We study mathematical methods and models for analyzing and representing data. Our research combines probability theory and stochastic processes with abstract and linear algebra to understand uncertainty, randomness, and the structure of statistical models.
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Pauliina Ilmonen Professor Multivariate extreme values, functional data analysis, cancer epidemiology |
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Lasse Leskelä Professor Mathematical statistics, probability theory, network analysis |
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Kaie Kubjas Associate Professor Algebraic statistics |
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Vanni Noferini Associate Professor Network analysis, random matrix theory |
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Jukka Kohonen Senior University Lecturer Statistics, combinatorics |
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Jonas Tölle Senior University Lecturer Stochastic analysis, stochastic dynamics, stochastic processes |
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Pekka Pere University Lecturer Statistics |
See the complete list of current members and alumni.
A complete publication list for all group members is available in the Aalto research database.
Understanding the demand signal is important for forecasting, but the upstream demand signal is generally known to be harder to forecast due to the bullwhip effect. Consumer demand is transformed into a different signal after ordering policies are applied to it, forming the signal that is observed upstream and used for forecasting. This thesis extends the bullwhip literature by studying the full distributional shape of the upstream demand signal, not only its variance. Consumer demand is modelled with a count distribution, the negative binomial, whereas it is usually modelled with continuous Gaussian or AR(1) demand. The objective is to analyse how consumer demand characteristics and retailer ordering policy jointly shape the statistical properties and distributional form of the sell-in signal. The method used to study this is a two-echelon supply chain simulation where an order-up-to policy is applied to negative binomial consumer demand. Multiple non-linearities are also added to the ordering policy: batch rounding, minimum order quantity, and a non-negativity constraint. The simulation is run for 5 184 parameter and demand-scenario combinations, and the resulting sell-in signals are analysed using summary statistics, Spearman correlation, Morris-style sensitivity analysis, and distribution fitting using MLE with model selection based on AIC and BIC. The results show that the dominant drivers of demand signal transformation from ordering policies are the review period and the lead time. An elevated zero proportion is a characteristic of the upstream sell-in signal compared to consumer demand. Of the tested count data distributions, Poisson-Tweedie dominates for the raw sell-in signals, but transforming the unit data to batch-count data changes the situation so that ZINB and ZIP win over Poisson-Tweedie for most runs. The batch-count transform is itself an important finding, as it reduces dispersion and removes the lattice structure that batch sizes impose, making the signal more suitable for count distributions.
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We teach courses in probability and statistics at all levels. Some of the offered courses are eligible as a basis for an SHV degree in insurance mathematics. Doctoral education in probability and statistics is coordinated by the Finnish Doctoral Education Network in Stochastics and Statistics (FDNSS).
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