the problems associated with determining the effectiveness of a treatment.
  
  
• (1840) "Calcul des probabilités. Solution d'une probléme du calcul des probabilités se rettachant avec élections"  Soc. Philomat. Paris Extraits, Ser. 5, 23-26. L'Institut, 327, Vol. 8, pp. 119-120.  One supposes the very great number of the electors of a great country divided between two opinions in a known ratio; one supposes moreover the electors apportion at random into numerous colleges, and one demands what is, with a great probability, the number of the colleges in which the majority will belong to the opinion which possesses a known plurality in the electoral body.
  
  
• (1840) "Quelques propriétés des moyens arithmétiques de puissances de quantités positives." Soc. Philomat. Paris Extraits, Ser. 5, 67-68. L'Institut, 342, Vol. 8, pp. 216-217.
  
  
• (1841) "Notice sur un nouveau quantiéme perpétuel." Comptes Rendus Acad. Sci. Paris, 13, 1103.
  
  
• (1843) [Untitled communication in the area: Histoire des mathématiques, concerning Pascal] Soc. Philomat. Paris Extraits, Ser. 5, 49-50. 
  
  
• (1845) "De la loi de multiplication et de la durée des familles." Société philomatique de Paris. Extraits des procés-verbaux des séances. 5th ser., 10, pp. 37-39. Also in L'Institut, Paris. No. 589, Vol. 13. pp 131-132. On the extinction of families. This anticipates the theory of branching processes and gives the Criticality Theorem.
  

Least Squares

• (1852) "Mémoire sur la probabilité des erreurs d'aprés la méthode des moindres carrés," Journal des mathématiques pures et appliquées, 17, pp. 33-78; Reprinted in Mémoires presentés par savants étrangers é l'Académie des sciences. 15 (1868), pp. 615-663. See also Antoine Augustine Cournot's   Exposition de la Théorie des Chances which is cited by Bienaymé in this paper. The concern of Bienaymé here is the correct estimation of probabilites when there are several random variables involved. See Comptes Rendus Acad. Paris 34, pp. 90-92 or Liouville's Jour. Math. 17, pp. 31-32 for a review: "Sur un Mémoire de M. Jules Bienaymé, concernant la probabilité des erreurs d'après la méthode des moindres carrés.". Also see Meyer's Calcul des Probabilités pp. 377-408.
  
  
• (1853) "Sur les différences qui distinguent l'interpolation de M. Cauchy de la méthode des moindres carrés, et qui assurent la supériorité de cette méthode." Comptes Rendus Acad. Sci., Paris, 37, 5-13. Liouville's J. Math. Pures Appl. (1) 18, 299-308. Read 4 July 1853. This paper refers back to the 1835 paper of Cauchy, "Mémoire sur l'interpolation." Bienaymé is very concerned that no one confuse Cauchy's method of solving systems of equations with the method of least squares. He argues that the method of elimination of Cauchy is no different from that used by Gauss. Moreover, he observes that Cauchy shows in the paper "Mémoire sur l'évaluation d'inconnues déterminées par un grand nombre d'équations approximatives du premier degré" that his own method can be used to computed the least squares values.
  
  
• (1853) "Remarques de M. Bienaymé à l'occasion des Notes inserées par M. Cauchy dans les Comptes Rendus de deux des séances précédentes." Comptes Rendus Acad. Sci., Paris, 37, pp. 197-198. Read 8 August 1853.
  
  
• (1853) "Considérations à l'appui de la découverte de Laplace sur la loi de probabilité dans la méthode des moindres carrés," Comptes Rendus... de l'Académie des sciences, 37, pp. 309-324. Reprinted in Journal des mathématiques pures et appliquées, 2nd ser., 12 (1867), pp. 158-176. Read 20 August 1853. Here Bienaymé defends Laplace against Cauchy. See on the page devoted to Cauchy a discussion of the controversy between the methods of interpolation and of least squares. Of interest also is a demonstration that least squares is superior to all other least positive integer powers. We should also note that in this paper he derives the Bienaymé-Chebyshev Inequality. See also "Des valeurs moyennes," by Chebyshev.
  
  
• (1855) "Sur un principe que M. Poisson avait cru découvir et qu'il avait appelé Loi des grands nombres." Comptes Rendus Acad. Sci. Morales et Politiques (3) 11, pp. 379-389. Also J. Soc. Statist. Paris, (1876), pp. 199-204. Here Bienaymé denies the existence of the Law of Large Numbers. He refers first to the Poisson's two papers delivered to the Academy:   "Recherches sur la probabilité des jugements, principalement en matiére criminelle." and  "Note sur la loi des grands nombres" and also to his own paper "Théoréme sur la probabilité des résultats moyens des observations. Sur la probabilité des résultats moyens lorsque les causes sont variables durant les observations."

Other papers

• (1851) De la mise é alignement des maisons. Publications de la Revue municipale. Dondey-Dupré, Paris (24 pp).
  
• (1852) Notice sur les travaux scientifiques de M. I.-J. Bienaymé. Bachelier, Paris (4 pp.)
  
• (1870) "Traduction de deux passages de Stobée inexpliqués jusqu'ici." Comptes Rendus Acad. Sci., Paris, 71, pp. 460-462.
• (1871) "Rectification de listes d'articles détachés de M. Cauchy, publiées dans deux Catalogues différents, et restitution é M. Cournot de quelques-uns de ces articles." Comptes Rendus Acad. Sci., Paris, 72, pp. 25-29.
  
• (1873) "Rapport sur le Concours pour le prix de Statistique, fondation Montyon." Comptes Rendus Acad. Sci., Paris, 75 , pp. 1306, 1349 - séance du 25 nov. 1872). Liouville's J. Math. Pures Appl., (2) 18 , pp. 164-179.
• (1874) "Sur une question de probabilités." Bull. Soc. Math. France, 2, pp. 153-154. Bienaymé considers the distribution of extrema in a sequence of observations, essentially a test for randomness. This same problem is applied in the following.
  
• (1875) "Application d'un théoréme nouveau du calcul des probabilités." Comptes Rendus Acad. Sci., Paris, 81, pp. 417-423. Bull. Math. Astr., 9, pp. 219-225. Apparently first published in Bull. Soc. Math. France, 2 (1874). pp. 153-154.