Cramer Rao-Type Bounds for Sparse Bayesian Learning

In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. It is found that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.Comment: Accepted for publication in the IEEE Transactions on Signal Processing, 11 pages, 10 figure

Power relations, ethnicity and privatisation: A tale of a telecommunications company

The purpose of this paper is to demonstrate the confluence of political and economic interests of the Fijian elite in transforming state assets into private property and financial gain. Drawing on a Habermasian theoretical framework applied to a privatised state monopoly (Telecom Fiji), it is demonstrated how an implementation of privatisation concealed social and political interests. Thus privatisation provided a convenient rhetoric and tool of implementation for social and political gain by a ruling elite. For those inside the Telecom company, the ethos of public service could not withstand the messengers of capitalism with their rhetoric of the need for greater efficiency, effectiveness and consumer awareness. However, as for many other privatisation programmes around the world, the results are not reflected in the improved organisational performance or wellbeing of the ordinary citizen when state monopolies are privatised