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Abstract

‘Hard’ and ‘soft’ methods in analyses of territorial structures’. This article refers to two distinct approaches to investigations of territorial structures and their changes: the ‘intuitive’ of ‘soft’ approach and a more rigid, formalized or ‘hard’ one. The examples of analyzing the regional patterns in Poland over a almost 40 year span are called to illustrate these relations between two methodological standpoints. The conclusion states that both of them are valid and useful, however their strengths can be fully exposed when both are applied in an comprehensive way, supporting each other in a difficult process of investigation multidimensional and dynamic changes of the social territorial systems.
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Abstract

The s-period ahead Value-at-Risk (VaR) for a portfolio of dimension n is considered and its Bayesian analysis is discussed. The VaR assessment can be based either on the n-variate predictive distribution of future returns on individual assets, or on the univariate Bayesian model for the portfolio value (or the return on portfolio). In both cases Bayesian VaR takes into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. In the case of a large portfolio, the applicability of the n-variate approach to Bayesian VaR depends on the form of the statistical model for asset prices. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this multivariate approach and the much simpler univariate approach based on modelling volatility of the value of a given portfolio.
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Abstract

Electroencephalogram (EEG) is one of biomedical signals measured during all-night polysomnography to diagnose sleep disorders, including sleep apnoea. Usually two central EEG channels (C3-A2 and C4- A1) are recorded, but typically only one of them are used. The purpose of this work was to compare discriminative features characterizing normal breathing, as well as obstructive and central sleep apnoeas derived from these central EEG channels. The same methodology of feature extraction and selection was applied separately for the both synchronous signals. The features were extracted by combined discrete wavelet and Hilbert transforms. Afterwards, the statistical indexes were calculated and the features were selected using the analysis of variance and multivariate regression. According to the obtained results, there is a partial difference in information contained in the EEG signals carried by C3-A2 and C4-A1 EEG channels, so data from the both channels should be preferably used together for automatic sleep apnoea detection and differentiation.
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Abstract

Popular statistical techniques, such as Spearman's rank correlation matrix, principal component analysis (PCA) and multiple linear regression analysis were applied to analyze a large set of water quality data of the Rybnik Reservoir generated during semiannual monitoring. Water samples collected at 9 sampling sites located along the main axis of the reservoir were tested for 14 selected parameters: concentrations of co-occurring elements, ions and physicochemical parameters. The aim of this study was to estimate the impact of those parameters on inorganic arsenic occurrence in Rybnik Reservoir water by means of multivariate statistical methods. The spatial distribution of arsenic in Rybnik Power Station reservoir was also included. Inorganic arsenic As(III), As(V) concentrations were determined by hydride generation method (HG-AAS) using SpectrAA 880 spectrophotometer (Varian) coupled with a VGA-77 system for hydride generation and ECT-60 electrothermal furnace. Spearman's rank correlation matrix was used in order to find existing correlations between total inorganic arsenic (AsTot) and other parameters. The results of this analysis suggest that As was positively correlated with PO43-; Fe and TDS. PCA confirmed these observations. Principal component analysis resulted in three PC's explaining 57% of the total variance. Loading values for each component indicate that the processes responsible for As release and distribution in Rybnik Reservoir water were: leaching from bottom sediments together with other elements like Cu, Cd, Cr, Pb, Zn, Ni, Ca (PC1) and co-precipitation with PO43-, Fe and Mn (PC3) regulated by physicochemical properties like T and pH (PC2). Finally, multiple linear regression model has been developed. This model incorporates only 8 (T, pH, PO43-, Fe, Mn, Cr, Cu, TDS) out of initial 14 variables, as the independent predictors of total As contamination level. This study illustrates the usefulness of multivariate statistical techniques for analysis and interpretation of complex environmental data sets.
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