# PhD Studies

Studies at the research level in statistics are designed to provide broad subject knowledge in the central parts of statistics, deep knowledge in one statistical area of expertise, ability to apply statistical methods to practical problems and the ability to follow the scientific literature on the subject and conduct their own scientific research.

# Optimisation algorithms in Statistics I (4 ECTS credits)

Optimisation (computation of minima or maxima) is frequently needed in statistics. Maximum likelihood estimates, optimal experimental designs, risk minimization in decision theoretic models are examples where solutions of optimisation problems usually do not have a closed form but need to be computed numerically with an algorithm. Moreover, the field of machine learning depends on optimisation and has new demands on algorithms for computation of minima and maxima. In this course, we will start with discussing properties of gradient based algorithms like the Newton method and the gradient descent method. We will then look in developments especially triggered by machine learning and discuss stochastic gradient based methods. Recent developments recognised the value of gradient free algorithms and we will consider so-called metaheuristic algorithms, e.g. particle swarm optimisation. The last topic of the course will deal with handling of restrictions during optimisation like equality and inequality restrictions. We will implement these algorithms in R. Examples from machine learning and optimal design will illustrate the methods.