Topics for Bachelor Theses, Master Theses and Lab Rotations in Statistics
This page lists different topics that can be turned into bachelor theses, master theses and lab rotations for students in applied statistics, data science, economics, etc., depending on individual qualifications. If you are interested, get in contact with the responsible person listed for the topic.
Short description: First hitting time models relate the duration until an event of interest happens (e.g. time until hospital discharge, time until failure of a technical component, etc.) to a latent process describing the temporal evolution of a quantity related to the event of interest (e.g. health status of a patient, condition of the technical component, etc.) where the event is triggered once this latent process hits a pre-specified boundary. The main difficulty in applying such models is how distributional properties of the latent process are related to the duration time distribution. Various topics can be defined based on this general problem set, e.g. related to numerical approximations of the implied distribution of the duration time, joint models for duration times and longitudinal models, extensions to competing risks models, etc.
Contact: Thomas Kneib (tkneib@uni-goettingen.de)
Short description: When analysing spatially aligned data, it is common practice to include spatially correlated random effects as a surrogate for unobserved confounding variables with the ultimate goal of enabling proper, unbiased inference about the regression relations of interest. However, this only really works under the strong assumption that the unobserved confounders which are approximated by the spatial random effect are independent of the covariates of interest. Otherwise, the inclusion of such random effects bears the risk of so-called spatial confounding which leads to biased effect estimates and therefore potentially misleading conclusions. Different topics can be derived within this context, for example relating to the extension of existing results for the spatial confounding bias, the investigation of links to causal inference, the generalization to more complex spatial and spatio-temporal models, or the derivation of practical guidance for empirical analyses with spatial regression models.
Contact: Thomas Kneib (tkneib@uni-goettingen.de)
Short description: One commong challenge in the analysis of questionnaire data using ordinal regression models is the presence of (different types of) non-response mechanisms. For example, participants may report that they do not know the answer to a specific question, that they prefer not to disclose their answer, etc. Usually, this creates an informative missingness pattern if the non-response is not independent of the answer that would have been given. Hierarchical formulations of the decision process lead to multivariate regression models with correlated responses which describe the simultaneous answer pattern for a participant. Based on this general framework, different specific topics can be defined, e.g. on three-dimensional hierarchies, practical applications of the methdodology, etc.
Contact: Thomas Kneib (tkneib@uni-goettingen.de)
Short description: Endogeneity of covariates in observational data, i.e. the non-independence between the error term in the regression specification and the covariate of interest has received a lot of interest in economics. While instrumental variable approaches are still the de facto standard, instrument-free approaches based on copula specifications that explicitly model the dependence between error terms and covariates have been identified as a promising alternative. This project concerns different extensions in this context, for example relating to non-Gaussian response data, the consideration of multiple endogeneous covariates, practical applications of the approach, etc.
Contact: Thomas Kneib (tkneib@uni-goettingen.de)
Short description: Statistical fairness criteria describe the idea of fair treatment through independence or conditional independence between outcomes, decisions and sensitive attributes such as gender, migration background or the education level of parents. Graphical models, in particular mixed graphical models, provide a framework for investigating such dependence structures. Using the German Socio-Economic Panel (SOEP), we want to explore how graphical models can contribute to the analysis of socioeconomic data from a fairness perspective. Particularly the distinction between statistical associations and (causal) conclusions about fairness should be investigated. Different scopes suitable for a bachelor or master thesis can be defined within this topic. They range from a focus on a specific socioeconomic research question applying models to the data, to methodological extensions with simulation studies.
Contact: Matthias Herp (matthias.herp@uni-goettingen.de)
Short description: Omics data provide detailed information on molecular processes and their relationships with health and disease. Graphical models describe conditional dependence structures between molecular variables and can help investigate complex biological relationships. This topic considers the application of Gaussian graphical models (GGM) or there extensions Multivariate Conditional Transformation Models (MCTM) and Graphical Transformation Models (GTM )in a bioinformatics context. The project is in collaboration with the Institute of Bioinformatics at the University Medical Center Göttingen (UMG). Possible applications cover a broad range of omics data, with a particular focus on medical research questions. Different scopes suitable for a bachelor or master thesis can be defined within this topic. They range from investigating a specific biological or medical question using existing models to small methodological extensions with a stronger focus on simulation studies.
Contact: Matthias Herp (matthias.herp@uni-goettingen.de)
Short description: Generalized additive models for location, scale and shape (GAMLSS) extend regression beyond the conditional mean by modelling multiple parameters of the response distribution. Group lasso penalties can be used to select location and scale effects separately, while joint selection requires a penalty that groups effects across distributional parameters. A particular challenge is the appropriate scaling of these effects to ensure balanced penalization, for which different approaches are available in the literature. This project aims to investigate these approaches and implement a joint group lasso penalty for location and scale effects in the existing GAMLSS package. Such a penalty would support the estimation of sparse regression and dependence models. The topic is primarily suitable for a master thesis and combines a methodological extension with a simulation study and potentially a small empirical application.
Contact: Matthias Herp (matthias.herp@uni-goettingen.de)
Short description: Graphical transformation models (GTMs) provide a flexible framework for modelling multivariate distributions with complex marginal distributions and nonlinear dependence structures. This project aims to extend GTMs to conditional models in which discrete covariates, such as cell type or disease status, define different biological settings. The extension should accommodate both models with varying marginal distributions and a shared dependence structure, and models in which the dependence structure also varies between settings. Regularization of differences between settings should allow information to be shared while retaining relevant biological differences. The topic is primarily suitable for a master thesis and combines methodological development and implementation with a simulation study investigating the recovery of shared and setting-specific distributional features. A small application to omics data, for example comparing molecular dependence structures across cell types, may complement the methodological work.
Contact: Matthias Herp (matthias.herp@uni-goettingen.de)
Short description: Assessing the risk of financial portfolios requires models that capture complex dependence between asset returns, particularly during joint extreme losses. Vine copulas provide a flexible framework for constructing multivariate dependence models from bivariate copulas, allowing for nonlinear relationships and asymmetric tail dependence. This project explores their application to financial assets and the estimation of portfolio risk measures such as Value at Risk and Expected Shortfall. Different scopes suitable for a bachelor or master thesis can be defined within this topic. They range from an empirical comparison of existing copula models for a selected portfolio to methodological extensions, for example allowing for time-varying dependence, supported by simulation studies and an empirical application.
Contact: Matthias Herp (matthias.herp@uni-goettingen.de)
Short description: This thesis investigates simulation-based calibration (SBC) as a diagnostic tool for Bayesian additive distributional regression models. Additive distributional regression extends classical regression by modeling not only the mean but all parameters of a response distribution, such as scale, shape, or skewness, through structured additive predictors. This flexibility allows rich, data-driven modeling. SBC is an approach based on repeated simulation from the prior and refitting the model to assess whether posterior inferences are well-calibrated. The thesis outlines the SBC procedure, discusses practical choices such as summary statistics and rank-based diagnostics, and adapts it to the specific structure of additive distributional regression. Through simulation experiments, the thesis evaluates how violations of model assumptions, prior choices, or numerical issues affect calibration. The thesis implements SBC in Python in the probabilistic programming framework Liesel. Prior programming experience in Python is an essential prerequisite for this project.
Talts, S., Betancourt, M., Simpson, D., Vehtari, A., & Gelman, A. (2020). _Validating Bayesian Inference Algorithms with Simulation-Based Calibration_ (No. arXiv:1804.06788). arXiv. https://doi.org/10.48550/arXiv.1804.06788 Klein, N., Kneib, T., Lang, S., & Sohn, A. (2015). Bayesian structured additive distributional regression with an application to regional income inequality in Germany. _The Annals of Applied Statistics_, _9_(2), 1024–1052. https://doi.org/10.1214/15-AOAS823
Contact: Johannes Brachem (brachem@uni-goettingen.de)
Short description: Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive predictors. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. One current limitation for Bayesian PTMs is slow Markov Chain monte carlo (MCMC) sampling, making large datasets challenging for PTMs. This thesis develops a fast and numerically robust Iteratively Re-Weighted Least Squares (IWLS) sampler for PTMs in Python in the probabilistic programming framework Liesel. Prior programming experience in Python is an essential prerequisite for this project. Brachem, J., Wiemann, P. F. V., & Kneib, T. (2025). Bayesian penalized transformation models: Structured additive location-scale regression for arbitrary conditional distributions (No. arXiv:2404.07440v4). arXiv. https://doi.org/10.48550/arXiv.2404.07440 Contact: Johannes Brachem brachem@uni-goettingen.de
Short description: Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive predictors. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. This thesis develops a spike-and-slab prior for PTMs, which essentially provides an off-switch for the flexible conditional distributional shape. Work is done in Python in the probabilistic programming framework Liesel. Prior programming experience in Python is an essential prerequisite for this project. Brachem, J., Wiemann, P. F. V., & Kneib, T. (2025). Bayesian penalized transformation models: Structured additive location-scale regression for arbitrary conditional distributions (No. arXiv:2404.07440v4). arXiv. https://doi.org/10.48550/arXiv.2404.07440 Contact: Johannes Brachem brachem@uni-goettingen.de
Short description: Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive predictors. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. Current model formulations assume tails that belong to the reference distribution's family, often Gaussian. This thesis explores options for adating PTMs to heavy-tailed data. Work is done in Python in the probabilistic programming framework Liesel. Prior programming experience in Python is an essential prerequisite for this project. Brachem, J., Wiemann, P. F. V., & Kneib, T. (2025). Bayesian penalized transformation models: Structured additive location-scale regression for arbitrary conditional distributions (No. arXiv:2404.07440v4). arXiv. https://doi.org/10.48550/arXiv.2404.07440 Contact: Johannes Brachem brachem@uni-goettingen.de
Short description: In many studies, the event of interest is only detected at scheduled examinations, e.g. tumour recurrence found at a follow-up scan or a disease detected at a routine check-up. The true event time is then only known to lie between two visits, i.e. it is interval-censored. In practice, analysts often replace this interval by its right endpoint or its midpoint and then apply standard methods for right-censored data such as the Cox model. This thesis investigates when this shortcut is harmless and when it leads to biased covariate effects and survival curves. In a simulation study, the spacing of visits, the censoring rate and the sample size are varied, and proper interval-censored models are compared with the imputation shortcuts. The methods are then applied to a real data set, e.g. the classic breast cosmesis data. The topic is suitable for a bachelor thesis. Basic knowledge of survival analysis and R is required; the R packages survival, icenReg and flexsurv are used.
Lindsey, J. C. & Ryan, L. M. (1998). Methods for interval-censored data. Statistics in Medicine, 17(2), 219–238.
Anderson-Bergman, C. (2017). icenReg: Regression models for interval censored data in R. Journal of Statistical Software, 81(12).
Contact: Jinbo Hao (jinbo.hao@uni-goettingen.de)
Short description: Simulation studies are the main tool for comparing survival models, but their conclusions depend on design choices that are rarely discussed. These include how censoring times are generated (administrative end of study, random drop-out, or a simple Bernoulli censoring indicator), whether censoring depends on covariates, and how the censoring rate is controlled. This thesis systematically varies these choices for right, left and interval censoring, calibrates each mechanism to a target censoring rate and re-runs a model comparison under each mechanism, e.g. the Cox model versus parametric and flexible accelerated failure time models. The central question is whether the ranking of competing models stays stable across mechanisms, and the thesis derives practical guidance for designing survival simulation studies. The topic is primarily suitable for a master thesis and combines a methodological review with an extensive simulation study. Good knowledge of survival analysis and programming experience in R are required.
Bender, R., Augustin, T. & Blettner, M. (2005). Generating survival times to simulate Cox proportional hazards models. Statistics in Medicine, 24(11), 1713–1723.
Morris, T. P., White, I. R. & Crowther, M. J. (2019). Using simulation studies to evaluate statistical methods. Statistics in Medicine, 38(11), 2074–2102.
Contact: Jinbo Hao (jinbo.hao@uni-goettingen.de)
Short description: Ratings on bounded scales, such as visual analogue scales, sliders or 0–10 items, often pile up exactly at the end points, e.g. a mark at "no pain at all". Most models for bounded continuous responses, including beta regression and continuous ordinal regression, assign probability zero to these values. The usual workaround moves all observations slightly into the interior of the scale by an ad hoc rule that depends on the sample size, so that the same answer is recoded differently in different studies, and many tied values at the boundary are treated as continuous data. This thesis develops a principled alternative for transformation models in which end-point responses are treated as censored observations, so that the end points behave like the lowest and highest categories of an ordinal model while the interior remains continuous. The approach is compared with the workaround and with existing models for bounded data with end points, such as zero-one inflated beta, ordered beta and extended-support beta regression, in a simulation study and in applications to visual analogue scale and survey data. The topic is primarily suitable for a master thesis. Good knowledge of likelihood-based inference and programming experience in R are required; familiarity with censoring from survival analysis is helpful.
Manuguerra, M., Heller, G. Z. & Ma, J. (2020). Continuous ordinal regression for analysis of visual analogue scales: The R package ordinalCont. Journal of Statistical Software, 96(8). https://doi.org/10.18637/jss.v096.i08
Kubinec, R. (2023). Ordered beta regression: A parsimonious, well-fitting model for continuous data with lower and upper bounds. Political Analysis, 31(4), 519–536.
Kosmidis, I. & Zeileis, A. (2025). Extended-support beta regression for [0, 1] responses (No. arXiv:2409.07233). arXiv. https://doi.org/10.48550/arXiv.2409.07233
Contact: Jinbo Hao (jinbo.hao@uni-goettingen.de)
Short description: Questionnaires increasingly record answers on bounded rating scales, such as sliders, visual analogue scales or 0–10 items. In applied work, these answers are usually averaged into a sum score and analyzed by linear regression, or cut into a few categories and analyzed with ordinal item response models. Both shortcuts ignore that the scale is bounded and that equal distances on the scale need not correspond to equal differences in the underlying latent trait. This thesis compares these common practices with item response models for continuous responses, in which each answer is related to a latent person trait through an item-specific monotone transformation of the response scale. Using real survey data with person covariates, e.g. from the European Social Survey, the thesis investigates whether covariate effects, person rankings and model fit change between the approaches and how much information is lost when a continuous scale is categorized. The topic is suitable for a bachelor thesis. Knowledge of linear and ordinal regression and R is required; interest in psychology, medicine or survey methodology is helpful.
Heller, G. Z., Manuguerra, M. & Chow, R. (2016). How to analyze the visual analogue scale: Myths, truths and clinical relevance. Scandinavian Journal of Pain, 13, 67–75.
Tutz, G. & Jordan, P. (2024). Latent trait item response models for continuous responses. Journal of Educational and Behavioral Statistics, 49(4), 499–532.
Contact: Jinbo Hao (jinbo.hao@uni-goettingen.de)
Neural additive models make predictions that can be read feature by feature, and a recent extension adds images to this framework by encoding them with a diffusion autoencoder. In this thesis you will extend this model with ideas of your own. You will make the effect of the image clearly separable from the other variables, add interpretable interactions between the image and tabular features, and apply the model to a new image domain. You will implement the extensions in PyTorch, test them on synthetic data with known effects and on real data, and compare them with existing interpretable models. Contact: Michael Schlee (michael.schlee@uni-goettingen.de)