PhD Courses in Denmark

Welcome to Mathematical Kaleidoscope III (2026)

The five subjects to be covered by the course are described below.

1. J. Eduardo Vera-Valdés: Missing data and multiple imputation methods.

2. Charisios Grivas: Resampling techniques in Statistics and Data science.

3. Claus Dethlefsen: Trends in Pharmaceutical Statistics for Regulatory Submissions.

4. Matteo Bonini: Error correcting codes and their cryptographic applications

5. Morten Nielsen: Bases in Banach spaces and their approximation properties.

Description:

1. Missing data is a common problem in all branches of data science. They can occur due to human error in capturing the data or equipment fail, for example. To address the issue, we will analyze several imputation methods. Of particular interest will be the Multivariate Imputation by Chained Equations (MICE) method. The multiple imputations account for the statistical uncertainty. In addition, the chained equations approach can handle complexities such as measurement bounds due to old equipment. 

2. Resampling techniques are a powerful tool in the hands of statisticians and data scientists. They provide a way to estimate the distribution of a statistic without stringent assumptions about the underlying data-generating process. This is particularly useful when the data is not normally distributed, the sample size is small, or no closed form solutions exist. Resampling techniques are widely used in a variety of applications, including hypothesis testing, confidence interval estimation, and model selection. The course will be covering topics such as i.i.d. Bootstrap, block Bootstrap, Stationary bootstrap, Model based bootstrap and subsampling.

3. This session offers a foundational understanding of how randomized clinical trials (RCTs) generate robust evidence for evaluating new drug candidates. Participants will explore the estimand framework to enhance cross-functional clarity in interpreting trial outcomes. We will examine how multiple hypotheses can support diverse claims for a single compound. A key focus will be on statistical methods that control the risk of false positives in efficacy conclusions. The course introduces multiplicity adjustment strategies using the R package gMCP. Hands-on sessions will guide participants through real-world trial scenarios and decision-making. No prior experience with R is required, but basic statistical literacy is recommended.

4. Error-correcting codes are essential tools in digital communication and data integrity. They allow for the detection and correction of errors that occur during data transmission or storage. This lecture provides an introduction to the theoretical foundations of coding, with a focus on constructions derived from algebra and geometry. Topics will include linear codes, Reed-Solomon codes, and codes from algebraic curves. Particular emphasis will be placed on how these structures enable secure information sharing through secret sharing schemes.

5. I will give an introduction to the rich theory of bases in Banach spaces. The focus will be on so-called Schauder bases and unconditional bases, and I will give some of the well-known results on such bases.

The second part is concerned with approximation properties of bases in Banach spaces. The notion of best m-term approximation in a Banach space is introduced, and we study the related (and quite recent) concept of a greedy basis. Examples from wavelet theory will be considered. 

Prerequisites: Basic knowledge in mathematics and statistics.

The participants are evaluated by solving exercises or any other means which provide a proof of the understanding of the presented material. In order to pass the course, at least four out of five topics should be satisfactory evaluated.

For additional information, updates, and registration, please refer to AAU PhDMoodle via the link provided on the right side of this page.