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The LiU Seminar Series in Statistics and Mathematical Statistics

Tuesday, February 6, 3.15 pm, 2024. Seminar in Statistics.

Copula-based Bayesian Networks
Dorota Kurowicka
, Delft Institute of Applied Mathematics, Delft University of Technology
Abstract: Bayesian Networks (BNs) have become a popular tool for specifying high-dimensional probabilistic models. Their popularity is a result of the graphical representation effectively capturing engineers' intuitive understanding of complex systems, and at the same time serving as a user interface for sophisticated software implementations.
A BN consists of a directed acyclic graph, that expresses conditional independence among random variables and a list of conditional probability distributions of variables given their parents in the graph. BNs have become very popular as a tool for reasoning under uncertainty. However, they are mostly applied to model dependencies for discrete and/or Gaussian distributions due to the available powerful computational algorithms and numerous computer implementations.
The assumption of Gaussian distributions of nodes is often not justified in applications and recently this assumption has been relaxed by the introduction of copula-based BNs. Gaussian copula BNs have been implemented in the standalone software UNINET and successfully applied in many applications. Allowing copulas beyond the Gaussian case into the BN framework has not been very successful so far, due to a few important reasons:
  1. Approach based on pair copula (PC) is very promising, but in general leads to expensive numerical integration.
  2. Conditioning on the observed information in these models is very challenging.
In this talk I present the recent advancements in the pair copula based BNs (PCBNs), which provide a step towards the development of a unified theory and efficient algorithms for PCBNs. To address the efficiency of computations (without expensive integration), the restrictions on the graph structure are provided.
This is a joint work with N. Horsman and A. Derumigny (Delft University of Technology).
Location: Alan Turing

Tuesday, February 13 , 3.15 pm, 2024. Seminar in Statistics.

Estimating Causal Effects from Panel Data with Dynamic Multivariate Panel Models
Jouni Helske, INVEST Research Flagship Centre, University of Turku
Abstract: Longitudinal data consisting of various measurements from multiple subjects followed over several time points, are commonly studied in social sciences and other fields. Such data can naturally be analyzed in various ways, depending on the research questions and the characteristics of the data. Popular, somewhat overlapping modelling approaches include fixed effect models, variations of cross-lagged panel models, and dynamic structural equation models. In this talk, I present the dynamic multivariate panel model (DMPM), a flexible Bayesian approach that extends many existing modelling approaches. The DMPM supports ordinary time-invariant effects, individual-level random effects as well as effects varying smoothly in time. Moreover, it can handle multiple simultaneous responses across a wide variety of mixed distributions and allows estimating long-term causal effects of interventions.
Location: Alan Turing.

Tuesday, March 19, 3.15 pm, 2024. Seminar in Statistics.

Bayesian Aggregation of Opinion Polls in Multi-Party Systems for Inference and Forecasting
Måns Magnusson
, Department of Statistics, Uppsala University
Abstract: Political opinions are often measured with opinion polls, and in some situations, such as the measurement of party preferences, a large number of measurements are available over time. We introduce a new longitudinal model for opinion polls with multiple, correlated party proportions, as is common in multi-party democratic systems. The model combines multiple measurement effects, such as house bias and design effects. In addition, we introduce a new measurement component we call industry bias, a bias common to all polling houses that has been observed in many multi-party settings.
We show the proposed model in two different multi-party systems, Germany and Sweden, to model party preference over more than 15 years. We also used the model to predict the Swedish election in 2022 with the major Swedish newspaper Svenska Dagbladet, and the final point prediction came closer than any other poll, prediction, or poll of polls.
Location: Alan Turing.

Tuesday, April 2, 3.15 pm, 2024. Seminar in Mathematical Statistics.

The central limit theorem for random walks on bounded domains
Magnus Herberthson
, Department of Mathematics, Linköping University
Abstract: The standard central limit theorem typically assumes independent identically distributed (i.i.d.) random variables Xi (with E[Xi]=0 and finite variance V[Xi]). A scaled average of N terms will then converge to a normal distribution as N→∞, and the variance of this normal distribution is directly related to V[Xi]. We consider a random walk in a bounded domain Omega (for simplicity in the in the plane) which will imply that the the random walk variables Xi are not any longer independent. A central limit theorem still ensures a limiting distribution for the rescaled averages as the number of terms increases, but now the covariance matrix of the limiting distribution is not so obvious. We will discuss how this covariance matrix is given by the geometry of the bounding domain Omega.
Location: Hopningspunkten.

Tuesday, April 23, 3.15 pm, 2024. Seminar in Statistics.

TreePPL: Universal Probabilistic Programming for Phylogenetics and Evolutionary Biology
Fredrik Ronquist
, Department of Bioinformatics and Genetics, Swedish Museum of Natural History
Abstract: Probabilistic programming aims to completely separate model specification from inference in statistical analysis, such that the user can focus on describing the model and then get inference for free. Within this general framework, there is considerable research both on expressive model languages that are easy to use, and generic algorithms that provide efficient inference for these languages. In the TreePPL project, we are developing a probabilistic programming platform for phylogenetics and evolutionary biology. Models in this domain typically include structures that must be described using stochastic recursion, requiring the most powerful type of model description languages we know, universal probabilistic programming languages. These model descriptions can be thought of as programs that simulate from the model conditional on the observed data. Interestingly, phylogenetic models reveal several generic challenges in developing efficient automatic inference for such programs. These challenges include alignment across possible execution traces, which is important for efficiency in both sequential Monte Carlo and Markov chain Monte Carlo inference strategies. They also include Rao-Blackwellization of latent variables, which is well known to be critical for efficient inference in standard phylogenetic models. Rao-Blackwellization involves summing or integrating out latent variables, and is based either on the exploitation of conjugacy relations or the summation over small discrete state spaces. Ideally, the user should be able to rely on the automatic inference machinery for Rao-Blackwellization, and there is good recent progress in this direction. A general difficulty with probabilistic programming is that many of the generic inference algorithms are most easily applied to model descriptions in functional programming languages, and those are difficult to use for most empiricists. Nevertheless, probabilistic programming is becoming more widespread, and it arguably represents an important first step towards communicating model descriptions to more powerful inference systems based on artificial intelligence.
Location: Alan Turing.

Tuesday, May 14, 3.15 pm, 2023. Seminar in Statistics.

Alexandra Jauhiainen, Sofia Tapani, AstraZeneca
Location: Alan Turing.

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Last updated: 2024-04-14