**Marcelo Costa **Durham University

**Stochastic Processes with Reinforcement**

(joint work with M. Menshikov)

I will first provide an account on urn models and their variants, surveying what is known, as well as some methods of analysis. Then, I will discuss a certain similarity between Generalised Polya’s Urn models (GPU), the Multi-type Branching Process and present how the Perron-Frobenius theory can be applied to GPU models. Secondly, I will introduce the Stochastic Approximation Algorithm and show how to translate the analysis of some stochastic processes into a dynamical system approach, based on notions of stability for the approximating system of ODE’s. Finally, I will propose a new model and present a result, and a conjecture, highlighting to what extent the aforementioned techniques can or cannot be applied to the model we propose.

**Aoife O’Neill ** University of Limerick

**Risk Profiles and their Association with the Development of
New Pain in Older Irish Adults: a Latent Class Analysis
**

The aim of this study is to examine the association between health risk profiles and

the development of new pain, in a population of older Irish adults. Latent class

analysis (LCA) is a model-based approach used to measure categorical variables,

with the aim of identifying underlying subgroups based on some measured characteristics.

LCA was used to identify health risk profiles, for a sample of people aged

over 50, who reported being pain-free at Wave 1 (N=4349) and the association between

these health risk groups and future pain was examined using the LCA with a

Distal Outcome approach. Four latent classes were identified at Wave 1, based on

11 health risk variables. Two years later, 777 (17.87%) participants developed new

pain; with those in the high risk group most likely to develop new pain.

**Hana Alqifari** Durham University

**Nonparametric predictive inference for reproducibility of two basic tests based on order statistics**

Reproducibility of statistical hypothesis tests is an issue of major importance in applied statistics: if the test were repeated, would the same conclusion be reached about rejectance of the null hypothesis? Nonparametric predictive inference (NPI) provides a natural framework for such inferences, as its explicitly predictive nature fits well with the core problem formulation of a repeat of the test in the future. For inference on reproducibility of statistical tests, NPI provides lower and upper reproducibility probabilities (RP) of some tests based on order statistics, namely a population quantile test and a basic precedence test.

**Cheng Chen** London School of Economics

**Functional Linear Model with Dependent Regressors in High Dimensions**

Existing functional linear model assume either independent and identically distributed functional regressors or a fixed number of dependent functional regressors. In this paper, we propose a new class of partially functional linear models to characterize the linear relationship between a scalar response and high dimensional regressors, involving both dependent scalar and functional variables. We develop a penalized least squares approach to simultaneously perform variable selection for dependent scalar and functional regressors.

**Hermes Marques Da Silva Junior** Durham University

**An R Package to Compute Improved Score Tests in Generalized Linear Models**

Improved score tests are modifications of the score test such that the null distribution of the modified test statistic is better approximated by the chi-squared distribution. The literature includes theoretical and empirical evidence favoring the improved test over its unmodified version. However, the developed methodology seems to have been overlooked by data analysts in practice, possibly because of the difficulties associated with the computation of the modified test. In this article, we describe the mdscore package to compute improved score tests in generalized linear models, given a fitted model by the glm() function in R. The package is suitable for applied statistics and simulation experiments. Examples based on real and simulated data are discussed.

**Kevin Brosnan** University of Limerick

**False Starts in Elite Athletics: Are they truly fair?**

The 100 ms ruling for false start disqualification at athletic competitions governed by the International Association of Athletics Federations has been in force since the early 1990s. Throughout this period, there have been marked changes to the rules that govern the disqualification of athletes from sprint events incorporating starts from blocks. This study analysed all available World and European Championship response-time (RT) data from 1999 to 2014 to examine effects of rule changes on competition RT at major championships. The exponentially modified Gaussian distribution was used to model RT and make comparisons relative to athletes’ sex, ruling periods and competition rounds. Results will include a revision of the false start disqualification limits and question some results in the 2016 Rio Olympics.

**Andrew Garthwaite** University of Greenwich

**Doubly stochastic Poisson processes for fine time-scale rainfall modelling**

Doubly stochastic Poisson processes have been applied to modelling rainfall through a variety of methods. We explore some single-site parsimonious seasonal models with meteorological covariates for fine time-scale rainfall, based on three state Markov modulated Poisson processes. Other research concerned with sub-hourly aggregations of rainfall considers a model with exponentially decaying rainfall pulses.

**Mai Alfahad** University of Leeds

**Identify kinks in helices**

The alpha helix (α-helix) is a common secondary structure of proteins, which is a chain of amino acids forms itself into three-dimensional space. The 3D protein structure is very important, the registration parameters (rotation angles and shift vector) ; and the structural parameters (radius, pitch and spacing (known)) of the alpha-helix. An alpha helix can be described as unlinked or linked. A kink is a point in the helix where a huge difference in the direction of the helix axis. Our main aim is to estimate the kinked helix.

In order to fit the kinked helix we first identify a change point (kink). Every points on the helix could be a change point (kink). We cut the helix into two and calculated the resideual sum of squares for each cut and add them together. The helix with minimum RSS is corresponds to the change point.

**Nawapon Nakharutai** Durham University

When modelling uncertainty, specifying precise probabilities for outcomes may lead to erroneous conclusions. To facilitate the modelling process, sets of desirable gambles provide a more general representation of uncertainty. Such representation is equivalent to probability bounding. Williams (1975) introduced a consistency principle for sets of desirable gambles called *avoiding sure loss*.

In this talk, I present linear programming problems for checking avoiding sure loss. I will discuss previous work by Walley (1991), and explain how we can effectively solve these linear programming problems by looking at three different methods and exploiting the structure of the problem.

**Amirah Alharthi** University of Leeds

**Weighted sampling in random forest**

Recently the amount of data being produced has increased greatly. As a result of this increase in quantity of data, specifically the focus of this research is labelled data, efficient methods to extract knowledge from and to predict how new data should be classified are essential. Classification trees and random forests methods are two powerful predictive models that are used for these tasks.

In this research, classification trees are fitted on bootstraps of weighted observations based on a given distribution, these are then aggregated by taking the majority vote. This procedure is considered as a generalization of the current method known as bagging. The main goal is to test whether this different technique will change each tree structure and the prediction or not.

**Ayon Mukherjee** Queen Mary University of London

**Covariate-Adjusted Response-Adaptive Designs in Clinical Trials where the Survival Responses of Patients Follow a Semi-Parametric Model**

Covariate-adjusted response-adaptive (CARA) designs use the available responses to skew the treatment allocation in a clinical trial in favour of the treatment found at an interim stage of the trial to be best for a given patient’s covariate profile.

There has recently been extensive research on diverse aspects of CARA design with the patient responses assumed to follow a theoretical model. However the range of application for such designs becomes limited in real life clinical trials where the responses of the patients infrequently fit a certain parametric form. On the other hand, the parametric assumption yields robust estimates about the covariate adjusted treatment effect. To balance these two requirements, designs are hereby developed without any distributional assumption about the survival responses, relying only on the assumption of proportional hazards of patients between the two treatment arms.

The proposed designs have been developed in two ways, namely, by deriving two variants of optimum allocation, and also by using an appropriate link-function. The optimal designs are based on the doubly-adaptive biased coin design (DBCD) in one case, and the efficient randomized adaptive design (ERADE) in the other. The derived treatment allocation proportions for these designs converge towards the expected targeted values. The design based on the link function is derived using the distribution function of a Gumbel model. The comparative merits of the proposed designs have been elaborated, their preferred application has been discussed in detail, and their operating characteristics have also been established through extensive simulation study. An existing clinical trial has been redesigned by applying the proposed methods.

**Abdullah Ali H Ahmadini** Durham University

**An imprecise statistical method for accelerated life testing using the Arrhenius-Weibull model.**

Accelerated life testing (ALT) has been used frequently may obtain information on the life

time of devices. Testing items under normal conditions require a lot of time and a heavy

cost. To determine the reliability of the devices tested in short time of period, accelerated

life testing is used frequently in these scenarios. The idea behind ALT is to test a unit under

physical high stress levels (for example, temperature, voltage, or pressure) that are greater

than the normal stress level. Therefore, the devices will fail more quickly, which enables

the estimation of the lifetime at the normal conditions using the extrapolations based on

an accelerated life testing model.

There are usually two components concerning ALT; the life distribution (example, Weibull or Lognormal) and the relationship between failure time and stress level (e.g. Arrhenius-law or power-law) to extrapolate to lifetime at normal use condition. The latter is often suggested by engineers on the basis of physical or chemical theory. The Arrhenius model may be used when the failure mechanism is driven by temperature.

This work represents an examination of the statistical methods based on imprecise probabilities for accelerated life testing where nonparametric predictive inference at normal stress levels is integrated with a projected parametric Arrhenius-Weibull model. We consider predictive inference at the normal stress level, in combination with an estimated parametric Arrhenius model linking observations at dierent stress levels. In this light, imprecision provides some robustness. For further robustness, we explore imprecision in the Arrhenius model, which results in observations of increased stress levels to be transformed to interval-valued observations at the normal stress level. Simulation studies are presented to investigate the performance of the proposed method in order to establish appropriate links between stress-test levels.

** Samira Abushilah** University of Leeds

**Permutation Free Homogeneity Test for Bivariate Von-Mises Models**