Title: The Department of Statistics & Operations Research celebrates 25th anniversary
Date: Tuesday 3 May
Time: 11:00
Venue: Lab 602, Maths and Physics building
The Department of Statistics and Operations Research is celebrating its 25th anniversary since it was founded, and for that reason, a series of departmental seminars will be held in May. The first seminar will be held on Tuesday, 3 May 2022, and it will be comprised of four 15-minute talks given by Statistics and OR academics. Please see the abstracts of the talks below.
Cultures of Statistical Discourse - with a Local Flavour
The Statistics & OR Department, instituted within the Science Faculty of UM, was intended to produce statistical instruction and research at high academic levels. That was 1997. Surely very late. The push came from the government. Malta was struggling to convince EU it would qualify for membership. Statistical discourse is often resorted to belatedly. Whether as a quantification aid in applications where randomness rules or risks have to be taken. Or entertained with mathematical sophistication. But then all such activities play out within worldwide networks. Therein lies a multitude of traditions, practices, paradigms, conflicting attitudes, and prejudices some of which will be highlighted in this talk. Major developments like Fisherian inference, the Bayesian comeback, the huge advances made by stochastics or data science can only be understood properly when contextualized. Like mathematics, statistics is a human activity which vows allegiance to logic though it ranges wildly. Running ANOVA tests, pushing through a Central Limit theorem over a class of functions, optimizing on experimental design, generalizing classification results for manifold-valued variates, estimating SDE volatility coefficients, harnessing probabilities on Hilbert spaces as priors or proving consistency through martingale convergence theorems ... the scope extends over many wide areas. And so Statistics lends itself to interaction with a multitude of fields of investigation. And to mathematics at large. But also to loads of controversies, some mathematical, others philosophical. Bayesian statistics and stochastic processes offer a wide representative demonstration of this. They will be contemplated with stronger emphasis.
Latent Variable Modelling in Time Series with Applications
Latent variable modelling refers to the inference of unobserved variables from observable data. In this talk, we look at a number of models from time series which have the ability to infer latent variables. The first is state-space models, which can be used to determine hidden states from an observed series using Kalman recursions - in particular, this model can be used for time series decomposition. We then move on to looking at hidden Markov and hidden semi-Markov models, which can both be used to infer a discrete state-space model from an observed series. For hidden Markov models, it is also easy to include covariates. Finally, we also look at how cluster analysis can be used on time series data. Cluster analysis refers to a popular group of methods for determining unknown groupings within observation sets. In particular, we look at a distance metric specific to time series data called dynamic time warping. A number of practical examples will also be given to illustrate these methods.
Dr Monique Borg Inguanez
Regularization in Statistical Techniques
In the good old days, statistical techniques were simple and easy to use. Data was scant, having few distinct variables and everything was assumed to be normally distributed. Generalized Linear Models showed us a way forward away from normality but still within the exponential family. As data collection methods evolved, one could not help but notice that data was not as well behaved as we thought but rather more irregular and certainly insistent in exposing the naivete of our models. High-dimensional data sets, for which the number of explanatory variables rival or exceed the number of observations, are increasingly important in modern-day applications. Experience showed us that most traditional statistical techniques, such as the Ordinary Least Square (OLS) and the Maximum Likelihood estimation methods do not perform well with such data and are either ill-conditioned or undefined. This has prompted us to look at more sophisticated techniques such as regularization methods which will be the protagonist of this talk. I shall give a general overview of these methods: outlining their use and look back at their origin and development.
Dr Maria Kontorinaki
The Role of Optimization in Statistics
Statistical theory and practice are helping us to make optimal decisions under uncertainty. Towards this direction, exploiting mathematical techniques developed in Optimization is necessary. As a matter of fact, the majority of statistical problems are naturally formulated as optimization problems. For instance, the problem of parameter estimation in statistical modeling reduces to a special type of optimization problem, in the sense that we aim at maximizing a likelihood function or minimizing the norm of residuals by using the least-squares approach. Optimization has been utilized in solving traditional statistical problems, but it has also played a crucial role in more recent areas such as statistical learning; in statistical learning models, one learns the best parameters for the model by minimizing some cost function under certain constraints. Optimization is also used at the stage of data collection, for example, when we design an experiment or a survey to minimize experimental or sampling errors. This talk will present a brief overview of the applications of optimization techniques in Statistics and will highlight the need for integrating a thorough and comprehensive Optimization syllabus in a Statistics course.
