The student needs to have basic knowledge about principles of statistical inference, linear models, and generalized linear models.

The course is devoted to optimization and other numerical methods in the context of statistical modeling and other statistical computation.
Chapter 2 introduces a number of motivating problems: the univariate model and the linear normal regression modes; this permits us to touch upon the least squares and maximum likelihoodprinciples. Also, proportions, logistic regression, and contingency tables are introduced. Further topics involve: gamma regression, linear mixed models, generalized linear mixed models, principalcomponents analysis, and cluster analysis.
In Chapter 3, basic numerical tools are reviewed, such as Taylor series expansions and vector derivatives. The exponential family and a number of examples are considered. The basics oflikelihood based inference are presented.
In Chapter 4, we move from non-iterative to iterative procedures; this is done via estimation in the context of the normal and linear regression models on the one hand, and proportions and logisticregression on the other. Solving the score equations is considered, involving Newton-Raphson and Fisher-scoring. Finally, iterative reweighted least squares and the iterative proportional fittingalgorithm are considered.
The topic of Chapter 5 is least squares. The general principle is presented and applied to a variety of situations. These include closed forms and situations where iterative procedures are needed. Someextensions include: alternating/constrained/weighted least squares.
Iteration-based function optimization is discussed in Chapter 6, including: the regula falsi, Newton’s method, and Newton-Raphson. The numerical calculation of derivatives is discussed, as well as theNelder-Mead Simplex Algorithm.
The MM algorithm is discussed in Chapter 7, together with a number of applications in regularized regression. Attention is given to lasso, elastic net, smooth regression, and regularized PCA.
Chapter 8 is concerned with constrained optimization. A number of situations tackled are: variance estimation, success probabilities in binomial models, finite mixtures, and mixed models. Lagrangemultipliers are discussed as well.
An overview of maximum likelihood estimation and ensuing inferences is given in Chapter 9. This includes Wald and likelihood ratio tests. The delta method is described as well.
Chapter 10 treats numerical integration, specifically in the context of mixed models and generalized linear mixed models. Precisely, attention is given to Gaussian quadrature and adaptive Gaussianquadrature.
A wholesome treatment of the Expectation-Maximization algorithm can be found in Chapter 11. The EM algorithm is described through a number of applications on the one hand and via a more in-depthtreatment on the other.
Chapter 12 treats Monte Carlo methods for Bayesian computation. This includes Monte Carlo integration and Markov Chain Monte Carlo methods.