We consider signal denoising via transform-domain shrinkage based on a novel risk criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an ε-neighborhood of the true value. The underlying parameter is assumed to be deterministic. The MPE, similar to the mean-squared error (MSE), depends on the ground-truth parameter, and therefore, has to be estimated from the noisy observations. The optimum shrinkage parameter is obtained by minimizing an estimate of the MPE. When the probability of error is integrated over ε, it leads to the expected ℓ1 distortion. The proposed MPE and ℓ1 distortion formulations are applicable to various noise distributions by invoking a Gaussian mixture model approximation. Within the realm of MPE, we also develop a specific extension to subband shrinkage. The denoising performance of MPE turns out to be better than that obtained using the minimum MSE-based approaches formulated within Stein's unbiased risk estimation (SURE) framework, especially in the low signal-to-noise ratio (SNR) regime. Performance comparisons with three benchmarking algorithms carried out on electrocardiogram signals and standard test signals taken from the Wavelab toolbox show that the MPE framework results in SNR gains particularly for low input SNR.

This paper describes a statistical method for learning and estimating the risk posed by other craft in the vicinity of a vessel and an overview of its possible spatial application, simulating how professional mariners perceive and assess such risk and using navigational data obtained from a standard integrated bridge. We propose a non-linear model for risk estimation which attempts to capture mariners' judgement. Questionnaire data has been collected that captures and quantifies mariners’ judgements of risk for craft in the vicinity, where each craft is described by measurements that can be obtained easily from the data already present in the ship's navigational equipment. The dataset has then been used for analysis, training and validating Ordered Probit models in order to obtain a computationally efficient data driven model for estimating the risk probability vector posed by other craft. Finally, we discuss how this risk model can be incorporated into decision making and path finding algorithms.

In this paper we are interested in the decision problem faced by an agent when requesting bids for collections of tasks with complex time constraints and interdependencies. In particular, we study the problem of specifying an appropriate schedule for the tasks in the request for bids. We expect bids to require resource commitments, so we expect different settings of time windows to solicit different bids and different costs. The agent is interested in soliciting “desirable” bids, where desirable means bids that can be feasibly combined in a low-cost combination that covers the entire collection of tasks. Since the request for bids has to be issued before the agent can see any bids, in this decision process there is a probability of loss as well as a probability of gain. This requires the decision process to deal with the risk posture of the person or organization on whose behalf the agent is acting. We describe a model based on Expected Utility Theory and show how an agent can attempt to maximize its profits while managing its financial risk exposure. We illustrate the operation and properties of the model and discuss what assumptions are required for its successful integration in multiagent contracting applications.