The objective behind this study was to mathematically analyse, model and forecast the vital rates (mortality and fertility) of Nepal. In order to attain this goal, the data have been converted into tables and analysed intensively using several softwares such as Mocrosoft Excel, SPSS, Mathematica. The margin of error of data has been analysed. In Chapter 4, the error and uncertainity in the data have been analysed using Bayesian analysis. The reliability of the data of Nepal has been compared with the reliability of the data of Germany. The mortality and fertility conditions of Nepal have been compared from two angles. Data on India (particularly north India) have provided comparison on the socio-economic grounds whereas data on Germany(with accurate and abundant data) have provided comparison on the ground of data availability and accuracy. Thus in addition to analysing and modeling the data, the regional behaviour has been studied. The limited and defective data of Nepal have posed a challange at every stage and phase. Because of this very long term forecasting of mortality could not be made. But the model has provided a lot of information on the mortality for the years for which the data were lacking. But in the comming future, with new data at hand and with the new models developed here, it could be possible to do long term projections. In the less developed world, rural and urban areas have a big impact on the mortality and fertility of a country. The rural and urban effects on mortality and fertility have been studied individually. While analyzing the mortality scene of Nepal, it has been observed that the mortality is decreasing. The decrease is slow, but it reflects the advancement in medical facilities and health awareness. The fertility is also decreasing. There is a decrease in the number of children per woman and per family. This decrease is more pronounced in the urban areas as compared to the rural areas. This also reflects that the family planning programmes launched are showing results, particularly in urban areas.

This thesis investigates time series analysis tools for prediction, as well as detection and characterization of dependencies, informed by dynamical systems theory. Emphasis is placed on the role of delays with respect to information processing in dynamical systems, as well as with respect to their effect in causal interactions between systems. The three main features that characterize this work are, first, the assumption that time series are measurements of complex deterministic systems. As a result, functional mappings for statistical models in all methods are justified by concepts from dynamical systems theory. To bridge the gap between dynamical systems theory and data, differential topology is employed in the analysis. Second, the Bayesian paradigm of statistical inference is used to formalize uncertainty by means of a consistent theoretical apparatus with axiomatic foundation. Third, the statistical models are strongly informed by modern nonlinear concepts from machine learning and nonparametric modeling approaches, such as Gaussian process theory. Consequently, unbiased approximations of the functional mappings implied by the prior system level analysis can be achieved. Applications are considered foremost with respect to computational neuroscience but extend to generic time series measurements.