Necessary and Sufficient Condition for Nonsingular Fisher Information Matrix in ARMA and Fractional ARIMA Models

It is demonstrated that a necessary and sufficient condition for the Fisher information matrix of a causal and invertible ARMA to be nonsingular is that the model not be redundant; that is, the autoregressive and moving-average polynomials have no roots in common. This result is also extended to fractional ARIMA models.     

Bayesian texture segmentation of weed and crop images using reversible jump Markov chain Monte Carlo methods

Summary. A Bayesian method for segmenting weed and crop textures is described and implemented. The work forms part of a project to identify weeds and crops in images so that selective crop spraying can be carried out. An image is subdivided into blocks and each block is modelled as a single texture. The number of different textures in the image is assumed unknown. A hierarchical Bayesian procedure is used where the texture labels have a Potts model (colour Ising Markov random field) prior and the pixels within a block are distributed according to a Gaussian Markov random field, with the parameters dependent on the type of texture. We simulate from the posterior distribution by using a reversible jump Metropolis–Hastings algorithm, where the number of different texture components is allowed to vary. The methodology is applied to a simulated image and then we carry out texture segmentation on the weed and crop images that motivated the work.     

Coal demand,market forces,and U.S. coal mine closures

Economic transitions have the potential to displace workers and cause social unrest. Coal mine closures and the resulting employment losses in rural areas have become salient issues. Using data on coal mine and power plant operation, we model closure as a function of expected profits, which allows us to compare the effects on mine closure of specific demand and supply shocks to expected mine profits. Increasing costs of production have had a large impact on closures, but lower natural gas prices and lower electricity demand have played more recently important roles.     

State estimation for nonlinear state-space transmission models of tuberculosis

Given the high prevalence of tuberculosis (TB) and the mortality rate associated with the disease, numerous models, such as the Gammaitoni and Nucci (GN) model, were developed to model the risk of transmission. These models typically rely on a quanta generation rate as a measurement of infectivity. Since the quanta generation rate cannot be measured directly, the unique contribution of this work is to develop state estimators to estimate the quanta generation rate from available measurements. To estimate the quanta generation rate, the GN model is adapted into an augmented single-room GN model and a simplified two-room GN model. Both models are shown to be observable, i.e., it is theoretically possible to estimate the quanta generation rate given available measurements. Kalman filters are used to estimate the quanta generation rate. First, a continuous-time extended Kalman filter is used for both adapted models using a simulation and measurement sampling rate of 60 s. Accurate quanta generate rate estimates are achieved in both cases. A more realistic scenario is also considered with a measurement sampling rate of one day. For these estimates, a hybrid extended Kalman filter (HEKF) is used. Accurate quanta generation rate estimates are achieved for the more realistic scenario. Future work could potentially use the HEKFs, the adapted models, and real-time measurements in a control system feedback loop to reduce the transmission of TB in confined spaces such as hospitals.