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Clustering misaligned dependent curves applied to varved lake sediment for climate reconstruction
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Politecnico di Milano, Italy.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. (Arcum)
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2017 (Engelska)Ingår i: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 31, nr 1, s. 71-85Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

In this paper we introduce a novel functional clustering method, the Bagging Voronoi K-Medoid Aligment (BVKMA) algorithm, which simultaneously clusters and aligns spatially dependent curves. It is a nonparametric statistical method that does not rely on distributional or dependency structure assumptions. The method is motivated by and applied to varved (annually laminated) sediment data from lake Kassjön in northern Sweden, aiming to infer on past environmental and climate changes. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

Ort, förlag, år, upplaga, sidor
Springer, 2017. Vol. 31, nr 1, s. 71-85
Nyckelord [en]
Functional data, Clustering, Dependence, Misalignment, Sediment data
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-130727DOI: 10.1007/s00477-016-1287-6ISI: 000394278600006OAI: oai:DiVA.org:umu-130727DiVA, id: diva2:1069687
Tillgänglig från: 2017-01-30 Skapad: 2017-01-30 Senast uppdaterad: 2018-06-09Bibliografiskt granskad
Ingår i avhandling
1. Functional clustering methods and marital fertility modelling
Öppna denna publikation i ny flik eller fönster >>Functional clustering methods and marital fertility modelling
2017 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Umeå: Umeå universitet, 2017. s. 24
Nyckelord
censoring, Coale-Trussell model, EM-algorithm, functional data analysis, functional clustering, marital fertility, normal approximation, Poisson process, varved lake sediments, warping
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematisk statistik
Identifikatorer
urn:nbn:se:umu:diva-130734 (URN)978-91-7601-669-5 (ISBN)
Disputation
2017-02-24, Hörsal 1, Lindellhallen, Umeå Universitet, Umeå, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2017-02-03 Skapad: 2017-02-01 Senast uppdaterad: 2018-06-09Bibliografiskt granskad

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Abramowizc, KonradArnqvist, PerSjöstedt de Luna, Sara

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