Browsing by Author "Blais, J. A. Rod"
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- ItemOpen AccessDiscrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data(Versita, 2010-12) Blais, J. A. Rod
- ItemOpen AccessDiscrete Spherical Harmonic Transforms of Nearly Equidistributed Global Data(Versita, 2011-06) Blais, J. A. Rod
- ItemOpen AccessDiscrete Spherical Harmonic Transforms: Numerical Preconditioning and Optimization(2008) Blais, J. A. Rod
- ItemOpen AccessDistributed Geocomputations and Web Collaboration(2009) Blais, J. A. Rod
- ItemOpen AccessExploring Monte Carlo Simulation Strategies for Geoscience Applications(2008) Blais, J. A. Rod; Grebenitcharsky, R.; Zhang, Z.
- ItemOpen AccessExploring Various Monte Carlo Simulations for Geoscience Applications(2010) Blais, J. A. Rod
- ItemOpen AccessGeocomputations and Related Web Services(2008) Blais, J. A. Rod
- ItemOpen AccessGeomatics and the New Cyber-infrastructure(Canadian Institute of Geomatics, 2008) Blais, J. A. Rod; Esche, Harold
- ItemOpen AccessLeast Squares for Practitioners(Hindawi Publishing Corporation, 2010-08-16) Blais, J. A. Rod
- ItemOpen AccessLeast Squares for Practitioners(2010-09-23) Blais, J. A. RodIn experimental science and engineering, least squares are ubiquitous in analysis and digital data processing applications. Minimizing sums of squares of some quantities can be interpreted in very different ways and confusion can arise in practice, especially concerning the optimality and reliability of the results. Interpretations of least squares in terms of norms and likelihoods need to be considered to provide guidelines for general users. Assuming minimal prerequisites, the following expository discussion is intended to elaborate on some of the mathematical characteristics of the least-squares methodology and some closely related questions in the analysis of the results, model identification, and reliability for practical applications. Examples of simple applications are included to illustrate some of the advantages, disadvantages, and limitations of least squares in practice. Concluding remarks summarize the situation and provide some indications of practical areas of current research and development.
- ItemOpen AccessLomb-Scargle Spectral Analysis of Nonequispaced Data.(2008) Orlob, M.; Blais, J. A. Rod; Braun, A.
- ItemOpen AccessModeling Precipitation Uncertainty Effect on Flood Flows in a Medium Sized Watershed(2010) Mutulu, P.; Blais, J. A. Rod
- ItemOpen AccessMonte Carlo Simulations of Gravimetric Terrain Corrections Using LIDAR Data(2010) Blais, J. A. Rod
- ItemOpen AccessOn Monte Carlo Methods and Applications in Geoscience(2009) Zhang, Z.; Blais, J. A. Rod
- ItemOpen AccessOptimal Data Structures for Spherical Multiresolution Analysis and Synthesis(2011) Blais, J. A. Rod
- ItemOpen AccessOptimal Modeling and Filtering of Stochastic Time Series for Geoscience Applications(Hindawi Publishing Corporation, 2013-04-23) Blais, J. A. Rod
- ItemOpen AccessOptimal Modeling and Filtering of Stochastic Time Series for Geoscience Applications(2013-05-16) Blais, J. A. RodSequences of observations or measurements are often modeled as realizations of stochastic processes with some stationary properties in the first and second moments. However in practice, the noise biases and variances are likely to be different for different epochs in time or regions in space, and hence such stationarity assumptions are often questionable. In the case of strict stationarity with equally spaced data, the Wiener-Hopf equations can readily be solved with fast Fourier transforms (FFTs) with optimal computational efficiency. In more general contexts, covariance matrices can also be diagonalized using the Karhunen-Loève transforms (KLTs), or more generally using empirical orthogonal and biorthogonal expansions, which are unfortunately much more demanding in terms of computational efforts. In cases with increment stationarity, the mathematical modeling can be modified and generalized covariances can be used with some computational advantages. The general nonlinear solution methodology is also briefly overviewed with the practical limitations. These different formulations are discussed with special emphasis on the spectral properties of covariance matrices and illustrated with some numerical examples. General recommendations are included for practical geoscience applications.
- ItemOpen AccessRandomness Characterization in Computing and Stochastic Simulations(2013) Blais, J. A. Rod
- ItemOpen AccessSome Reflections on Advanced Geocomputations and the Data Deluge(2012) Blais, J. A. Rod