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Stochastic Modelling (stochastic + modelling)
Selected AbstractsStochastic Modelling for Systems Biology by D. J. WilkinsonJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2007John Haigh No abstract is available for this article. [source] Stochastic modelling of global solar radiation measured in the state of KuwaitENVIRONMETRICS, Issue 7 2002S. A. Al-Awadhi Abstract Two stochastic models that capture the main features of daily exposure of global radiation in Kuwait are proposed. The development of these models is based on removing the annual periodicity and seasonal variation of solar radiation. Thus the daily radiation is decomposed as the sum of the trend component and a stochastic component. In many situations, there are dramatic changes in the radiation series through the year due to the condition of the weather, as is the case of the data from Kuwait. This would affect the accuracy of the model, and therefore the series is divided into two regimes: one corresponds to clear days where the value of the global radiation would be normal and the other to non-clear days where the value of global radiation would be very low. Then the trend component is expressed as a Fourier series taking into account such apparent breaks in the series. The stochastic component is first tested for linearity and Gaussianity and it is found that it does not satisfy these assumptions. Therefore, a linear time series model (ARMA modeling) may not be adequate and, to overcome this problem, a bilinear time series is used to model the stochastic component of daily global radiation in Kuwait. The method proposed considers first fitting an AR model to the data and then seeing whether a further reduction in the mean sum of squares can be achieved by introducing extra bilinear terms. The Akaike Information Criterion (AIC) is used to select the best model. Copyright © 2002 John Wiley & Sons, Ltd. [source] Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec, Canada)HYDROLOGICAL PROCESSES, Issue 1 2007Behrouz Ahmadi-Nedushan Abstract Successful applications of stochastic models for simulating and predicting daily stream temperature have been reported in the literature. These stochastic models have been generally tested on small rivers and have used only air temperature as an exogenous variable. This study investigates the stochastic modelling of daily mean stream water temperatures on the Moisie River, a relatively large unregulated river located in Québec, Canada. The objective of the study is to compare different stochastic approaches previously used on small streams to relate mean daily water temperatures to air temperatures and streamflow indices. Various stochastic approaches are used to model the water temperature residuals, representing short-term variations, which were obtained by subtracting the seasonal components from water temperature time-series. The first three models, a multiple regression, a second-order autoregressive model, and a Box and Jenkins model, used only lagged air temperature residuals as exogenous variables. The root-mean-square error (RMSE) for these models varied between 0·53 and 1·70 °C and the second-order autoregressive model provided the best results. A statistical methodology using best subsets regression is proposed to model the combined effect of discharge and air temperature on stream temperatures. Various streamflow indices were considered as additional independent variables, and models with different number of variables were tested. The results indicated that the best model included relative change in flow as the most important streamflow index. The RMSE for this model was of the order of 0·51 °C, which shows a small improvement over the first three models that did not include streamflow indices. The ridge regression was applied to this model to alleviate the potential statistical inadequacies associated with multicollinearity. The amplitude and sign of the ridge regression coefficients seem to be more in agreement with prior expectations (e.g. positive correlation between water temperature residuals of different lags) and make more physical sense. Copyright © 2006 John Wiley & Sons, Ltd. [source] A domain decomposition method for modelling Stokes flow in porous materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002Guangli Liu Abstract An algorithm is presented for solving the Stokes equation in large disordered two-dimensional porous domains. In this work, it is applied to random packings of discs, but the geometry can be essentially arbitrary. The approach includes the subdivision of the domain and a subsequent application of boundary integral equations to the subdomains. This gives a block diagonal matrix with sparse off-block components that arise from shared variables on internal subdomain boundaries. The global problem is solved using a biconjugate gradient routine with preconditioning. Results show that the effectiveness of the preconditioner is strongly affected by the subdomain structure, from which a methodology is proposed for the domain decomposition step. A minimum is observed in the solution time versus subdomain size, which is governed by the time required for preconditioning, the time for vector multiplications in the biconjugate gradient routine, the iterative convergence rate and issues related to memory allocation. The method is demonstrated on various domains including a random 1000-particle domain. The solution can be used for efficient recovery of point velocities, which is discussed in the context of stochastic modelling of solute transport. Copyright © 2002 John Wiley & Sons, Ltd. [source] On stochastic modelling of linear circuitsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2010Tarun Kumar Rawat Abstract In this paper, the deterministic modelling of linear circuits is replaced by stochastic modelling by including variance in the parameters (resistance, inductance and capacitance). Our method is based on results from the theory of stochastic differential equations. This method is general in the following sense. Any electrical circuit that consists of resistances, inductances and capacitances can be modelled by ordinary differential equations, in which the parameters of the differential operators are the functions of circuit elements. The deterministic ordinary differential equation can be converted into a stochastic differential equation by adding noise to the input potential source and to the circuit elements. The noise added in the potential source is assumed to be a white noise and that added in the parameters is assumed to be a correlated process because these parameters change very slowly with time and hence must be modelled as a correlated process. In this paper, we model a series RLC circuit by using the proposed method. The stochastic differential equation that describes the concentration of charge in the capacitor of a series RLC circuit is solved. Numerical simulations in MATLAB are obtained using the Euler,Maruyama method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Residual Autocorrelation Distribution in the Validation Data SetJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2000Alessandro Fasso Testing model performance on a data set other than the data set used for estimation is common practice in econometrics, technological stochastic modelling and environmetrics. In this paper, using an ARMAX model, the asymptotic distribution of the residual autocorrelations in the validation data set is given and a ,2 test for overall residual incorrelation is considered. [source] Continuous-time stochastic modelling of capital adequacy ratios for banksAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2006Casper H. Fouche Abstract Regulation related to capital requirements is an important issue in the banking sector. In this regard, one of the indices used to measure how susceptible a bank is to failure, is the capital adequacy ratio (CAR). We consider two types of such ratios, viz. non-risk-based (NRBCARs) and risk-based (RBCARs) CARs. According to the US Federal Deposit Insurance Corporation (FDIC), we can further categorize NRBCARs into leverage and equity capital ratios and RBCARs into Basel II and Tier 1 ratios. In general, these indices are calculated by dividing a measure of bank capital by an indicator of the level of bank risk. Our primary objective is to construct continuous-time stochastic models for the dynamics of each of the aforementioned ratios with the main achievement being the modelling of the Basel II capital adequacy ratio (Basel II CAR). This ratio is obtained by dividing the bank's eligible regulatory capital (ERC) by its risk-weighted assets (RWAs) from credit, market and operational risk. Mainly, our discussions conform to the qualitative and quantitative standards prescribed by the Basel II Capital Accord. Also, we find that our models are consistent with data from FDIC-insured institutions. Finally, we demonstrate how our main results may be applied in the banking sector. Copyright © 2005 John Wiley & Sons, Ltd. [source] | |||||||||||||