Department of Mathematical Sciences

– a national centre for teaching and research in the mathematical sciences

Recent events

FRINATEK project funding

The Research Council of Norway. Logo.The Department of Mathematical Sciences has been granted 2 new projects within the FRINATEK funding programme:

  • Complex analysis and dynamics (John Erik Fornæss)
  • Penalised Complexity-priors: A new tool to define default priors and robustify Bayesian models (Håvard Rue)
10th December 2014

FRINATEK project funding

The Research Council of Norway. Logo.The Department of Mathematical Sciences has been granted 2 new projects within the FRINATEK funding programme:

  • Complex analysis and dynamics (John Erik Fornæss)
  • Penalised Complexity-priors: A new tool to define default priors and robustify Bayesian models (Håvard Rue)

Facts

  • The granting committee for Mathematics, Physical Sciences and Technology (FRINATEK) has awarded NOK 292 million to 53 projects with starting date in 2015.
  • In total NOK 2070 million was sought for the years 2015 - 2019. The amount awarded represents 14,1% of this amount.

Distribution of approved projects

  • 22 out of 182 Researcher Projects
  • 13 out of 78 Young Research Talents projects
  • 5 out of 29 Personal Post-Doctoral Research Fellowships
  • 3 out of 6 FRIPRO Mobility Grants
  • 10 out of 10 Support for Events grants

Visit the Reseach Council of Norway's pages for details.

 

About the projects

Complex analysis and dynamics

John Erik Fornæss. Photo.

Newtons method is a classical approach to finding roots of polynomials P. This is an important tool in science and engineering. Complex dynamics takes into account that the roots Z might be complex numbers. One investigates those initial guesses of a root, W, such that the points given by Newtons method approaches Z. This can be done in higher dimension as well and gives rise to pseudoconvex sets. The systematic investigation of pseudoconvex sets is a basic part of higher dimensional complex analysis. This project is concerned with modern topics in complex dynamics, complex analysis and their interaction.

Penalised Complexity-priors: A new tool to define default priors and robustify Bayesian models

Håvard Rue. Photo.

A long lasting problem within Bayesian statistics, is the choice of prior distributions. Although various approaches have been suggested to approach this issue, the current practice among applied statisticians is not good. In this project we will develop a recent proof of concept idea of Penalised Complexity (PC) priors, which is a principled approach to construct priors. This approach constructs priors that are invariant to reparameterisations, are designed to support Occam's razor and seem to have excellent robustness properties.

We will develop this idea further and define default priors suitable for routine applied use. The priors and with them model robustness against possible model deviations can be controlled by the user in a transparent, consistent and intuitive way. Instead of considering each model component separately, the user needs only to provide an intuition about the linear predictor as a whole, which is then like a chain reaction transferred to the single model components.

The framework will be integrated into the program-system R-INLA for doing Bayesian inference in latent Gaussian models.

Interview in StatsLife

Håvard Rue. Photo.

Interview with Håvard Rue in StatsLife:
Streamlining Bayesian analysis: a Q&A with Håvard Rue

In statistical journals, every now and again a paper comes along that examines what seems like a very specific issue. But the discoveries made can have wide reaching applications in multiple fields, which even the original authors did not envisage.

One such paper was published in the RSS Series B journal in 2009. The paper was titled ‘Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations’, written by Håvard Rue, Sara Martino and Nicolas Chopin. The idea would later be given the abbreviation INLA.

15th December 2015

Interview in StatsLife

Håvard Rue. Photo.

Interview with Håvard Rue in StatsLife:
Streamlining Bayesian analysis: a Q&A with Håvard Rue

In statistical journals, every now and again a paper comes along that examines what seems like a very specific issue. But the discoveries made can have wide reaching applications in multiple fields, which even the original authors did not envisage.

One such paper was published in the RSS Series B journal in 2009. The paper was titled ‘Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations’, written by Håvard Rue, Sara Martino and Nicolas Chopin. The idea would later be given the abbreviation INLA.

Their new INLA approach tried to find a different way of computationally analysing models that are too complex for normal Markov chain Monte Carlo (MCMC) methods. Subsequently, an R statistical software package was developed and this enabled the method to be applied in a diverse range of fields from econometrics to ecology.

In the years since its publication, new uses and tools for implementing the method have been developed and new applications are being discovered all the time. An online community has also been set-up to foster knowledge in the area.

Håvard Rue, who has led the project from the beginning, talked to us about how the method was developed and how interest in its various uses has grown since then.

Read the full interview here

Three PhD fellowships at IMF

Three PhD fellowships have just been announced at jobbnorge.no.

The deadline for application is February 13.

22nd January 2015

Three PhD fellowships at IMF

Three PhD fellowships have just been announced at jobbnorge.no.

The deadline for application is February 13.

The vacant PhD fellowships are intended to give promising candidates an opportunity to pursue a research activity on an advanced level leading to a doctoral degree. The Department of Mathematical Sciences conducts research on an international high level within the disciplines of algebra, analysis, differential equations, numerical analysis, optimization, geometry/topology, statistics and didactics of mathematics. Part of the research is also done in close cooperation with other fields of science and technology within NTNU, as well as in cooperation with industry and external research institutions.

Read the full announcement here

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