# Imperial-UCL Joint Statistics Symposium

## Table of Contents

- Details
- Timetable
- 14.00 - 14.30:
*Spectral Matrix Inversion: Uses and Methodology* - 14.30 - 15.00:
*Diffusion modeling of motion trajectories under the inﬂuence of covariates* - 15.00 - 15.30:
*Developing Multi-Scale Virtual Karyotype Libraries for Cancer Analysis* - 15.30 - 16.15: Coffee Break
- 16.15 - 16.45:
*A longitudinal model for latent cognitive function* - 16.45 - 17.15:
*Modelling Electricity Day-Ahead Prices* - 17.15 - 17.45:
*Modelling Network Data* - 18.00 - ∞: Social gathering at a local pub

- 14.00 - 14.30:

## Details

The Statistics section of the Mathematics department of Imperial College London and the Department of Statistical Science of University College London are hosting a joint half-day event to explore joint interests, exploiting our collocation.

The event takes place **between 14.00 and 17.45** on **Wednesday,
19th of September, 2012** and consists of a series of talks which
will take place in the Read Lecture Theatre in the Sherfield Building
(Level Five) at Imperial College London (building number 22
on this
map). After the event there will be a social gathering at a local
pub, which will provide an ideal opportunity for the groups to meet
discuss and exchange ideas in a friendly atmosphere. The groups will
start making their way to the pub at **18.00**.

The detailed timetable of the event is given below.

## Timetable

### 14.00 - 14.30: *Spectral Matrix Inversion: Uses and Methodology*

- Presenter:
**Andrew Walden**, Imperial - Abstract: Multi-channel frequency-domain statistical methods such as multiple and partial coherence analysis and graphical modelling involve the inversion of spectral matrices over a range of frequencies. We discuss such inversion and show how the problem has some features which make it distinct from concentration matrix estimation in multivariate analysis. The addition of some amount of white noise to the series can effectively aid inversion and suppress spectral leakage and has been used for 30 years. The lasso-type estimator is an alternative approach and also involves a parameter choice. A real-data example shows how the parameters of the two methods can be chosen to produce almost the same Frobenius norms for the inverse spectral matrices. Another approach involves shrinkage-type ideas applied to the spectral matrix. It will be shown how the multitaper spectral estimation method is particularly suited to this scheme through estimation of the shrinkage weight parameter.

### 14.30 - 15.00: *Diffusion modeling of motion trajectories under the inﬂuence of covariates*

- Presenter:
**Ioanna Manolopoulou**, UCL - Abstract: We present dynamic spatial modelling and computational methods for the analysis of collections of objects moving in a spatially inhomogeneous force field under the influence of covariates. Core motivating examples come from movement ecology, where multiple animals are tracked moving in 2-D or 3-D largely driven by the external environmental characteristics. Interest lies in identifying the role of different covariates in guiding the motion, both in terms of the shape of their implied field, as well as their overall presence or absence of influence. Models are based on discrete-time, dynamic state-space models for locations and directional velocities of each of a set of animals, combined with a latent force-field over the temporal domain that drives changes in velocities. We extend models for the force fields using dynamic Bayesian radial basis function regression to define a potential surface varying in space but also in the space of covariates, with the force field given by the gradient of the potential in 3-D. Corresponding variable selection priors allow us to detect which covariates play a role in shaping the motion, and provide a basis for understanding their precise functional form. We exemplify the work with analysis of GPS tracking data from a set of toucans in central America, where primary interest lies in characterizing the birds' response and contribution to different temperature levels.

### 15.00 - 15.30: *Developing Multi-Scale Virtual Karyotype Libraries for Cancer Analysis*

- Presenter:
**Christopher Yau**, Imperial - Abstract: In this talk, I will discuss a variety of signal segmentation problems motivated by the analysis of cancer genomics data. I will introduce methods based on novel auxiliary counting variables, decision theoretic and multi-scale approaches that we are currently utilising to make sense of the complex genetic abnormalities seen in cancer and the efforts we are making to utilise state-of-the-art computational hardware to facilitate the analysis of massive quantities of data.

### 15.30 - 16.15: Coffee Break

### 16.15 - 16.45: *A longitudinal model for latent cognitive function*

- Presenter:
**Ardo Van Den Hout**, UCL - Abstract: A mixed-effects regression model with a non-linear predictor is formulated to describe change in latent cognitive function over time in the older population. As a latent variable cognitive function is linked to longitudinal questionnaire data by using an item response theory model. Bayesian inference is used, where the Deviance Information Criterion is applied for model comparison. The model is an alternative to a regression model with the manifest sum score as response. Special attention is given to the identifiability of the item response parameters. Item response theory makes it possible to use dichotomous and polytomous test items, and to take into account missing data. This will be illustrated in an application where data stem from the Cambridge City over-75s Cohort Study.

### 16.45 - 17.15: *Modelling Electricity Day-Ahead Prices*

- Presenter:
**Almut Veraart**, Imperial - Abstract: This paper presents a new modelling framework for day–ahead electricity prices based on multivariate Levy semistationary (MLSS) processes. Day–ahead prices specify the prices for electricity delivered over certain time windows on the next day and are determined in a daily auction. Since there are several delivery periods per day, we use a multivariate model to describe the different day–ahead prices for the different delivery periods on the next day. We extend the work by Barndorff-Nielsen, Benth & Veraart (2012) on univariate Levy semistationary processes to a multivariate setting and discuss the probabilistic properties of the new class of stochastic processes. Furthermore, we provide a detailed empirical study using data from the European Energy Exchange (EEX) and give new insights into the intra–daily correlation structure of electricity day–ahead prices in the EEX market. The flexible structure of MLSS is able to reproduce the stylised facts of such data rather well. Furthermore, the new modelling framework allows to model negative prices in electricity markets which started to occur recently and cannot be described by many classical models. This is joint work with Luitgard Veraart (LSE).

### 17.15 - 17.45: *Modelling Network Data*

- Presenter:
**Patrick J. Wolfe**, UCL - Abstract: Networks are fast becoming a primary object of interest in statistical data analysis, with important applications spanning the social, biological, and information sciences. A common aim across these fields is to test for and explain the presence of structure in network data. In this talk we show how characterizing the structural features of a network corresponds to estimating the parameters of various random network models, allowing us to obtain new results for likelihood-based inference and uncertainty quantification in this context. We discuss asymptotics for stochastic blockmodels with growing numbers of classes, the determination of confidence sets for network structure, and a more general point process modelling for network data taking the form of repeated interactions between senders and receivers, where we show consistency and asymptotic normality of partial-likelihood-based estimators related to the Cox proportional hazards model (arXiv:1201.5871, 1105.6245, 1011.4644, 1011.1703).