Research Interests

• Applied  statistics
• Statistical analysis of stochastic processes

Degrees

• PhD in Mathematics, School of Mathematics, Cardiff University, 2024;
  Thesis: Stochastic models for increments of EEG recordings using heavy-tailed and multimodal diffusions. Supervisor: N. N. Leonenko
• MSc in Mathematics, Financial and Business Mathematics, Department of Mathematics, University of Osijek, Croatia, 2014
• BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2011

Publications

1. N.N. Leonenko, Ž. Salinger, A. Sikorskii, N. Šuvak, M. Boivin, Generalized Gaussian time series model for increments of EEG data, Statistics and its Interface 16/1 (2023), 17-29
   Abstract

   We propose a new strictly stationary time series model with marginal generalized Gaussian distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram (EEG) data collected from Ugandan children during coma from cerebral malaria. The model inherits its appealing properties from the strictly stationary strong mixing Markovian diffusion with invariant generalized Gaussian distribution (GGD). The GGD parametrization used in this paper comprises some famous light-tailed distributions (e.g., Laplace and Gaussian) and some well known and widely applied heavy-tailed distributions (e.g., Student). Two versions of this model fit to the data from each EEG channel. In the first model, marginal distributions is from the light-tailed GGD sub-family, and the distribution parameters were estimated using quasi-likelihood approach. In the second model, marginal distributions is heavy-tailed (Student), and the tail index was estimated using the approach based on the empirical scaling function. The estimated parameters from models across EEG channels were explored as potential predictors of neurocognitive outcomes of these children 6 months after recovering from illness. Several of these parameters were shown to be important predictors even after controlling for neurocognitive scores immediately following cerebral malaria illness and traditional blood and cerebrospinal fluid biomarkers collected during hospitalization.
2. N.N. Leonenko, A. Sikorskii, Ž. Salinger, M. Boivin, N. Šuvak, Multimodal diffusion model for increments of electroencephalogram data, Stochastic Environmental Research and Risk Assessement 37 (2023)
   Abstract

   We propose a new strictly stationary strong mixing diffusion model with marginal multimodal (three-peak) distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram data collected from Ugandan children during coma from cerebral malaria. We treat the increments as discrete-time observations and construct a diffusion process where the stationary distribution is viewed as a mixture of three non-central generalized Gaussian distributions and we state some important properties related to the moments of this mixture. We estimate the distribution parameters using the expectation-maximization algorithm, where the added shape parameter is estimated using the higher order statistics approach based on an analytical relationship between the shape parameter and kurtosis. The derived estimates are then used for prediction of subsequent neurodevelopment and cognition of cerebral malaria survivors using the elastic net regression. We compare different predictive models and determine whether additional information obtained from multimodality of the marginal distributions can be used to improve the prediction.

Projects

• Scaling in stochastic models (IP-2022-10-808, December 15, 2023. – December 14, 2027).
  Project funded by Croatian Science Foundation. Principal investigator: Danijel Grahovac