Throughover the workshop in Chennai floated (!) the figure of Jean/André Ville, with his inequality generalising Markov’s, who invented martingales. He is not such a well-known figure in France—at least to me!—, despite having led a rather exceptional life, from being a visiting scholar in Berlin (in the Maison académique de Berlin, along with a certain Jean-Paul Sartre) and Vienna in the 1930s, to his wife being (in Berlin) one of the many (disposable and despised) lovers of JP Sartre (to whom an open-minded or clueless Ville later sent his thèse d’université on martingales and collectives, a much more substantial piece of work than the current PhD), to him working with German and Austrian mathematicians and logicians, such as Popper, Gödel, and Wald–who, what a coïncidence!, died in India from a plane crash in 1950 that had left from Chennai–and being impressed enough by the latter to passing an economics degree in the Sorbonne when back in Paris, establishing a minimax result for a zero-sum matrix game with two players, to his counter-example to von Mises’ kollectiv, to his nickname of the King of Counterexamples in the Viennese mathematics seminar, to him operating the first (Bull) computer at the Université de Paris. (Glenn Shafer wrote a detailed accounting of his youth, on which this post is based, up to his thesis defence but a few days from France mobilising for war–where his collegue Wolfgang Doeblin would kill himself the year after, to avoid capture–. With Bernard Bru, Edmond Malinvaud and Alain Trognon among the people who helped.) After the war, he worked several years as a prépa maths teacher before working for a French State electricity companion on signal theory and Monte Carlo methods, and then returning to Université de Paris as a professor in 1957.
Archive for Wolfgang Doeblin
André ou Jean Ville (1910-1989)
Posted in Books, pictures, Travel, University life with tags 25w5482, Abraham Wald, Alain Trognon, André Ville, Andrey Markov, École Normale Supérieure, Berlin, Bernard Bru, BIRS-CMI, Bull computers, Chennai, Edmond Malinvaud, Emile Borel, George Darmois, Glenn Shafer, history of Monte Carlo, history of statistics, India, Jean Ville, Jean-Paul Sartre, Karl Popper, Kurt Gödel, martingales, Maurice Fréchet, minimax strategy, Monte Carlo methods, Paris, Paul Lévy, plane crash, Richard von Mises, signal theory, Simone de Beauvoir, Sorbonne, supermartingale, two-player game, Université de Paris, Vienna, Ville's inequality, Wolfgang Doeblin, WW II on August 12, 2025 by xi'anadaptive independent Metropolis-Hastings
Posted in Statistics with tags adaptive MCMC, convergence, Doeblin's condition, independent Metropolis-Hastings algorithm, Markov chains, MCMC algorithms, Wolfgang Doeblin on May 8, 2018 by xi'an
When rereading this paper by Halden et al. (2009), I was reminded of the earlier and somewhat under-appreciated Gåsemyr (2003). But I find the convergence results therein rather counter-intuitive in that they seem to justify adaptive independent proposals with no strong requirement. Besides the massive Doeblin condition:
“The Doeblin condition essentially requires that all the proposal distribution [sic] has uniformly heavier tails than the target distribution.”
Even when the adaptation is based on an history vector made of rejected values and non-replicated accepted values. Actually convergence of this sequence of adaptive proposals kernels is established under a concentration of the Doeblin constants a¹,a²,… towards one, in the sense that
E[(1-a¹)(1-a²)…]=0.
The reason may be that, with chains satisfying a Doeblin condition, there is a probability to reach stationarity at each step. Equal to a¹, a², … And hence to ignore adaptivity since each kernel keep the target π invariant. So in the end this is not so astounding. (The paper also reminded me of Wolfgang [or Vincent] Doeblin‘s short and tragic life.)
![Wolfgang [or Vincent] Doeblin](https://upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Alfred_D%C3%B6blin_Gravestone.jpg/440px-Alfred_D%C3%B6blin_Gravestone.jpg){kind=link}