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The Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) methodology was applied to detect changes in perennial vegetation cover at marshland sites in Northern California reported to have undergone restoration between 1999 and 2009. Results showed extensive contiguous areas of restored marshland plant cover at 10 of the 14 sites selected. Gains in either woody shrub cover and/or from a recovery of herbaceous cover that remains productive and evergreen on a year round basis could be mapped out from the image results. However, LEDAPS may not be highly sensitive changes in wetlands that have been restored mainly with seasonal herbaceous cover (e.g., vernal pools), due to the ephemeral nature of the plant greenness signal. Based on this evaluation, the LEDAPS methodology would be capable of fulfilling a pressing need for consistent, continual, low-cost monitoring of changes in marshland ecosystems of the Pacific Flyway.
This paper considers efficient set mathematics for the case where the covariance matrix of asset returns is assumed known but ex ante the vector of expected returns is replaced by an estimated or forecast value. It is shown that the ex post mean and variance differ from the standard results. Consequently the maximum Sharpe ratio portfolio also differs from the standard result. However, even with uncertainty about the vector of expected returns, subject to the assumptions made about the joint distribution of actual returns and estimated mean returns, ex post Sharpe ratio maximisers hold the ex post market portfolio. The properties of the zero beta portfolio are similar to the standard results leading to a capital market line. The ex post Capital Asset Pricing Model incorporates an intercept and the betas are not the same as those computed ex ante. The results are illustrated with an example.