پديد آورنده :
نوزري صالح باوري، نگين
عنوان :
فرايندهاي زاد و مرگ: براورد و كاربرد
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
آمار رياضي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، ۷۲ص.: مصور
استاد راهنما :
صفيه محمودي
توصيفگر ها :
فرايندهاي تصادفي , روش نيوتن - رافسون , فرايندهاي زاد و مرگ , الگوريتم EM
استاد داور :
افشين پرورده، زهرا صابري
تاريخ ورود اطلاعات :
1396/11/03
چكيده انگليسي :
Birth and death process Estimation and application Negin Nozarisalehbavari n nozarisalehbavari@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sa eh Mahmoodi mahmoodi@cc iut ac ir 2010 MSC 05C15 53C42 Keywords Continuous time Markov chain Birth death process Quasi birth death process Max imum likelihood estimation EM algorithm MM algorithm AbstractBirth death processes BDPs are continuous time Markov chains that model the number of particlesin a system over time While widely used in population biology genetics and ecology statistical in ference of the instantaneous particle birth and death rates remains largely limited to restrictive linearBDPs in which per particle birth and death rates are constant When individual birth and death ratesinstead depend on the size of the population as a whole the model is called a general BDP Fromstate X k transition to state k 1 happens with instantaneous rate k and transition to statek 1 happens with instantaneous rate k Researchers often observe the number of particles at discrete times necessitating data augmenta tion procedures such as expectation maximization EM to nd maximum likelihood estimates Amajor insight comes from the fact that the likelihood of the continuously observed process has asimple form which easily yields expressions for estimation of rate parameters This fact is the basisfor expectation maximization EM algorithms for maximum likelihood estimation in missing dataproblem Unfortunately nding conditional expectations for general BDPs poses challenges since thejoint distribution of the states and waiting times or its generating function is usually not availablein closed form The E step in the EM algorithm is available in closed form for some linear BDPs but otherwise previous work has resorted to approximation or simulation Remarkably the E stepconditional expectations can also be expressed as convolutions of computable transition probabilitiesfor any general BDP with arbitrary rates This important observation along with a convenient con
استاد راهنما :
صفيه محمودي
استاد داور :
افشين پرورده، زهرا صابري
