{"id":169,"date":"2019-09-19T12:00:49","date_gmt":"2019-09-19T16:00:49","guid":{"rendered":"http:\/\/people.clas.ufl.edu\/hdoss\/?page_id=169"},"modified":"2026-03-19T08:53:21","modified_gmt":"2026-03-19T12:53:21","slug":"sta-7828","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/hdoss\/courses\/sta-7828\/","title":{"rendered":"STA 7828"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">STA 7828<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Description and Goals<\/h3>\n\n\n\n<p>Monte Carlo methods are increasingly used in many scientific areas, including statistical physics (where they originated), Bayesian and frequentist statistical inference, and image reconstruction. The basic idea is to carry out a simulation to estimate quantities of interest that cannot be computed analytically. This course will begin with a brief discussion of some standard Monte Carlo schemes, before moving to Monte Carlo methods based on Markov chains. Consider the situation where there is a distribution \u03c0 on some space, and we are interested in estimating \u03c0 or R f d\u03c0 where f is some function, but \u03c0 is analytically intractable. Markov chain Monte Carlo proceeds as follows. We set up a Markov chain with the property that its transition function has \u03c0 as its stationary distribution. Then we run a chain X1, X2, . . . with this transition function. If the Markov chain converges to its stationary distribution (i.e. for large n, the distribution of Xn is approximately \u03c0), then by running the chain long enough, we can obtain a sample from \u03c0. This sample can be used to estimate \u03c0 or some feature of it such as R f d\u03c0. In this course I will explain the method in detail, describe the main implementations, and discuss some classes of problems in statistics, primarily in Bayesian inference, where it has had success. The method is not fool-proof. I will talk about some of the mathematical results pertaining to convergence issues, and also discuss some practical convergence diagnostics.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Grades<\/h3>\n\n\n\n<p>Exam 1: Wednesday October 2, 8:20 pm, room TBA. Note the evening time slot. 25%<br>\nExam 2: Wednesday November 6, 8:20 pm, room TBA. Note the evening time slot. 25%<br>\nFinal: Thursday December 12, 12:30pm\u20132:30pm. Comprehensive, but with<br>\nemphasis on material covered after Exam 2. 30%<br>\nHW: There will be about 8 homeworks assigned during the semester. 20%<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Attendance and Late Policy<\/h3>\n\n\n\n<p>Homework must be turned in at the beginning of the lecture on the due date.<br>\nLate homework will not be accepted. The solutions to the homework assignments must be<br>\nentirely your own (this applies also to R code).<\/p>\n\n\n\n\n\n<p>View the full course syllabus<a href=\"https:\/\/people.clas.ufl.edu\/hdoss\/content-removed\/\" target=\"_blank\" rel=\"noopener\"> here (PDF).<\/a><\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1075,"featured_media":0,"parent":8,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-169","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/pages\/169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/users\/1075"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/comments?post=169"}],"version-history":[{"count":7,"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/pages\/169\/revisions"}],"predecessor-version":[{"id":203,"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/pages\/169\/revisions\/203"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/pages\/8"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/hdoss\/wp-json\/wp\/v2\/media?parent=169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}