Tuesday, September 5, 3.15 pm, 2017. Seminar in Statistics.

Gibbs sampling for Latent Dirichlet Allocation
Johan Jonasson, Department of Mathematical Sciences, Chalmers University of Technology
Abstract: MCMC and in particular Gibbs sampling is ubiquitous in Bayesian machine learning models. In this talk I will shortly review the Latent Dirichlet Allocation model for text classification and a hidden Markov model thereof. The task is to infer topics from the text in an unsupervised way and a common way is to use collapsed Gibbs sampling (i.e. integrating out the unknown random parameters). It would be desirable to have these to converge fast, and we show that in a very simple special case, mixing time is polynomial in the number of tokens.
Location: Alan Turing.

Wednesday , September 20, 3.15 pm, 2017. Seminar in Mathematical Statistics.

Covering a subset of R^d by Poissonian random sets
Erik Broman, Department of Mathematical Sciences, Chalmers University of Technology
Abstract: The problem of covering a set A by a collection of random sets dates back to Dvoretzky in 1954. Since then, a host of papers have been written on the subject. In this talk we shall review some of this history and discuss two directions in which progress have recently been made.
In the first case we consider a statistically scale invariant collection of subsets of R^d, which are chosen at random according to a Poisson process of intensity lambda. The complement of the union of these sets is then a random fractal that we denote by C. Such random fractals have been studied in many contexts, but here we are interested in the critical value of lambda for which the set C is almost surely empty (so that R^d is completely covered). Such problems were earlier studied and solved in one dimension, while here we shall present recent progress which solves it in all dimensions. This part is based on joint work with J. Jonasson and J. Tykesson.
In the second direction we consider a dynamic version of coverings. For instance, the set A could be a box of side lengths n, and then balls are raining from the sky at unit rate. One then asks for the time at which A is covered. Together with F. Mussini I have recently studied a variant in which the balls are replaced by bi-infinite cylinders. This makes the problem fundamentally different as one no longer have independence between well separated regions. Thus, new methods and techniques must be used. Our main result is that we find the correct asymptotics for the cover time as the set A grows.
Location: Hopningspunkten.

Tuesday, October 3, 3.15 pm, 2017. Seminar in Statistics.

On Probabilistic Independence Models and Graphs
Kayvan Sadeghi, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
Abstract: The main purpose of this talk is to explore the relationship between the set of conditional independence statements induced by a probability distribution and the set of separations induced by graphs as studied in graphical models. I define one general type of graph and one separation criterion, and show that almost all known types of graphs and separation criteria are a special case of these. I introduce the concepts of Markov property and faithfulness, and provide conditions under which a given probability distribution is Markov or faithful to a graph. I discuss the implications of these conditions in statistics, probability theory, and machine learning.
Location: Alan Turing.

Tuesday, October 17, 3.15 pm, 2017. Seminar in Mathematical Statistics.

Stochastic Gene Switches
Joanna Tyrcha, Department of Mathematics, Stockholm University
Abstract: The timing of key events in the eukaryotic cell cycle is remarkably stochastic. Special attention had been paid to the START transition, when the cell starts to synthesize DNA. Experiments have shown that START in budding yeast proceeds in two distinct steps, both of which are stochastic. We look at the cellular reactions responsible for the stochasticity in these and similar transitions. Their dynamics can be described by stochastic differential equations, allowing us to write a path-integral representation for the transition rate. We study also the bursting limit in which we can eliminate the mRNA of our model if we study an appropriate time scale.
Location: Hopningspunkten.

Tuesday, October 31, 3.15 pm, 2017. Seminar in Statistics.

Frequentist model averaging in structural equation modelling
Shaobo Jin, Department of Statistics, Uppsala University
Abstract: Model selection from a set of candidate models plays an important role in many structural equation modelling applications. However, traditional model selection methods introduce extra randomness that is not accounted for by post-model selection inference. In the current study, we propose a model averaging technique within the frequentist statistical framework. Instead of selecting an optimal model, the contribution of all candidate models are acknowledged. Valid confidence intervals and a chi-square test statistic are proposed. A simulation study shows that the proposed method is able to produce a robust mean squared error, a better coverage probability, and a better goodness-of-fit test compared to model selection. It is an interesting compromise between model selection and the full model.
Location: Alan Turing.

Tuesday, November 14, 3.15 pm, 2017. Seminar in Mathematical Statistics.

Random coalescing geodesics in first-passage percolation
Daniel Ahlberg, Department of Mathematics, Stockholm University
Abstract: Since the work of Kardar-Parisi-Zhang in the mid 1980s, it has been widely believed that a large class of two-dimensional growth models should obey the same asymptotic behaviour. This behaviour stands in contrast to one-dimensional behaviour where fluctuations are dictated by the central limit theorem. To rigorously understand the predictions of KPZ-theory has become one of the most central themes in mathematical physics. One prominent model believed to belong to this class is known as first-passage percolation. It can be interpreted as the random metric on Z2 obtained by assigning non-negative i.i.d. weights to the edges of the nearest neighbour lattice. We shall discuss properties of geodesics in this metric and their connection to KPZ-theory. As a first step in this direction, we answer a question posed by Benjamini, Kalai and Schramm in 2003, that has come to be known as the 'midpoint problem'. This is joint work with Chris Hoffman.
Location: Hopningspunkten.

Tuesday, November 28, 3.15 pm, 2017. Seminar in Statistics.

Probabilistic programming for statistical phylogenetics
Fredrik Ronquist, Department of Bioinformatics and Genetics, Swedish Museum of Natural History
Abstract: Statistical inference based on phylogenetic models - models built around evolutionary trees - is widely used throughout the life sciences today. The field is completely dominated by Bayesian MCMC methods, which were introduced about 20 years ago. The flexibility and computational efficiency of this approach have resulted in explosive development of phylogenetic models. It has been quite challenging for computational biologists to keep up with the rapidly expanding model space, and the field is dominated today by a plethora of software packages, each dealing with a specific subset of models. There is a clear need for more generic approaches to model construction and inference. We have tried to address these challenges by developing Rev, a probabilistic programming language for statistical phylogenetics based on probabilistic graphical models. Unlike most other such languages, Rev is designed for use in an interactive computing environment, allowing users to build phylogenetic models step by step, and examine the model components as they go. I describe some of the challenges involved in developing an interactive probabilistic programming language and some of the potential and limitations of probabilistic graphical models in phylogenetics.
Location: Alan Turing.

Tuesday, December 12, 3.15 pm, 2017. Seminar in Mathematical Statistics.

Asumptotic Behaviour in Time for a Singular Stochastic Newton Equation
Astrid Hilbert, Department of Mathematics, Linnaeus University
Abstract: download
Location: Hopningspunkten.