The production data of mineral resources are noisy, nonstationary, and nonlinear. Therefore, some... more The production data of mineral resources are noisy, nonstationary, and nonlinear. Therefore, some techniques are required to address the problem of nonstationarity and complexity of noises in it. In this paper, two hybrid models (EMD-CEEMDAN-EBT-MM and WA-CEEMDAN-EBT-MM) flourish to improve mineral production prediction. First, we use empirical mode decomposition (EMD) and wavelet analysis (WA) to denoise the data. Second, ensemble empirical mode decomposition (EEMD) and complete ensemble empirical mode decomposition (CEEMDAN) are used for the decomposition of nonstationary data into intrinsic mode function (IMF). Then, empirical Bayesian threshold (EBT) is applied on noise dominant IMFs to consolidate noises, which are further used as input in the data-driven model. Next, other noise-free IMFs are used in the stochastic model as input for the prediction of minerals. At last, the predicted IMFs are ensemble for final prediction. The proposed strategy is exemplified using Pakistan...
The standardized precipitation index (SPI) is one of the most widely used indices for characteriz... more The standardized precipitation index (SPI) is one of the most widely used indices for characterizing and monitoring drought in various regions. SPI's applicability has regional and time-scale constraints when it observes in several homogeneous climatic regions with similar characteristics. It also does not provide sufficient knowledge about precipitation deficits and the spatiotemporal evolution of drought. Therefore, a new method, the regional spatially agglomerative continuous drought probability monitoring system (RSACDPMS), is proposed to obtain spatiotemporal information and monitor drought characteristics more expeditiously. The proposed framework uses spatially agglomerative precipitation (SAP) and copulas’ functions to continuously monitor the drought probability in the homogenous region. The RSACDPMS is validated in the region of the Northern area of Pakistan. The outcomes of the current study provide a better quantitative way to obtain appropriate information about pre...
River inflow prediction plays an important role in water resources management and power-generatin... more River inflow prediction plays an important role in water resources management and power-generating systems. But the noises and multi-scale nature of river inflow data adds an extra layer of complexity towards accurate predictive model. To overcome this issue, we proposed a hybrid model, Variational Mode Decomposition (VMD), based on a singular spectrum analysis (SSA) denoising technique. First, SSA his applied to denoise the river inflow data. Second, VMD, a signal processing technique, is employed to decompose the denoised river inflow data into multiple intrinsic mode functions (IMFs), each with a relative frequency scale. Third, Empirical Bayes Threshold (EBT) is applied on non-linear IMF to smooth out. Fourth, predicted models of denoised and decomposed IMFs are established by learning the feature values of the Support Vector Machine (SVM). Finally, the ensemble predicted results are formulated by adding the predicted IMFs. The proposed model is demonstrated using daily river in...
Extremes precipitation may cause a series of social, environmental, and ecological problems. Esti... more Extremes precipitation may cause a series of social, environmental, and ecological problems. Estimation of frequency of extreme precipitations and its magnitude is vital for making decisions about hydraulic structures such as dams, spillways, and dikes. In this study, we focus on regional frequency analysis of extreme precipitation based on monthly precipitation records (1999–2012) at 17 stations of Northern areas and Khyber Pakhtunkhwa, Pakistan. We develop regional frequency methods based on L-moment and partial L-moments (L- and PL-moments). The L- and PL-moments are derived for generalized extreme value (GEV), generalized logistic (GLO), generalized normal (GNO), and generalized Pareto (GPA) distributions. The Z-statistics and L- and PL-moments ratio diagrams of GNO, GEV, and GPA distributions were identified to represent the statistical properties of extreme precipitation in Northern areas and Khyber Pakhtunkhwa, Pakistan. We also perform a Monte Carlo simulation study to exami...
According to the experimental results maximum days to root appearance, number of roots, root leng... more According to the experimental results maximum days to root appearance, number of roots, root length and root diameters were obtained in silt media. Minimum number of days to root appearance, number of roots and root length were obtained in sawdust while minimum root diameter, was noted in farm yard manure. Maximum number of roots, root length were obtained in layers made on June 18, while maximum days to root appearance, root diameter were noted in layers made on July 18. Minimum number of days to root appearance, number of roots, root length, root diameter were obtained in layers made on May 18.
Sulfate causes various health issues for human if
on average daily intake of sulfate is more than... more Sulfate causes various health issues for human if on average daily intake of sulfate is more than 500 mg from drinking-water, air, and food. Moreover, the presence of sulfate in rainwater causes acid rains which has harmful effects on animals and plants. Food is the major source of sulfate intake; however, in areas of South-Punjab, Pakistan, the drinking-water containing high levels of sulfate may constitute the principal source of intake. The spatial behavior of sulfate in groundwater is recorded for South-Punjab province, Pakistan. The spatial dependence of the response variable (sulfate) is modeled by using various variograms models that are estimated by maximum likelihood method, restricted maximum likelihood method, ordinary least squares, and weighted least squares. The parameters of estimated variogram models are utilized in ordinary kriging, universal kriging, Bayesian kriging with constant trend, and varying trend and the above methods are used for interpolation of sulfate concentration. The K-fold cross validation is used to measure the performances of variogram models and interpolation methods. Bayesian kriging with a constant trend produces minimum root mean square prediction error than other interpolation methods. Concentration of sulfate in drinking water within the study area is increasing to the Northern part, and health risks are really high due to poor quality of water.
In the present paper, a new Gamma cost function is proposed for an optimum allocation
in multivar... more In the present paper, a new Gamma cost function is proposed for an optimum allocation in multivariate stratified random sampling with linear regression estimator. Extended lexicographic goal programming is used for solution of multi-objective non-linear integer allocation problem. A real data set is used to illustrate the application.
Sulfate is a key parameter for water quality and is commonly used in manufacturing of fertilizers... more Sulfate is a key parameter for water quality and is commonly used in manufacturing of fertilizers, soaps, glass, papers, and common household items. If sulfate quantity is more than a threshold, it is hazardous for health. In the present paper, we use Bayesian kriging with external drift and Gaussian spatial predictive process model to analyze the spatial behavior of response variable (Sulfate). Different informative and non-informative priors are utilized to estimate the correlation parameters. The performance of these models are compared by means of twofold cross validation with deviance information criterion, and root mean square prediction as criterion. In summary, the inclusion of covariates plays an important role in minimizing the mean square prediction error. Bayesian kriging with external drift performs better than Gaussian spatial predictive process. The predictive distribution of Bayesian kriging with external drift is also applicable for interpolation of sulfate concentration at unobserved locations.
Modeling the spatio-temporal distribution and characteristics of particulate matter remains a foc... more Modeling the spatio-temporal distribution and characteristics of particulate matter remains a focal point of research. In the present study we model the spatio-temporal structure of 10 PM with and without a spatial trend made of environmental covariates. (i) Spatio-temporal interpolation without accounting for covariates is done by using ordinary space-time kriging. (i) To include covariates into the model we propose the following methodology, a combination of methods that has not been investigated before: generalized additive regression is employed to capture the effects of the covariates by partitioning the output into a trend and a residual component. Furthermore, the unknown trend components at ungauged locations are estimated by spatial artificial neural networks and the corresponding residual components are predicted by means of ordinary space-time kriging based on a nested spatio-temporal covariance function that is optimized by a particle swarm algorithm. The results of both methods (i and ii) are compared by means of cross validation and it is found that the new methodology which takes the covariates into account performs significantly better, in particular, it yields a smaller mean squared error.
The approximate Bayesian computation (ABC) algorithm is used to estimate parameters from complica... more The approximate Bayesian computation (ABC) algorithm is used to estimate parameters from complicated phenomena, where likelihood is intractable. Here, we report the development of an algorithm to choose the tolerance level for ABC. We have illustrated the performance of our proposed method by simulating the estimation of scaled mutation and recombination rates. The result shows that the proposed algorithm performs well.
The space-time interpolation of precipitation has significant contribution to river control, rese... more The space-time interpolation of precipitation has significant contribution to river control, reservoir operations, forestry interest and flash flood watches etc. The changes in environmental covariates and spatial covariates make space-time estimation of precipitation a challenging task. In the present paper, we use a generalized additive model with Gaussian link function to account for the effect of covariates; the resulting output is partitioned into two parts; trend component and residual component. The trend component is modeled on the basis of spatial artificial neural network (SANN) architecture. The residual component is assumed to be a spatio-temporal random field and is modeled using hierarchical Bayesian interpolation (HBI) method. The separable stationary space-time nested covariance model and purely spatial non-stationary non-parametric covariance model for interpolation of the residual component are used. For the interpolation of the amount of precipitation at ungauged locations the interpolated residual components for ungauged locations are added to the respective interpolated trend components. The results of two covariance functions are compared by means of cross-validations and suggest that HBI including covariates provides minimum mean square prediction error if the nested spatio-temporal stationary covariance model is used.
The space-time interpolation of precipitation has significant contribution to river control,reser... more The space-time interpolation of precipitation has significant contribution to river control,reservoir operations, forestry interest and flash flood watches etc. The changes in environmental covariates and spatial covariates make space-time estimation of precipitation a challenging task. In our earlier paper [1], we used transformed hirarchical Bayesian sapce-time interpolation method for predicting the amount of precipiation. In present paper, we modified the [2] method to include covarites which varaies with respect to space-time. The proposed method is applied to estimating space-time monthly precipitation in the monsoon periods during 1974 - 2000. The 27-years monthly average data of precipitation, temperature, humidity and wind speed are obtained from 51 monitoring stations in Pakistan. The average monthly precipitation is used response variable and temperature, humidity and wind speed are used as time varying covariates. Moreovere the spatial covarites elevation, latitude and longitude of same monitoring stations are also included. The cross-validation method is used to compare the results of transformed hierarchical Bayesian spatio-temporal interpolation with and without including environmental and spatial covariates. The software of [3] is modified to incorprate enviornmental covariates and spatil covarites. It is observed that the transformed hierarchical Bayesian method including covarites provides more accuracy than the transformed hierarchical Bayesian method without including covarites. Moreover, the five potential monitoring cites are selected based on maximum entropy sampaling design approach. References [1] I.Hussain, J.Pilz,G. Spoeck and H.L.Yu. Spatio-Temporal Interpolation of Precipitation during Monsoon Periods in Pakistan. submitted in Advances in water Resources,2009. [2] N.D. Le, W. Sun, and J.V. Zidek, Bayesian multivariate spatial interpolation with data missing by design. Journal of the Royal Statistical Society. Series B (Methodological), 501-510, 1997. [3] N.D. Le, and J.V. Zidek, Statistical analysis of environmental space-time processes, Springer Verlag, (2006), PP. 272-294
The restrictions of the analysis of natural processes which are observed at any point in space or... more The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974-2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.
The restrictions of the analysis of natural processes which are observed at any point in space or... more The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974-2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.
The main objective of this study was to evaluate the salinity of ground water of the shallow well... more The main objective of this study was to evaluate the salinity of ground water of the shallow wells and delineation of maps using spatial statistics approach. The water samples were collected from 833 wells located in the rural areas at shallow depth (<100 ft) of Lahore district and recorded their geographic coordinates. In order to achieve this objective, all samples were analyzed for electrical conductivity (EC). Regarding electrical conductivity (EC) in the shallow ground water, 432 samples (51.9% of the samples) were found fit for irrigation, 160 samples (19.2%) were found marginally fit and 241 samples (28.9%) unfit when compared with the standard values for irrigation purpose. Ordinary Kriging and Bayesian Kriging are used to interpolate and observe the behavior of EC in the entire domain of the study. The performance of ordinary Kriging and Bayesian Kriging were compared by means of cross validation. It is concluded that Bayesian Kriging produced less mean square prediction error as compared with that by Ordinary Kriging. It was observed that the value of electric conductivity was very high between longitude 74 o 27′ to 74 o 33′ and latitude 31 o 3′ to 31 o 34′ whereas in North-East of Lahore district the electric conductivity was very low. Overall, electric conductivities of the ground waters examined in the present study were higher with reference to the standard values used for crop irrigation.
The production data of mineral resources are noisy, nonstationary, and nonlinear. Therefore, some... more The production data of mineral resources are noisy, nonstationary, and nonlinear. Therefore, some techniques are required to address the problem of nonstationarity and complexity of noises in it. In this paper, two hybrid models (EMD-CEEMDAN-EBT-MM and WA-CEEMDAN-EBT-MM) flourish to improve mineral production prediction. First, we use empirical mode decomposition (EMD) and wavelet analysis (WA) to denoise the data. Second, ensemble empirical mode decomposition (EEMD) and complete ensemble empirical mode decomposition (CEEMDAN) are used for the decomposition of nonstationary data into intrinsic mode function (IMF). Then, empirical Bayesian threshold (EBT) is applied on noise dominant IMFs to consolidate noises, which are further used as input in the data-driven model. Next, other noise-free IMFs are used in the stochastic model as input for the prediction of minerals. At last, the predicted IMFs are ensemble for final prediction. The proposed strategy is exemplified using Pakistan...
The standardized precipitation index (SPI) is one of the most widely used indices for characteriz... more The standardized precipitation index (SPI) is one of the most widely used indices for characterizing and monitoring drought in various regions. SPI's applicability has regional and time-scale constraints when it observes in several homogeneous climatic regions with similar characteristics. It also does not provide sufficient knowledge about precipitation deficits and the spatiotemporal evolution of drought. Therefore, a new method, the regional spatially agglomerative continuous drought probability monitoring system (RSACDPMS), is proposed to obtain spatiotemporal information and monitor drought characteristics more expeditiously. The proposed framework uses spatially agglomerative precipitation (SAP) and copulas’ functions to continuously monitor the drought probability in the homogenous region. The RSACDPMS is validated in the region of the Northern area of Pakistan. The outcomes of the current study provide a better quantitative way to obtain appropriate information about pre...
River inflow prediction plays an important role in water resources management and power-generatin... more River inflow prediction plays an important role in water resources management and power-generating systems. But the noises and multi-scale nature of river inflow data adds an extra layer of complexity towards accurate predictive model. To overcome this issue, we proposed a hybrid model, Variational Mode Decomposition (VMD), based on a singular spectrum analysis (SSA) denoising technique. First, SSA his applied to denoise the river inflow data. Second, VMD, a signal processing technique, is employed to decompose the denoised river inflow data into multiple intrinsic mode functions (IMFs), each with a relative frequency scale. Third, Empirical Bayes Threshold (EBT) is applied on non-linear IMF to smooth out. Fourth, predicted models of denoised and decomposed IMFs are established by learning the feature values of the Support Vector Machine (SVM). Finally, the ensemble predicted results are formulated by adding the predicted IMFs. The proposed model is demonstrated using daily river in...
Extremes precipitation may cause a series of social, environmental, and ecological problems. Esti... more Extremes precipitation may cause a series of social, environmental, and ecological problems. Estimation of frequency of extreme precipitations and its magnitude is vital for making decisions about hydraulic structures such as dams, spillways, and dikes. In this study, we focus on regional frequency analysis of extreme precipitation based on monthly precipitation records (1999–2012) at 17 stations of Northern areas and Khyber Pakhtunkhwa, Pakistan. We develop regional frequency methods based on L-moment and partial L-moments (L- and PL-moments). The L- and PL-moments are derived for generalized extreme value (GEV), generalized logistic (GLO), generalized normal (GNO), and generalized Pareto (GPA) distributions. The Z-statistics and L- and PL-moments ratio diagrams of GNO, GEV, and GPA distributions were identified to represent the statistical properties of extreme precipitation in Northern areas and Khyber Pakhtunkhwa, Pakistan. We also perform a Monte Carlo simulation study to exami...
According to the experimental results maximum days to root appearance, number of roots, root leng... more According to the experimental results maximum days to root appearance, number of roots, root length and root diameters were obtained in silt media. Minimum number of days to root appearance, number of roots and root length were obtained in sawdust while minimum root diameter, was noted in farm yard manure. Maximum number of roots, root length were obtained in layers made on June 18, while maximum days to root appearance, root diameter were noted in layers made on July 18. Minimum number of days to root appearance, number of roots, root length, root diameter were obtained in layers made on May 18.
Sulfate causes various health issues for human if
on average daily intake of sulfate is more than... more Sulfate causes various health issues for human if on average daily intake of sulfate is more than 500 mg from drinking-water, air, and food. Moreover, the presence of sulfate in rainwater causes acid rains which has harmful effects on animals and plants. Food is the major source of sulfate intake; however, in areas of South-Punjab, Pakistan, the drinking-water containing high levels of sulfate may constitute the principal source of intake. The spatial behavior of sulfate in groundwater is recorded for South-Punjab province, Pakistan. The spatial dependence of the response variable (sulfate) is modeled by using various variograms models that are estimated by maximum likelihood method, restricted maximum likelihood method, ordinary least squares, and weighted least squares. The parameters of estimated variogram models are utilized in ordinary kriging, universal kriging, Bayesian kriging with constant trend, and varying trend and the above methods are used for interpolation of sulfate concentration. The K-fold cross validation is used to measure the performances of variogram models and interpolation methods. Bayesian kriging with a constant trend produces minimum root mean square prediction error than other interpolation methods. Concentration of sulfate in drinking water within the study area is increasing to the Northern part, and health risks are really high due to poor quality of water.
In the present paper, a new Gamma cost function is proposed for an optimum allocation
in multivar... more In the present paper, a new Gamma cost function is proposed for an optimum allocation in multivariate stratified random sampling with linear regression estimator. Extended lexicographic goal programming is used for solution of multi-objective non-linear integer allocation problem. A real data set is used to illustrate the application.
Sulfate is a key parameter for water quality and is commonly used in manufacturing of fertilizers... more Sulfate is a key parameter for water quality and is commonly used in manufacturing of fertilizers, soaps, glass, papers, and common household items. If sulfate quantity is more than a threshold, it is hazardous for health. In the present paper, we use Bayesian kriging with external drift and Gaussian spatial predictive process model to analyze the spatial behavior of response variable (Sulfate). Different informative and non-informative priors are utilized to estimate the correlation parameters. The performance of these models are compared by means of twofold cross validation with deviance information criterion, and root mean square prediction as criterion. In summary, the inclusion of covariates plays an important role in minimizing the mean square prediction error. Bayesian kriging with external drift performs better than Gaussian spatial predictive process. The predictive distribution of Bayesian kriging with external drift is also applicable for interpolation of sulfate concentration at unobserved locations.
Modeling the spatio-temporal distribution and characteristics of particulate matter remains a foc... more Modeling the spatio-temporal distribution and characteristics of particulate matter remains a focal point of research. In the present study we model the spatio-temporal structure of 10 PM with and without a spatial trend made of environmental covariates. (i) Spatio-temporal interpolation without accounting for covariates is done by using ordinary space-time kriging. (i) To include covariates into the model we propose the following methodology, a combination of methods that has not been investigated before: generalized additive regression is employed to capture the effects of the covariates by partitioning the output into a trend and a residual component. Furthermore, the unknown trend components at ungauged locations are estimated by spatial artificial neural networks and the corresponding residual components are predicted by means of ordinary space-time kriging based on a nested spatio-temporal covariance function that is optimized by a particle swarm algorithm. The results of both methods (i and ii) are compared by means of cross validation and it is found that the new methodology which takes the covariates into account performs significantly better, in particular, it yields a smaller mean squared error.
The approximate Bayesian computation (ABC) algorithm is used to estimate parameters from complica... more The approximate Bayesian computation (ABC) algorithm is used to estimate parameters from complicated phenomena, where likelihood is intractable. Here, we report the development of an algorithm to choose the tolerance level for ABC. We have illustrated the performance of our proposed method by simulating the estimation of scaled mutation and recombination rates. The result shows that the proposed algorithm performs well.
The space-time interpolation of precipitation has significant contribution to river control, rese... more The space-time interpolation of precipitation has significant contribution to river control, reservoir operations, forestry interest and flash flood watches etc. The changes in environmental covariates and spatial covariates make space-time estimation of precipitation a challenging task. In the present paper, we use a generalized additive model with Gaussian link function to account for the effect of covariates; the resulting output is partitioned into two parts; trend component and residual component. The trend component is modeled on the basis of spatial artificial neural network (SANN) architecture. The residual component is assumed to be a spatio-temporal random field and is modeled using hierarchical Bayesian interpolation (HBI) method. The separable stationary space-time nested covariance model and purely spatial non-stationary non-parametric covariance model for interpolation of the residual component are used. For the interpolation of the amount of precipitation at ungauged locations the interpolated residual components for ungauged locations are added to the respective interpolated trend components. The results of two covariance functions are compared by means of cross-validations and suggest that HBI including covariates provides minimum mean square prediction error if the nested spatio-temporal stationary covariance model is used.
The space-time interpolation of precipitation has significant contribution to river control,reser... more The space-time interpolation of precipitation has significant contribution to river control,reservoir operations, forestry interest and flash flood watches etc. The changes in environmental covariates and spatial covariates make space-time estimation of precipitation a challenging task. In our earlier paper [1], we used transformed hirarchical Bayesian sapce-time interpolation method for predicting the amount of precipiation. In present paper, we modified the [2] method to include covarites which varaies with respect to space-time. The proposed method is applied to estimating space-time monthly precipitation in the monsoon periods during 1974 - 2000. The 27-years monthly average data of precipitation, temperature, humidity and wind speed are obtained from 51 monitoring stations in Pakistan. The average monthly precipitation is used response variable and temperature, humidity and wind speed are used as time varying covariates. Moreovere the spatial covarites elevation, latitude and longitude of same monitoring stations are also included. The cross-validation method is used to compare the results of transformed hierarchical Bayesian spatio-temporal interpolation with and without including environmental and spatial covariates. The software of [3] is modified to incorprate enviornmental covariates and spatil covarites. It is observed that the transformed hierarchical Bayesian method including covarites provides more accuracy than the transformed hierarchical Bayesian method without including covarites. Moreover, the five potential monitoring cites are selected based on maximum entropy sampaling design approach. References [1] I.Hussain, J.Pilz,G. Spoeck and H.L.Yu. Spatio-Temporal Interpolation of Precipitation during Monsoon Periods in Pakistan. submitted in Advances in water Resources,2009. [2] N.D. Le, W. Sun, and J.V. Zidek, Bayesian multivariate spatial interpolation with data missing by design. Journal of the Royal Statistical Society. Series B (Methodological), 501-510, 1997. [3] N.D. Le, and J.V. Zidek, Statistical analysis of environmental space-time processes, Springer Verlag, (2006), PP. 272-294
The restrictions of the analysis of natural processes which are observed at any point in space or... more The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974-2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.
The restrictions of the analysis of natural processes which are observed at any point in space or... more The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974-2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.
The main objective of this study was to evaluate the salinity of ground water of the shallow well... more The main objective of this study was to evaluate the salinity of ground water of the shallow wells and delineation of maps using spatial statistics approach. The water samples were collected from 833 wells located in the rural areas at shallow depth (<100 ft) of Lahore district and recorded their geographic coordinates. In order to achieve this objective, all samples were analyzed for electrical conductivity (EC). Regarding electrical conductivity (EC) in the shallow ground water, 432 samples (51.9% of the samples) were found fit for irrigation, 160 samples (19.2%) were found marginally fit and 241 samples (28.9%) unfit when compared with the standard values for irrigation purpose. Ordinary Kriging and Bayesian Kriging are used to interpolate and observe the behavior of EC in the entire domain of the study. The performance of ordinary Kriging and Bayesian Kriging were compared by means of cross validation. It is concluded that Bayesian Kriging produced less mean square prediction error as compared with that by Ordinary Kriging. It was observed that the value of electric conductivity was very high between longitude 74 o 27′ to 74 o 33′ and latitude 31 o 3′ to 31 o 34′ whereas in North-East of Lahore district the electric conductivity was very low. Overall, electric conductivities of the ground waters examined in the present study were higher with reference to the standard values used for crop irrigation.
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Papers by Ijaz Hussain
on average daily intake of sulfate is more than 500 mg from
drinking-water, air, and food. Moreover, the presence of sulfate
in rainwater causes acid rains which has harmful effects
on animals and plants. Food is the major source of sulfate
intake; however, in areas of South-Punjab, Pakistan, the
drinking-water containing high levels of sulfate may constitute
the principal source of intake. The spatial behavior of
sulfate in groundwater is recorded for South-Punjab province,
Pakistan. The spatial dependence of the response variable
(sulfate) is modeled by using various variograms models that
are estimated by maximum likelihood method, restricted
maximum likelihood method, ordinary least squares, and
weighted least squares. The parameters of estimated variogram
models are utilized in ordinary kriging, universal kriging,
Bayesian kriging with constant trend, and varying trend
and the above methods are used for interpolation of sulfate
concentration. The K-fold cross validation is used to measure
the performances of variogram models and interpolation
methods. Bayesian kriging with a constant trend produces
minimum root mean square prediction error than other interpolation methods. Concentration of sulfate in drinking
water within the study area is increasing to the Northern part,
and health risks are really high due to poor quality of water.
in multivariate stratified random sampling with linear regression estimator. Extended
lexicographic goal programming is used for solution of multi-objective non-linear integer
allocation problem. A real data set is used to illustrate the application.
on average daily intake of sulfate is more than 500 mg from
drinking-water, air, and food. Moreover, the presence of sulfate
in rainwater causes acid rains which has harmful effects
on animals and plants. Food is the major source of sulfate
intake; however, in areas of South-Punjab, Pakistan, the
drinking-water containing high levels of sulfate may constitute
the principal source of intake. The spatial behavior of
sulfate in groundwater is recorded for South-Punjab province,
Pakistan. The spatial dependence of the response variable
(sulfate) is modeled by using various variograms models that
are estimated by maximum likelihood method, restricted
maximum likelihood method, ordinary least squares, and
weighted least squares. The parameters of estimated variogram
models are utilized in ordinary kriging, universal kriging,
Bayesian kriging with constant trend, and varying trend
and the above methods are used for interpolation of sulfate
concentration. The K-fold cross validation is used to measure
the performances of variogram models and interpolation
methods. Bayesian kriging with a constant trend produces
minimum root mean square prediction error than other interpolation methods. Concentration of sulfate in drinking
water within the study area is increasing to the Northern part,
and health risks are really high due to poor quality of water.
in multivariate stratified random sampling with linear regression estimator. Extended
lexicographic goal programming is used for solution of multi-objective non-linear integer
allocation problem. A real data set is used to illustrate the application.