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This paper presents an R package, fdaMocca, that provides routines for model-based functional cluster analysis for functional data with optional covariates. The idea is to cluster functional subjects (often called functional objects) into homogenous groups by using spline smoothers (for functional data) together with scalar covariates. The spline coefficients and the covariates are modelled as a multivariate Gaussian mixture model, where the number of mixtures corresponds to the number of clusters. The parameters of the model are estimated by maximizing the observed mixture likelihood via an EM algorithm. The usefulness of fdaMocca and its clustering methods is illustrated on a functional data set with covariates from 6400 annual seasonal patterns of varved lake sediment from Lake Kassjön (Northern Sweden). Each varve contains information about the weather the year the varve was formed and thus may be used to reconstruct past climate.

We have developed a homemade neutron flux detection module with 3He tube hot-swap capability and control-rich Android software interface. Real-time data analysis is done by a smartphone with Android application interfaced with the detector via a USB cable. This setup can be used as a neutron and gamma ray background detector or as a compact, mobile 3He tubes calibration tool making it a cheap and easy-to-use alternative for the stationary setups. A fast neutron detection algorithm was implemented as a set of Java scripts and tested for real-time signal analysis. The modular structure of the device allows easy deployment and customization with further software development and regular upgrades. The current prototype was tested at the Nuclear Physics Research Institute under different neutron flux intensity conditions from the VVR-K water-cooled research reactor. Its simplicity and significantly lower cost, compared with conventional detector equipment, make it valuable for easy repetitive tasks with medium requirements for precision and neutron flux intensities.

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.

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.

Annually laminated (varved) lake sediments constitutes excellent environmental archives, and have the potential to play an important role for understanding past seasonal climate with their inherent annual time resolution and within-year seasonal patterns. We propose to use functional data analysis methods to extract the relevant information with respect to climate reconstruction from the rich but complex information in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates. In particular we analyze varved sediment from lake Kassjon in northern Sweden, covering the past 6400 years. The properties of each varve reflect to a large extent weather conditions and internal biological processes in the lake the year that the varve was deposited. Functional clustering is used to group the seasonal patterns into different types, that can be associated with different weather conditions. The seasonal patterns were described by penalized splines and clustered by the k-means algorithm, after alignment. The observed (within-year) variability in the data was used to determine the degree of smoothing for the penalized spline approximations. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

BACKGROUND AND AIMS: Little is known about health impacts of climate in pre-industrial societies. We used historical data to investigate the association of temperature and precipitation with total and age-specific mortality in Skellefteå, northern Sweden, between 1749 and 1859.

METHODS: We retrieved digitized aggregated population data of the Skellefteå parish, and monthly temperature and precipitation measures. A generalized linear model was established for year to year variability in deaths by annual and seasonal average temperature and cumulative precipitation using a negative binomial function, accounting for long-term trends in population size. The final full model included temperature and precipitation of all four seasons simultaneously. Relative risks (RR) with 95% confidence intervals (CI) were calculated for total, sex- and age-specific mortality.

RESULTS: In the full model, only autumn precipitation proved statistically significant (RR 1.02; CI 1.00-1.03, per 1cm increase of autumn precipitation), while winter temperature (RR 0.98; CI 0.95-1.00, per 1 °C increase in temperature) and spring precipitation (RR 0.98; CI 0.97-1.00 per 1 cm increase in precipitation) approached significance. Similar effects were observed for men and women. The impact of climate variability on mortality was strongest in children aged 3-9, and partly also in older children. Infants, on the other hand, appeared to be less affected by unfavourable climate conditions.

CONCLUSIONS: In this pre-industrial rural region in northern Sweden, higher levels of rain during the autumn increased the annual number of deaths. Harvest quality might be one critical factor in the causal pathway, affecting nutritional status and susceptibility to infectious diseases. Autumn rain probably also contributed to the spread of air-borne diseases in crowded living conditions. Children beyond infancy appeared most vulnerable to climate impacts.

Processes controlling sediment yield vary over a range of timescales, although most process-based observations are extremely short. Lake sediments, however, can be used to extend the observational timescale and are particularly useful when annually laminated (varved) sediment is present. The sediment record at Kassjön (N. Sweden) consists of ∼6400 varves, each 0·5–1 mm thick. Image analysis was used to determine grey-scale variation and varve thickness from which annual minerogenic accumulation rate (MinAR) (mg cm⁻² year⁻¹) was inferred for the period 4486 BC – AD 1900. MinAR varies on annual to centennial scales and mainly reflects channel bank erosion by the inflow streams. The mineral input reflects the intensity of the spring run-off, which is dependent on the amount of snow accumulated during the winter, and hence MinAR is a long-term record of variability in past winter climate; other factors will be a variable response to catchment uplift, vegetation succession and pedogenesis. A major shift from low to high MinAR occurred ∼250 BC, and peaks occurred around AD 250, 600, 1000, 1350 and 1650. Wavelet power spectrum analysis (confirmed by Fourier analyses) indicated significantly different periodicities throughout the period 4000 BC – AD 1700, including 275 years for the period 4000 BC – 2900 BC, 567 years for the period 2901 BC – 1201 BC, and 350 and 725 years for the period 1200 BC – AD 1700. The long-term, centennial scale variability (∼350 years) may reflect solar forcing (cf the 385-year peak in tree-ring calibrated ¹⁴C activity) but interestingly, there is no obvious link to high frequency forcing, such as the North Atlantic Oscillation. The high resolution component of the record highlights the relevance of varved lake sediment records for understanding erosion dynamics in undisturbed forested catchments and their link to long-term climate dynamics and future climate change.