Bucknell Mathematics Department Blog

Title: Twitter’s Influence on TV Ratings, And Other TV Mathematics

Abstract: Nielsen’s TV Ratings are used as the currency with which key business decisions are made across the media industry. What TV programs remain on the air, which advertisements you see during commercial breaks, and when you are able to watch your favorite shows on Hulu are all questions answered by analyzing ratings and other Nielsen data. Recent technology has rapidly changed how and when people watch TV, thus quickly increasing the demand for enhanced data to give TV Networks and Advertisers a thorough understanding of the current TV landscape. Using various forms of TV Mathematics, exciting new conclusions, like whether Twitter influences TV Ratings, can be made.

Bio: Allison Gibson, an Associate Media Analytic Consultant at Nielsen, graduated from Bucknell in May 2013 with a double major in Mathematics and Italian Studies and a minor in Film Studies. While at Bucknell, she was a Tour Guide and Tour Guide Student Coordinator, Co-Founder and Musical Director of The Offbeats A Cappella group, and Vice President of Food (Public Relations) for the Mathematical Association of America. Allison has been working at Nielsen, a Fortune 500 Company known for the Nielsen TV Ratings system, since graduating about a year and a half ago. She started her career as a Research Analyst providing a wide variety of media-related data to many of Nielsen’s TV, Advertiser, and Agency clients. As of August of this year, she is an Associate Media Analytic Consultant working primarily with clients like FOX Networks, AMC Networks, Tech companies (i.e. Amazon, EBay) and the Telecom sector (i.e. Verizon, AT&T).

Title: Identifying Boundaries in Spatial Modelling for Disease Mapping

Abstract: The aim of disease mapping is to estimate the spatial pattern in disease risk across a set of areal units, in order to identify units which have elevated disease risk. Existing methods use Bayesian hierarchical models with spatially smooth conditional autoregressive priors to estimate disease risk, but these methods cannot identify the geographical extent of spatially contiguous high-risk clusters of areal units. We propose a two stage approach, which first produces a set of potential cluster structures for the data and then chooses the optimal structure by fitting an extension of the Bayesian hierarchical model. The first stage uses a hierarchical agglomerative clustering algorithm, spatially adjusted to account for the neighbourhood structure of the data. This algorithm is applied to data prior to the study period, and produces a set of n potential cluster structures. The second stage fits a Poisson log-linear model to the data, in which the optimal cluster structure and the spatial pattern in disease risk is estimated via a Markov Chain Monte Carlo (MCMC) algorithm. After assessing the methodology with a simulation study, it was applied to a study of respiratory disease risk in Glasgow, Scotland, where a number of high risk clusters were identified.

Title:  How many groups?  Visual tools for assessing cluster structure in data.

Abstract: Cluster analysis is a set of methods designed to explore and find unknown group structure in (multivariate) data. There are a wide variety of methods available, the application of which can result in many different proposed cluster structures. Particularly for more heuristic methods (e.g. hierarchical clustering), it can be difficult to make an objective decision on which method/number of clusters gives the “best” answer. One alternative that claims to address this flaw is the model-based clustering methodology – the application of, often Gaussian, mixture models usually with some likelihood based criterion for selection of the best model/number of mixture components. An issue with this approach can be its tendency to overestimate the number of groups when associating each mixture component with a cluster (estimated group). This talk seeks to present novel applications of an old fashioned clustering tool – the dendrogram – to visually assess either combination of mixture components into clusters or to assess the similarity/grouping of clustering solutions from a variety of methods (applied to the same data). The dendrogram’s tree diagram presentation is a particularly useful graphic as it can be easily understood by laypeople and is a visually appealing tool for exploratory analysis into group structure. It is also a good summary for data of arbitrary dimension.