This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on "Random Walks in Random Environment" presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately.
In Section 2 we will deal with the “discrete” case. Let S be a locally finite tree T endowed with the natural integer-valued distance function: the ...
... for in this case [yp](s)=s[yp](s), [yp](s)=s2[yp](s). As we will see in the examples, this assumption also makes it possible to deal with the initial ...
x,y∈S δ(x,y) is maximum. u(x) + ADDITIVE SUBSET CHOICE Input: A set X = {x1 ,x2 ... F Tractability cycle Test 8.2 How (Not) to Deal with Intractability 173.
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... partial differential equations have received a great deal of attention. For excellent bibliographical coverage, see Todd (1956), Richtmyer (1957), ...
Todd, P. A., McKeen, .l. ... ANALYTICAL SUPPORT PROBLEM SOLVING Cognitive Perspectives on Modelling HOW DO STUDENTS AND TEACHERS DEAL Sodhi and Son 219 NOTE ...