Durham University Statistics and Probability Group
Durham University Statistics and Probability

Previous Talks 2017/2018

Wednesday 20th June 2018:

We are going to start with 2 postgraduate talks by Nawapon Nakharutai and Jordan Oakley at 11:00 and 11:30 respectively (abstracts follow below), followed by an hour lunch break. At 13:00 Professor Nikolai Kolev from the University of Sao Paolo is going to give a lecture titled Introduction to Copulas. All the talks are going to be held in our usual room CM105. Everyone is welcome and probability and statistics postgraduate students are highly encouraged to attend.

Odds and free coupon: modelling by desirability axioms and checking avoiding sure loss via the Choquet integral

Speaker: Nawapon Nakharutai, Department of Mathematical Sciences

Abstract

In the UK betting market, bookmakers often offer a free coupon to new customers. These free coupons allow the customer to place extra bets, at lower risk, in combination with the usual betting odds. We are interested in whether a customer can exploit these free coupons in order to make a sure gain, and if so, how the customer can achieve this. To answer this question, we model the odds and free coupon as a set of desirable gambles for the bookmaker. We show that we can use the Choquet integral to check whether this set of desirable gambles incurs sure loss for the bookmaker, and hence, results in a sure gain for the customer. In the latter case, we also show how a customer can determine the combination of bets that make the best possible gain, based on complementary slackness. As an illustration, we look at some actual betting odds in the market and find that, without free coupons, the set of desirable gambles derived from those odds avoids sure loss. However, with free coupons, we identify some combinations of bets that customers could place in order to make a guaranteed gain.

Monitoring Renal Failure: An application of Dynamic Models

Speaker: Jordan Oakley, Department of Mathematical Sciences

Abstract

Evidence suggests that changes in the urine output and blood chemistries indicate injury to the kidney or impairment of kidney function. These changes are warnings of serious clinical consequences, but traditionally most studies emphasise the most severe reduction in kidney function. It has only been recently that minor decreases of kidney function have been recognised as potentially important in the critically ill. Identifying and intervening in patients with minor decreases in kidney function is clinically important as this can prevent patients from reaching more severe reductions in kidney failure. The KDIGO (Kidney Disease Improving Global Outcomes) guidelines are a clinical practice guideline for the diagnosis, evaluation, prevention, and treatment of kidney disease and are currently used worldwide to identify a whole range of levels of kidney failure. In this presentation I will discuss how the KDIGO guidelines are too sensitive when classifying adverse outcomes due to kidney deterioration and show how dynamic models and Bayesian forecasting offer a powerful framework for the modelling and analysis of noisy time series which are subject to abrupt changes in pattern.

Introduction to Copulas

Speaker: Professor Nikolai Kolev, Institute of Mathematics and Statistics, University of Sao Paulo

Wednesday 9th May 2018:

Cooperative Models of Stochastic Growth

Speaker: Marcelo Costa, Department of Mathematical Sciences, Durham University

Abstract

The problem we want to address in this talk is “Given an evolving population comprised of many types of individuals, how to simultaneously keep track of the size and composition of the population as time goes to infinity?” More specifically, consider a sequence of positive integer-valued random vectors denoted by x_n = (x_1(n), . . . , x_d(n)), where each coordinate accounts for the number of individuals of each type at time n=0,1,2,... To generate such a sequence, given x_n, choose a random coordinate k in {1, . . . , d}. The probability that a particular coordinate k is chosen is proportional to a non-decreasing function f_k evaluated at a certain linear combination of x_j, for j=1,...d, whose coefficients c_kj ≥ 0 measures how strongly j cooperates with k. Given the choice of k in {1,...,d}, update vector x_n by adding 1 to the k-th coordinate and then reiterate this procedure. Finally, given the functions f_k and coefficients c_kj for k,j=1,...,d, what can one say about the limiting behaviour of (1/n).x_n as n goes to infinity? In this talk we discuss some specific cases of the above formulation, and present our results and conjectures.

Wednesday 29th November 2017:

Estimating the effectiveness of digital commerce advertising campaigns using geo-experiment.

Speaker: Iman Al-Hasani, Department of Mathematical Sciences, Durham University

Abstract

A geo-experiment is an approach used to measure the effectiveness of digital commerce advertising campaigns where a region of interest is partitioned into geographical targeting areas called geos. The geos are then divided into two groups such that the campaign for geos in the second group is modified. The aim is to construct an efficient design for targeting the modified advertising campaign. A primary challenge is that covariates, such as socio-economic status are not recorded in available digital commerce data although these covariates are likely to affect the probability of making purchases. The population distribution of some covariates is known but it is likely that there are other important unknown and unobserved covariates. The challenge therefore is to design the campaign in a robust way which permits estimation of the effectiveness of the modified campaign. A stochastic simulation platform has been built for studying the effectiveness of advertising campaigns. However, due to the computational resource required, the use of simulation limits the complexity of study which can be carried out. A theoretical framework is developed to study the implications of unobserved covariates for inferences about estimated effects for geo-experiments. An important part of the framework is a proxy model linking the fitted model, without covariates, and the assumed truth which includes unobserved covariates. The proxy model makes possible the application of standard results in the literature on maximum likelihood estimation for mis-specified models.

Wednesday, 15 November 2017:

The next stats4grads is going to take place next Wednesday and it's going to be slightly different than the one's we are used to! Daniel, Tathagata, Jordan, Jonathan and Ahmad recently started their new postgraduate life in the department and they are going to give some brief presentations about themselves, their previous studies and their plans for their new work. The goal of this event is to make them feel welcome and comfortable and potentially make some first steps in order to build a big and strong postgraduate community for statistics and probability! So don't hesitate to come on Wednesday, meet them, listen to their talks and speak with them! The event is going to take place on Wednesday 15th November, 1pm, CM219.

Wednesday, 1st November 2017:

An American option pricing method based on Nonparametric Predictive Inference

Speaker: Ting He

Abstract: We applied the Nonparametric Predictive Inference (NPI), an imprecise probability method, to the American option pricing procedure, and found out it breaks the theory of rational option pricing: Never early exercise an American call option without dividends.

Wednesday, 25 October, 2017:

Random-Oriented Percolation

Speaker: Clare Wallace, Department of Mathematical Sciences, Durham University

Abstract: Models of random-oriented percolation have been studied for almost thirty years. We use a point-process approach to Grimmett’s model to give expressions for crossing probabilities in terms of expected numbers of pivotal edges, and describe how geometrical investigation of pivotal edges could lead to a new understanding of the critical probability of this model.

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