Keynote Lectures

We are delighted to announce that the esteemed speakers have graciously accepted our invitation to deliver keynote speeches at the Applied Statistics 2026 conference.

Parametric sparse models for distributional data

Prof. Paula Brito, Ph.D.
Professor of Statistics
University of Porto, Porto, Portugal
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Abstract [Monday, September 21, 9.00–10.00]

In classical multivariate statistics and machine learning, data are typically organized in a tabular format, where each row corresponds to an individual unit and each column records a single value for a given variable. However, this representation becomes inadequate when the data inherently involve variability. This situation arises when the units of analysis are not individual entities but rather abstract concepts—such as diseases instead of specific patients—or groups formed on the basis of shared characteristics. In such cases, for each descriptive variable, the variability observed within each concept or group should be taken into account, rather than relying solely on central tendencies (e.g., means, medians, or modes), in order to preserve potentially relevant information. Symbolic Data Analysis offers a framework for representing and analyzing such complex data, enabling aggregation at various levels of detail while retaining the associated variability. New types of variables have been introduced, where observations take the form of sets, intervals, or distributions over a given domain.

In this work, we focus on numerical data described by empirical distributions. We propose parametric models based on representing each distribution using a central statistic and the logarithms of inter-quantile ranges for a selected set of quantiles. Multivariate normal distributions are assumed for the full set of indicators, considering alternative sparse structures for the covariance matrix. Interval-valued data is a particular case within this framework. The proposed model enables multivariate parametric analysis of distributional data, including analysis of variance, discriminant analysis, and model-based clustering. Applications to real-world data illustrate the relevance and usefulness of the approach

The Firth correction – a recap and new developments

Prof. Georg Heinze, Ph.D.
Professor of Biostatistics
Medical University of Vienna, Vienna, Austria
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Abstract [Tuesday, September 22, 9.00–10.00]

Maximum likelihood estimates of statistical model parameters such as regression coefficients in generalized linear and related models are known to be asymptotically unbiased, but they can exhibit small-sample bias which in its extreme form may correspond to non-existent (quasi-infinite) estimates. This situation has been termed complete or quasi-complete separation (Albert and Anderson, 1984) for binary outcome models, or monotone likelihood (because the likelihood cannot be maximized by a finite regression coefficient) in Cox regression models. The Firth correction, originally developed by David Firth (1993) to reduce the small sample bias of maximum likelihood estimates, has been suggested as an assumption-lean solution to the problem of separation, providing finite estimates which clearly improve the properties of their maximum likelihood counterparts (Heinze and Schemper, 2002).

We will provide an overview over the phases of development, evaluation and application of the Firth correction, covering its application to logistic regression but also to other outcome models. We will also compare the Firth correction to other proposed solutions to separation such as log-F priors or Bayesian approaches (Greenland and Mansournia, 2015; Gelman et al, 2008).

Recently, progress has been made in several directions, which cover improving the calibration of Firth-corrected models (Puhr et al, 2017), modifying the strength of the penalty (Elgmati et al, 2015), and applying a Firth-type penalty to clustered data (Geroldinger et al, 2022; Sterzinger and Kosmidis, 2023). We will provide an overview over these developments, highlighting new areas of application.