The present study is divided into two parts: the first is on developing the statistical analysis and modeling of mortality (or incidence) trends using Bayesian joinpoint regression and the second is on fitting differential equations from time series data to derive the rate of change of carbon dioxide in the atmosphere. Joinpoint regression model identifies significant changes in the trends of the incidence, mortality, and survival of a specific disease in a given population. Bayesian approach of joinpoint regression is widely used in modeling statistical data to identify the points in the trend where the significant changes occur. The purpose of the present study is to develop an age-stratified Bayesian joinpoint regression model to describe mortality trends assuming that the observed counts are probabilistically characterized by the Poisson distribution. The proposed model is based on Bayesian model selection criteria with the smallest number of joinpoints that are sufficient to explain the Annual Percentage Change (APC). The prior probability distributions are chosen in such a way that they are automatically derived from the model index contained in the model space. The proposed model and methodology estimates the age-adjusted mortality rates in different epidemiological studies to compare the trends by accounting the confounding effects of age. The future mortality rates are predicted using the Bayesian Model Averaging (BMA) approach. As an application of the Bayesian joinpoint regression, first we study the childhood brain cancer mortality rates (non age-adjusted rates) and their Annual Percentage Change (APC) per year using the existing Bayesian joinpoint regression models in the literature. We use annual observed mortality counts of children ages 0-19 from 1969-2009 obtained from Surveillance Epidemiology and End Results (SEER) database of the National Cancer Institute (NCI). The predictive distributions are used to predict the future mortality rates. We also compare this result with the mortality trend obtained using joinpoint software of NCI, and to fit the age-stratified model, we use the cancer mortality counts of adult lung and bronchus cancer (25-85+ years), and brain and other Central Nervous System (CNS) cancer (25-85+ years) patients obtained from the Surveillance Epidemiology and End Results (SEER) data base of the National Cancer Institute (NCI). The second part of this study is the statistical analysis and modeling of noisy data using functional data analysis approach. Carbon dioxide is one of the major contributors to Global Warming. In this study, we develop a system of differential equations using time series data of the major sources of the significant contributable variables of carbon dioxide in the atmosphere. We define the differential operator as data smoother and use the penalized least square fitting criteria to smooth the data. Finally, we optimize the profile error sum of squares to estimate the necessary differential operator. The proposed models will give us an estimate of the rate of change of carbon dioxide in the atmosphere at a particular time. We apply the model to fit emission of carbon dioxide data in the continental United States. The data set is obtained from the Carbon Dioxide Information Analysis Center (CDIAC), the primary climate-change data and information analysis center of the United States Department of Energy. The first four chapters of this dissertation contribute to the development and application of joinpiont and the last chapter discusses the statistical modeling and application of differential equations through data using functional data analysis approach.

Tyrimo tikslas. Nustatyti mirtingumo nuo savižudybių ir išorinių priežasčių dinamikos tendencijas Lietuvoje ir kitose ES (Europos Sąjungos) šalyse 1996–2006 metais, pritaikant šiuolaikinius dinamikos analizės metodus. Metodai. Naudotas aprašomasis epidemiologinis tyrimas. Tirtas mirtingumas nuo visų išorinių priežasčių bendrai (pagal TLK-10 kodavimą V01-Y98), bei nuo savižudybių (pagal TLK-10 kodavimą X60-X84) 18-oje ES šalių. Darbe naudoti 18-os ES valstybių populiacijų vidurkiai ir mirusiųjų nuo išorinių priežasčių, ir nuo savižudybių skaičius 18-oje penkmetinių amžiaus grupių, iš viso 324 amžiaus grupės. Remiantis šiais duomenimis, tiesioginės standartizacijos būdu apskaičiuotas kiekvienos populiacijos standartizuotas (pagal Europos standartą) mirtingumo nuo išorinių priežasčių ir savižudybių rodiklis 100 000 gyventojų, nustatytos ir palygintos rodiklių tendencijos tarp šalių. Duomenų suvedimui ir analizei panaudotos MICROSOFT EXCEL 2003, WINPEPI modulis Describe (v. 1.78), JOINPOINT (v. 3.2.0), Harward Graphics 98 (v. 6.50), MAP WIEVER (v. 5.00) programos. Buvo skaičiuojami šie statistiniai rodikliai: standartizuoti mirtingumo rodikliai, standartinė paklaida (SE), kasmetinis absoliutus pokytis (KAP), kasmetinis procentinis kitimas (KPK), 95 proc. pasikliautinieji intervalai (95% PI), duomenys laikyti statistiškai reikšmingi, kai p<0,05. Rezultatai. Daugelyje ES šalių 1996–2006 m. buvo stebimos mirtingumo nuo išorinių priežasčių mažėjimo tendencijos, tačiau šio periodo... [toliau žr. visą tekstą] / SUMMARY The aim of study was to determine the trends of mortality from external causes and suicides in Lithuania and other EU (European Union) countries in 1996-2006, using advanced trend analysis methods. Methods. Study design – descriptive epidemiology. Mortality from all external causes (by ICD-10 coding V01-Y98) and from suicides (by ICD-10 coding X60-X84) was analyzed in eighteen EU countries. It was used midyear of every countries population, numbers of deaths from external causes and from suicides based on five-year age groups, which totaled to 324 groups. Age-standardized (European standard population) mortality rates (per 100 000 persons) from causes mentioned above was calculated calculated using direct method. These standardized values were used to determine the trends, comparisons with other countries was made. MICROSOFT EXCEL 2003, WINPEPI module Describe (v. 1.78), JOINPOINT (v. 3.2.0), Harward Graphics 98 (v. 6.50), MAP WIEVER (v. 5.00) statistical packages and programmes were used for data processing and analysis. The following indices was calculated: standardized mortality rates, weighted standard error (SE), annual absolute change (AAC), annual percentage change (APC), 95% confidence intervals, data considered significant, when p<0,05. Results. In most of the EU countries it was observed decreasing mortalityrates from external causes over the period 1996-2006, but at the earlier phase of this period in some countries mortality rates increased. At the latest... [to full text]

There has been a long discussion about macroeconomic variables influencing the level of aggregate credit risk in the economy. While literature provides both empirical evidence and theoretical explana- tion of the influence of the business cycle on credit risk, the effect of other macroeconomic variables has not been explored sufficiently. In addition, recent literature suggests the existence of a latent risk factor behind aggregate credit risk, which is regularly interpreted as the latent default cycle. This thesis provides in its first part a discussion of potential aggregate credit risk drivers, which have been previously suggested in literature. We verify using a linear regression model whether the effect of these macroeconomic variables is also apparent in the Czech Republic. Results seem to be stable for both different model specifications and different clients segments and are in line with previous studies. The second part of this thesis explicitly models the latent factor that is assumed behind aggregate credit risk by adding an unobserved component to the already existing model constructed earlier in this thesis. The unobserved component can be estimated by applying Kalman filter. We subsequently discuss the sources of the latent component and whether it can be interpreted as the default cycle. The...

In all of the developed countries, malignant neoplasms are, along with cardiovascular diseases, among the most frequent causes of death. This tendency persists in the European Union countries for many years. The goal of this diploma thesis is to analyze the development of mortality caused by selected malignant neoplasms in the European Union countries from the year 1996 until 2010. The analysis is divided into 4 sections. Aside from standard demographic methods of evaluating the mortality rates by means of age-adjusted death rates calculation, statistical methods are used in this thesis as well. Primary methods used are Joinpoint regression, analysis of the course of specific death rates according to age groups and cluster analysis. In the observed period of time, mortality caused by stomach, cervical, and within the male population also respiratory tract malignant neoplasms declines. On the contrary, within the female population, the death rate caused by respiratory tract malignant neoplasms increases. Malignant skin melanoma represent a great future danger concerning the male population, and malignant pancreatic neoplasms concerning both genders. Over the observed time period, malignant skin melanoma death rate almost doubled in some of the countries. Within the European Union, the variations...

Since the beginning of the global outbreak, the Swedish Public Health Agency has been closely monitoring the situation regarding COVID-19. Understanding and mapping the behaviour of the COVID-19 epidemic curve in Sweden is of great interest and conducting a descriptive analysis may yield additional important insights. This thesis focused on determining when a potential trend changes occurred by studying time series over the trend development of the COVID-19 incidence rates provided by the Swedish Public Health Agency. Joinpoint regression with grid search were used to analyse each individual region as well as the nation. Results from respective analyses were used to compare if a region notably differed from the national trend in regard to location and trend. The findings indicated that there are more potential changes in trends in the data than identified and that several regions appeared to differ from the nation, implying that more research is required.