Arrangementer

Cards are drawn, one at a time, with replacement, from a deck of n cards. I study the total time W_n needed until we have seen all n cards, via different perspectives, along with a Gumbel limiting distribution. Various non-trivial identities, involving different perspectives for moments and Laplace transformations, are found as corollaries. These findings are also used to estimate the number of different cards,if uknown. If I needed to sample 133 words from a document, before I had 50 different words, what is the vocabulary size for the document? How many words did Shakespeare know (including those he never used in his writing)? 

An Abels Tårn podcast about some of these themes, which attracted a fair amount of inspired comments and guesses from the public (specifically, finding the mean of W_n above, for the case of n = 52 cards), can be found on the Abels Tårn website, July 2021, as a conversation with Torkild Jemterud, Jo Røislien, and myself. 

The talk is elementary and discusses empirical modelling of single variables with insurance losses as example. There are in such cases little or no theory to go on, and the amount of data is many situation quite scarce. Why do we so often limit ourselves to fit two-parameter families? It will be suggested that it may be a good idea to work with more flexible models with three or four parameters and that this may provide a nice framework for automating the entire procedure for the computer to work alone. Sure, with little data the parameters may be unstably estimated, but that may not apply equally to the distributions they define. Many-parameter families suitable for insurance losses will be reviewed with some simple asymptotics in an example allowing this and with Monte Carlo to throw light on the issue in other cases.

In this talk I will discuss the variational form of Bayes theorem by Zellner (1988). This result is the rationale behind the variational (approximate) inference scheme, although it is not always that clear in modern presentations. I will discuss two applications of this results. First, I will show how to do a low-rank mean correction within the INLA framework (with amazing results), which is essential for the next generation of the R-INLA software currently in development. In the second one, I will introduce the Bayesian   learning rule, which unify many machine-learning algorithms from fields such as optimization, deep learning, and graphical models. This includes classical algorithms such as ridge regression, Newton's method, and Kalman filter, as well as modern deep-learning algorithms such as stochastic-gradient descent, RMSprop, and Dropout.

The first part of the talk is based on our recent research at KAUST, while the second part is based upon \texttt{arxiv.org/abs/2107.04562} with Dr. Mohammad Emtiyaz Khan, RIKEN Center for AI Project, Tokyo.

Marginal maximum likelihood estimation of longitudinal latent variable models for ordinal observed variables is challenging due to the high latent dimensionality required to accurately model residual dependencies for repeated measurements. We use second-order Laplace approximations to the high-dimensional integrals in the marginal likelihood function for longitudinal item response theory models and implement an efficient estimation method based on the approximations. The method is illustrated with items from the Montreal Cognitive Assessment, administered at four time points in a Hong Kong study of aging and well-being. We discuss the limitations of the proposed estimation method and outline a potential extension to the approach that uses a dimension-reduction technique.

Template Model Builder (TMB) is an R-package that is well suited for performing fast inference with latent Gaussian models when the likelihood can be written as a three times differentiable function. TMB automatically differentiates the likelihood and utilizes Markov structures to efficiently integrate over latent variables with the Laplace approximation. In this seminar I will first introduce TMB and then elaborate a fish stock assessment model implemented with use of TMB that provides quota advice for approximately 25 different fish species in Europe.

William Robert Paul Denault (Department of Genetics and Bioinformatics, Norwegian Institute of Public Health) will give a talk on December 8th at 14:15 (held with restricted attendance in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor and streamed in Zoom - the link will be sent by mail one day in advance).

Carla Janaina Ferreira (DNV GL) will give a talk on November 24th at 14:15 (held with restricted attendance in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor and streamed in Zoom - the link will be sent by mail one day in advance).

Steffen Grønneberg (Department of Economics, BI Norwegian Business School) will give a talk on November 10th at 14:15 (held with restricted attendance in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor and streamed in Zoom - the link will be sent by mail one day in advance).

Benjamin Kedem (Department of Mathematics, University of Maryland, USA) will give a talk on October 27th at 14:15 in Zoom - the link will be sent by mail one day in advance).

Christian Page (Department of Mathematics, University of Oslo) will give a talk on October 13th at 14:15 (held with restricted attendance in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor and streamed in Zoom - the link will be sent by mail one day in advance).

Mette Langaas (Department of Mathematical Sciences, Norwegian University of Science and Technology) will give a talk on May 19th at 14:15 in Zoom (the link to the event will be available soon).

Heidi Seibold (Department of Statistics, Ludwig-Maximilians-Universität of Munich, GER) will give a talk on May 5th at 14:15 in Zoom https://uio.zoom.us/j/66792241824.

Antonio Canale (Department of Statistical Sciences, University of Padova, ITA) will give a talk on April 21st at 14:15 in Zoom (https://uio.zoom.us/j/66042762975).

Due to travel restrictions related to the spread of Covid-19, the talk of  Lokukaluge Prasad Perera (Department of Technology and Safety, Artic University of Norway), supposedly held on March 16th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor, has been CANCELLED.

Morten Hjorth-Jensen (Department of Physics, University of Oslo and Department of Physics and Astronomy, Michigan State University, USA) will give a talk on March 3rd at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Haakon Bakka (formerly Computer Electrical Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, KSA, from 01.02.2020 Department of Mathematics, University of Oslo) will give a talk on February 25th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Johan Pensar (formerly Department of Mathematics and Statistics, University of Helsinki, from 01.02.2020 Department of Mathematics, University of Oslo) will give a talk on February 11th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Kristoffer H. Hellton (Department of Statistical Analysis, Machine Learning and Image Analysis, Norwegian Computing Center) will give a talk on January 28th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Kåre Bævre (Department of Health and Inequality, Norwegian Institute of Public Health) will give a talk on January 14th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Stein Andreas Bethuelsen (Department of Mathematics and Physics, University of Stavanger) will give a talk on December 10th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Øystein Sørensen (Department of Psychology, University of Oslo) will give a talk on November 26th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.