Dynamic Models and Nonlinear Filtering of Wave Propagation in Random Fields

In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the nonlinear filtering problems are given in the form of dynamic evolution equations of the estimated quantities. Finally, examples are provided to illustrate the practical applications of the proposed theory.Comment: 12 pages, 1 figur

Relative risk estimation of tuberculosis disease mapping with stochastic equations

Tuberculosis (TB) is one of the death leading causes in developing countries. The current monitoring of the disease is based only on the total cases reported. Alternatively, a better approach called disease mapping offers geographic distribution of the disease relative risk. Previous studies used Standard Mortality Ratio (SMR) and Poisson-gamma models to estimate relative risk but these models have several drawbacks. SMR model cannot detect relative risk for small areas while Poisson-gamma model cannot allow for covariate adjustments. Hence, the objective of this study is to develop an alternative statistical model in estimating the relative risk called stochastic Susceptible-Latently infected-Infectious-Recovered (SLIR). There are four phases in this study. Firstly, the deterministic SLIR model for TB disease transmission is developed. Then, the stochastic SLIR model is constructed. Next, the stochastic SLIR model is used to estimate the relative risk for the disease. Later, the performance of the stochastic SLIR model is compared with other existing models based on relative risk values. Finally, the TB risk maps are constructed. For numerical analysis, this study used a data set of Malaysia TB cases reported from 2008 to 2015. Findings show that there is a large difference of relative risk estimation values when using stochastic SLIR model compared to existing models. This is clearly visible through disease mapping as some locations change colour from low tone (low risk) to darker tone (higher risk). This is due to the inclusion of latent component in the stochastic SLIR model. As a conclusion, this study offers a better model in estimating relative risk for TB disease. The findings may assist the government in prioritizing locations which need further attention especially in terms of health policy and financial support

A nonparametric penalized likelihood approach to density estimation of space–time point patterns

In this work, we consider space-time point processes and study their continuous space-time evolution. We propose an innovative nonparametric methodology to estimate the unknown space-time density of the point pattern, or, equivalently, to estimate the intensity of an inhomogeneous space-time Poisson point process. The presented approach combines maximum likelihood estimation with roughness penalties, based on differential operators, defined over the spatial and temporal domains of interest. We first establish some important theoretical properties of the considered estimator, including its consistency. We then develop an efficient and flexible estimation procedure that leverages advanced numerical and computation techniques. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can effectively capture complex multi-modal and strongly anisotropic spatio-temporal point patterns; moreover, these point patterns may be observed over planar or curved domains with non -trivial geometries, due to geographic constraints, such as coastal regions with complicated shorelines, or curved regions with complex orography. In addition to providing estimates, the method's functionalities also include the introduction of appropriate uncertainty quantification tools. We thoroughly validate the proposed method, by means of simulation studies and applications to real-world data. The obtained results highlight significant advantages over state-of-the-art competing approaches

Spatial point pattern analysis with application to confocal microscopy data

Imperial Users onl

Modeling and estimation of space-time stochastic processes.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.Microfiche copy available in Archives and Engineering.Includes bibliographical references.Ph.D