{"id":250,"date":"2023-06-13T13:04:44","date_gmt":"2023-06-13T20:04:44","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/larry-goldstein\/?page_id=250"},"modified":"2023-10-27T14:14:14","modified_gmt":"2023-10-27T21:14:14","slug":"introduction-to-steins-method","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/introduction-to-steins-method\/","title":{"rendered":"Introduction to Stein’s Method"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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The calculation of precise probabilities in statistics, computer science, physics and biology under realistic model assumptions and sample sizes is often impractical, and approximation is typically required. Having a bound on the error of commonly used approximations is therefore necessary in many real applications. Stein’s method has proved itself to be a powerful tool in such situations.<\/p>\n

The course will cover the fundamentals of Stein’s method, starting with the Poisson and Normal distributions to illustrate the construction of the Stein equation and the derivation of the properties required on its solution. A number of coupling methods for use in the Stein equation will be presented, as well as it use in cases of local dependence. In addition to the basic case of independence, a sampling of potential applications in the Poisson case includes head runs, sequence matching, the birthday and occupancy problems, the Poisson subset numbers, extreme score distributions, and statistics of random graphs, and in the Normal case hierarchical sequences, the combinatorial central limit theorem, simple random sampling, occurrences of patterns in permutations and graphs, coverage processes, the anti-voter model, cone measure projections, and the lightbulb process. Multivariate normal approximation will also be covered, and, time permitting, additional applications of Stein’s method to the Beta, Geometric, Exponential and other distributions.<\/p>\n

The level and detailed content of the course will be determined along with the students according to their background and interests.<\/strong><\/p>\n

Prerequisite:<\/strong>\u00a0At least one advanced course in probability.<\/p>\n

Instructors:<\/strong>\u00a0Larry Goldstein<\/a>\u00a0and\u00a0Yosi Rinott<\/a><\/p>\n

Students will find themselves better prepared for the course by reading the following introductory papers by\u00a0Reinert<\/a>,\u00a0Raic<\/a>, and\u00a0Rinott and Rotar<\/a>.<\/p>\n

Interview<\/a>\u00a0with Charles Stein<\/p>\n

Course Notes<\/a><\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Structure and Evaluation<\/h5>\n

Lectures, Monday through Saturday mornings, 9:45-10:45, 11:00-12:00, Problem Sessions Monday through Friday 3-5:15 PM<\/p>\n