We have reduced recursive parameter estimation to Kalman filtering, with a few added fixes. By incorporating projections in the parameter gain updates and parameter variance estimates, the recursive maximum likelihood method asymptotically becomes a reformulation and fix-up of the extended Kalman filter used as a parameter estimator (EKFPE), except that an additional n x n linear symmetric matr...

Most mathematical models include parameters that need to be determined from measurements. The estimated values of these parameters and their uncertainties depend on assumptions made about noise levels, models, or prior knowledge. But what can we say about the validity of such estimates, and the influence of these assumptions? This paper is concerned with methods to address these questions, and ...

The uncertainty is proportional to the noise level, is dependent on the geology and is influenced by the acquisition geometry. Because of the nonlinearity of the inversion problem, azimuthal AVO inversion will always produce a positive estimate of the anisotropy gradient even if the media is isotropic; thus it is important that this attribute be examined along with its uncertainty. The interpre...

A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular , it is shown thatˆdN − d = OP ((Log N) 3 N), where d = (d1, d2) denotes the long memory parameter.

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In experiments involving many variables, investigators typically use multiple comparisons procedures to determine differences that are unlikely to be the result of chance. However, investigators rarely consider how the magnitude of the greatest observed effect sizes may have been subject to bias resulting from multiple testing. These questions of bias become important to the extent investigator...

Algorithms for retrieval of geophysical parameters from radiances measured by instruments onboard satellites play a large role in helping scientists monitor the state of the planet. Current retrieval algorithms based on neural networks are superior in accuracy and speed compared to physics-based algorithms like iterated minimum variance (IMV). However, they do not have any form of error estimat...

We discuss weighted least squares estimates of ill-conditioned linear inverse problems where weights are chosen to be inverse error covariance matrices. Least squares estimators are the maximum likelihood estimate for normally distributed data and parameters, but here we do not assume particular probability distributions. Weights for the estimator are found by ensuring its minimum follows a χ d...

Maps are frequently used to display spatial distributions of parameters of interest, such as cancer rates or average pollutant concentrations by county. It is well known that plotting observed rates can have serious drawbacks when sample sizes vary by area, since very high (and low) observed rates are found disproportionately in poorly-sampled areas. Unfortunately, adjusting the observed rates ...