Ilia received a BSc in Mathematics from the University of Patras, Greece and an MA and a Ph.D. in Mathematical Statistics from the University of Maryland, College Park, USA in 1992 (with Eric V. Slud). She worked at the University of Cyprus from 1993 to 2009. In 2008 she joined the faculty of the Department of Mathematics of the National Technical University of Athens. Between 2001 and 2007 she held the post of Vice President of the Eastern Mediterranean Region of the International Biometrics Society.

Ilia's research interests include survival analysis and reliability theory, nonparametric and semiparametric statistics. Additional areas of interest are medical statistics, model selection, biostatistics, divergence measures, goodness of fit tests, statistical quality control, time series.