Developments Under the Freedom of Information Act

This article reviews authors' recently developed algorithm for identification of nonlinear state-space models under missing observations and extends it to the case of unknown model structure. In order to estimate the parameters in a state-space model, one needs to know the model structure and have an estimate of states. If the model structure is unknown, an approximation of it is obtained using radial basis functions centered around a maximum a posteriori estimate of the state trajectory. A particle filter approximation of smoothed states is then used in conjunction with expectation maximization algorithm for estimating the parameters. The proposed approach is illustrated through a real application

On the construction of probabilistic Newton-type algorithms

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available

Newton-based maximum likelihood estimation in nonlinear state space models

Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher's identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results.Comment: 17 pages, 2 figures. Accepted for the 17th IFAC Symposium on System Identification (SYSID), Beijing, China, October 201

Dairy Farming and the Effects of Agricultural, Nonpoint-source Pollution on Stream Water Quality, Johnson Creek Watershed, Whatcom County, Washington

The Johnson Creek watershed, which supports one of the highest densities of dairy farms in Washington State, suffers from degraded stream water quality, primarily in the form of high fecal coliform concentrations, elevated nutrients, and low levels of dissolved oxygen. Despite the implementation of best management practices (BMPs) over the past two decades, poor stream water quality has persisted. The Washington State Department of Ecology (DOE) is therefore required under section 303(d) of the federal Clean Water Act, to establish a Total Maximum Daily Load (TMDL) policy for the basin as a means of remediating the impaired water bodies. The current project was undertaken to assist DOE with this task by conducting a water quality study to determine the present quality of the surface waters and determine the location and mode by which farm waste enters the stream. BMP effectiveness was also reassessed by conducting historical water quality comparisons. Currently, stream water quality within the watershed remains impaired by fecal coliform, ammonia, nitrates, phosphates, and dissolved oxygen. An examination of standard box plots shows a redundant pattern of water quality impairment at specific sampling sites, indicating the general location of potential source areas. Box plots arranged by sampling date also show that stream water quality is most severely impaired during the wettest portion of the year and tends to improve as precipitation diminishes through the summer months. This suggests that runoff from fertilizer-laden fields is the primary mode by which dairy waste enters the stream. Stream water models, constructed to predict nutrient transport, confirm the box plot interpretations and show, through a process of load-accounting, that the majority of the nutrient loading originates from specific dispersed (nonpoint) source areas. Historical comparisons of median data values, substantiated with Maim-Whitney hypothesis testing, showed decreasing trends for ammonia and fecal coliform concentrations, and improvements in the dissolved oxygen levels over the past 20 years, indicting BMPs have been at least partially successful at preventing the direct input of farm waste into the stream. Numerous farms within the basin, however, are presently operating without up-to-date farm waste management programs and a correspondence was found between these operators and the portions of the stream identified as farm waste input source areas. In addition, increasing trends were observed for nitrates and phosphates, which corresponds with a nearly two fold increase in the total herd size and subsequent manure production within the basin over the last two decades. To approach stream water quality compliant with state and federal regulations, at a minimum, all of the dairies operating within the watershed need to adhere to prudent waste management techniques. To attain complete water quality compliance, future regulatory policies within the Johnson Creek watershed may need to be more intrusive and could include herd size caps, a moratorium on winter manure spreading, or the establishment of a stream buffer