Methods of Statistical Inference in Mixed Models for the Identification of Individual Brain Signatures of Pain from Neuroimaging Data

PhD study program: Applied Mathematics
Akademic year: 2026-2027
Advisor: Doc. RNDr. Viktor Witkovský, CSc. (viktor.witkovsky@savba.sk)

External educational institution: Institute of Measurement Science SAS
Accepting university: Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Department of Applied Mathematics and Statistics

Annotation:

The dissertation is motivated by current challenges in personalised medicine and neuroscience, where traditional group-level statistical approaches fail to adequately capture pronounced inter-individual variability. The aim of the dissertation is the theoretical and algorithmic development of linear and nonlinear mixed models designed for the analysis of complex longitudinal data with repeated measurements, which are typical of modern neuroimaging studies and interventional neuroscience experiments.

The core focus of the dissertation will be the modelling of dynamic relationships between brain activity and subjectively experienced pain at the individual level, with an emphasis on rigorous statistical inference under non-standard distributional assumptions. Attention will be devoted to linear and nonlinear mixed models with fixed and random effects, the application of non-Gaussian distributions, as well as the use of characteristic function techniques and numerical inversion for the exact or numerically stable evaluation of the distributions of estimators, test statistics, and predictions in mixed models.

The methodological development will be closely linked to the international ERA-NET NEURON project (NeuroPain), which focuses on the identification of individual brain signatures of chronic pain and their use in targeted non-invasive neuromodulation using focused ultrasound (FUS). The statistical models will be employed to quantify and compare the effects of personalised, group-level, and control intervention strategies, as well as to analyse the relationship between the precision of FUS targeting and observed changes in neuroimaging and behavioural outcomes.

The dissertation will provide the doctoral student with the opportunity to work with real, methodologically demanding data, to develop new inferential procedures for mixed models, and to contribute to the establishment of a general methodological framework for the analysis of individually oriented longitudinal data in neuroscience and biomedicine.

The dissertation will be carried out at the partner external educational institution (EEI), the Institute of Measurement Science of the Slovak Academy of Sciences, Bratislava.

The aim of the dissertation is the development of theoretical and algorithmic methods of statistical inference in linear and nonlinear mixed models under non-standard distributional assumptions, with the goal of identifying individual brain signatures of pain from longitudinal neuroimaging data.

The dissertation is related to the implementation of the international research project ERA-NET NEURON (NeuroPain), focused on interdisciplinary research into the mechanisms of chronic pain and personalised approaches in neuroscience, within which advanced statistical methods for the analysis of longitudinal neuroimaging data are developed. Participation in the project will enable the doctoral student to engage in active international collaboration and to participate in major national and international conferences. The dissertation will be carried out at the partner external educational institution (EEI), the Institute of Measurement Science of the Slovak Academy of Sciences, Bratislava.

Literature:

L. R. LaMotte: Foundations of Multiple Regression and Analysis of Variance. CRC Press, 2026. DOI: 10.1201/9781003597322.