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Model based functional clustering of varved lake sediments
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Climate and environmental changes are today widely discussed, and in particular the impact of human activity. To understand variations in past climate over longer time periods, historical documents, year rings from trees, ice cores from glaciers as well as lake and sea sediments are being used.In this paper we introduce a model based functional cluster analysis, giving us possibility to use both the functional form and covariates in our analysis. It also allow us to model the dependency of the chosen basis coefficients and the covariates. We also allow for different covariance structure within each cluster and give suggestions on how to determine how many clusters to use.In particular we analyze varved sediment from lake Kassjön (N Sweden) which cover more than 6400 years.

Keyword [en]
Model based functional clustering, warping, annually lake sediment data
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-130767OAI: oai:DiVA.org:umu-130767DiVA: diva2:1070040
Available from: 2017-01-31 Created: 2017-01-31 Last updated: 2017-01-31
In thesis
1. Functional clustering methods and marital fertility modelling
Open this publication in new window or tab >>Functional clustering methods and marital fertility modelling
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population.

The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions.

A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods.

Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2017. 24 p.
Keyword
censoring, Coale-Trussell model, EM-algorithm, functional data analysis, functional clustering, marital fertility, normal approximation, Poisson process, varved lake sediments, warping
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-130734 (URN)978-91-7601-669-5 (ISBN)
Public defence
2017-02-24, Hörsal 1, Lindellhallen, Umeå Universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2017-02-03 Created: 2017-02-01 Last updated: 2017-02-09Bibliographically approved

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Citation style
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