Course Information

Course Name	Turkish	Hesaplamalı Bilim ve Mühendislik'te Özel Konular
	English	Special Topic.in Comp.Sci.&Eng
Course Code	HBM 597E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	3	-	-
Course Language		English
Course Coordinator		Murat Okatan
Course Objectives		1. To provide sufficient mathematical and programming background to understand the theory and application of generalized linear models. 2. To teach model selection using Akaike information criterion and parametric bootstrap. 3. To teach formal inference from more than one model. 4. To improve the student’s ability of designing, fitting and selecting generalized linear models and using them for statistical inference especially in the MATLAB programming environment.
Course Description		Likelihood function and its properties. Maximum likelihood estimation. Akaike information criterion and Kullback-Leibler divergence. Simple and multiple linear regression. Residuals, Normality, heteroscedasticity, linearity, multicollinearity. Generalized linear models (GLM). Binomial GLM and selection of the link function. Poisson and Negative Binomial GLM. Gamma and Inverse Gaussian GLM. Parametric bootstrap. Formal inference from more than one model. Model averaging. Modeling point processes using the GLM. Time-rescaling theorem.
Course Outcomes		M.Sc./Ph.D. students who successfully pass this course gain knowledge, skill and competency in the following subjects; 1. Understand and use the likelihood principle. 2. Assess the relative goodness-of-fit of likelihood models. 3. Perform linear regression and understand its generalization to the generalized linear models. 4. Assess the absolute goodness-of-fit of the models. 5. Use the Binomial, Poisson, Negative Binomial, Gamma and Inverse Gaussian GLMs. 6. Perform formal statistical inference using multiple models simultaneously. 7. Model point processes using the generalized linear models. 8. Perform the analyses in the MATLAB programming environment. (If the student wishes, he/she can perform homework, projects and exams in a programming language such as Python, C or R.)
Pre-requisite(s)		Calculus; Probability and Statistics
Required Facilities
Other
Textbook		1) P. McCullagh and J. A. Nelder, Generalized Linear Models (2nd Edition), Chapman and Hall/CRC, 1989. 2) Y. Pawitan, In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford University Press, 2013. 3) E. Parzen, K. Tanabe, G. Kitagawa, Selected Papers of Hirotugu Akaike, Springer-Verlag New York, 1998. 4) K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference, Springer-Verlag, New York, 2002. 5) D. J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Springer-Verlag, New York, 2003.
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