Costa Rica's payment for environmental services program: intention, implementation, and impact.

We evaluated the intention, implementation, and impact of Costa Rica's program of payments for environmental services (PSA), which was established in the late 1990s. Payments are given to private landowners who own land in forest areas in recognition of the ecosystem services their land provides. To characterize the distribution of PSA in Costa Rica, we combined remote sensing with geographic information system databases and then used econometrics to explore the impacts of payments on deforestation. Payments were distributed broadly across ecological and socioeconomic gradients, but the 1997-2000 deforestation rate was not significantly lower in areas that received payments. Other successful Costa Rican conservation policies, including those prior to the PSA program, may explain the current reduction in deforestation rates. The PSA program is a major advance in the global institutionalization of ecosystem investments because few, if any, other countries have such a conservation history and because much can be learned from Costa Rica's experiences.

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.