PGR Seminars

Over the past few years, emerging innovations in technology have facilitated data collection dramatically. As a result of these advances, nowadays in various fields such as finance, marketing, medicine, biology etc. data contain a large number of measurements. Accordingly, high dimensionality is a frequent issue in statistical modelling. In such large data sets, the number of predictors may be extremely large while the number of observations is limited . Variable screening or variable selection is an approach that can be used to reduce the original data by removing irrelevant information, in such a way that informative structure of data is preserved.

In cancer biology, gene expression data always contain tens of thousands of genes while only tens of genes may be responsible for the disease. In order to screen gene expressions of cancer cells , we introduce a variable filter and perform our variable screening approach using this filter, then we compare the performance of our method with some of the existing ones.​

Rational solutions of the Boussinesq equation give rise to water wave solitons, by examining the form of these solutions and considering the behaviour of the roots, the aim is to establish the behaviour of this family of solutions. In particular, the solutions considered are the second logarithmic derivative of polynomial functions in x and t of symmetric degree n(n+1) for n an integer. Solutions have been found up to n = 5.

Investigation into both the Boussinesq and the Non-linear Schrödinger equation will be discussed along with complex root and solution plots.

Ring-recovery data is a significant component of research on ecological conservation and management. It is possible to find historical data on the total number of ringed birds for several species, however information about the age of birds at the ringing event may not always be accessible. In most species of birds, the probability of surviving tends to be affected by age. While older birds are likely to have a more stable and higher survival rate, younger birds usually have a more varying and smaller chance of surviving. Therefore, it is important to build statistical models that take into account this age variation.

We will analyse standard ring-recovery models and explain the development of some model extensions that cope with the problem of age uncertainty. We will also cover some important aspects in statistical ecology, such as model selection and parameter redundancy.

Financial prices are usually modelled as continuous, often involving geometric Brownian motion with drift, leverage, and possibly jump components. An alternative modelling approach allows financial observations to take integer values that are multiples of a fixed quantity, the ticksize - the monetary value associated with a single change during the asset evolution. These samples are usually collected at irregularly-spaced time points, as in the case of high-frequency data, exhibiting diverse trading operations in a few seconds.

In the context, the observables are modelled in a Bayesian fashion via the Skellam process (defined as the difference between two Poisson processes). Volatility modelling is included in the analysis using the class of discretised Gaussian Ornstein-Uhlenbeck AR(1) processes. In particular, the variances of the two likelihood processes are linked with the AR(1) processes. Inference for the model is obtained via standard Gibbs sampling.

Cloud systems play a significant role in linking atmospheric and hydrological processes and have profound effects on regional and global climate. This presentation focuses on the cloud microphysics and how statistics and mathematics are employed in the cloud microphysics research.

Processes of two very different kinds are responsible for cloud formation and precipitation development. The first ones are relatively large-scale processes, all involving air motions, under the term cloud dynamics. Cloud microphysics, the second kinds of cloud processes, are on a smaller scale which is comparable in size of the dimensions of individual cloud droplet and rain particle. The purposes of this part of cloud physics is to explain the environment by which an individual aerosol particle can be activated as a cloud condensation nuclei, and develop to visible size as a cloud droplet.

To achieve these purposes, we develop a two-moment bin-solved cloud physics model: Aerosol-Cloud-Precipitation Interaction Model (ACPIM). In order to simulate cloud droplets formation and a cloud parcel rising through an atmosphere in hydrostatic balance, the model supports a prognostic treatment of aerosol with a lognormal size distribution and solves a set of 4 coupled ordinary differential equations for the water vapor mass mixing ration, total pressure, temperature and height.

I’ll talk about the Skyrme Model and about its key features and how we visualise the solutions (which we call Skyrmions). We will see that it is possible to identify these solutions with atomic nuclei. I will then discuss how we can try to quantise what is originally a classical model, which is necessary to relate the model to nuclear physics. We will see that there are some big problems in using standard quantisation techniques and look at some alternative ideas.

A model category is a category C with three distinguished classes of maps verifying certain axioms. One can construct the homotopy category Ho(C) associated to a model category C by taking the homotopy classes of morphisms in C.

Then we can construct an adjoint pair of suspension and loop functors on Ho(C). The category C is called stable if this previous adjunction is an equivalence of homotopy categories.

In this talk, I will give the definition of a model category, and explain how we pass to the associated homotopy category. Moreover, I will also explain what a stable model category is, and give some examples of non-stable and stable model categories.