Robust Benefit Function Transfer: A Bayesian Model Averaging Approach

A Benefit Function Transfer obtains estimates of Willingness-to-Pay (WTP) for the evaluation of a given policy at a site by combining existing information from different study sites. This has the advantage that more efficient estimates are obtained, but it relies on the assumption that the heterogeneity between sites is appropriately captured in the Benefit Transfer model. A more expensive alternative to estimate WTP is to analyse only data from the policy site in question while ignoring information from other sites. We make use of the fact that these two choices can be viewed as a model selection problem and extend the set of models to allow for the hypothesis that the benefit function is only applicable to a subset of sites. We show how Bayesian Model Averaging (BMA) techniques can be used to optimally combine information from all models. The Bayesian algorithm searches for the set of sites that can form the basis for estimating a Benefit function and reveals whether such information can be transferred to new sites for which only a small dataset is available. We illustrate the method with a sample of 42 forests from U.K. and Ireland. We find that BMA benefit function transfer produces reliable estimates and can increase about 8 times the information content of a small sample when the forest is ‘poolable’.Benefit Transfer; Bayesian Model Averaging; Exchangeability; Non-market Valuation; Panel Data

Using globular clusters to test gravity in the weak acceleration regime: NGC 7099

A test of Newton's law of gravity in the low acceleration regime using globular clusters is presented. New results for the core collapsed globular cluster NGC 7099 are given. The run of the gravitational potential as a function of distance is probed studying the velocity dispersion profile of the cluster, as derived from a set of 125 radial velocities with accuracy better than 1 km/s. The velocity dispersion profile is traced up to ~18 pc from the cluster center. The dispersion is found to be maximal at the center, then decrease until 10+-2 pc from the center, well inside the cluster tidal radius of 42 pc. After that the dispersion remains constant with average value 2.2+-0.3 km/s. Assuming for NGC 7099 a total V mag of M(V)=-7.43 mags and mass-to-light ratio M/L=1, the acceleration at 10 pc from the center is 1.1e-8 cm/s/s. Thus, the flattening of the velocity dispersion profile occurs for a value of the internal acceleration of gravity fully consistent with a_0=1.2e-8 cm/s/s observed in galaxies. This new result for NGC 7099 brings to 4 the clusters with velocity dispersion profile probing acceleration below a_0. All four have been found to have a flat dispersion profile at large radii where the acceleration is below a_0, mimicking qualitatively and quantitatively elliptical galaxies. Whether this indicates a failure of Newtonian dynamics in the low acceleration limit or some more conventional dynamical effect (e.g., tidal heating) is still unclear. However, the similarities emerging between very different globular clusters, as well as between globular clusters and elliptical galaxies seem to favor the first of these two possibilities.Comment: Accepted for publication in A&A Letters. Four pages in tota

Using globular clusters to test gravity in the weak acceleration regime

We report on the results from an ongoing program aimed at testing Newton's law of gravity in the low acceleration regime using globular clusters. It is shown that all clusters studied so far do behave like galaxies, that is, their velocity dispersion profile flattens out at large radii where the acceleration of gravity goes below 1e-8 cm/s/s, instead of following the expected Keplerian fall off. In galaxies this behavior is ascribed to the existence of a dark matter halo. Globular clusters, however, do not contain dark matter, hence this result might indicate that our present understanding of gravity in the weak regime of accelerations is incomplete and somehow incorrect.Comment: As published on the European Southern Observatory "the Messenger", Num. 128, June 2007. Seven pages, 4 figures, 2 table

Globular Clusters as a Test for Gravity in the Weak Acceleration Regime

Non-baryonic Dark Matter (DM) appears in galaxies and other cosmic structures when and only when the acceleration of gravity, as computed considering only baryons, goes below a well defined value a0=1.2e-8 cm/s/s. This might indicate a breakdown of Newton's law of gravity (or inertia) below a0, an acceleration smaller than the smallest probed in the solar system. It is therefore important to verify whether Newton's law of gravity holds in this regime of accelerations. In order to do this, one has to study the dynamics of objects that do not contain significant amounts of DM and therefore should follow Newton's prediction for whatever small accelerations. Globular clusters are believed, even by strong supporters of DM, to contain negligible amounts of DM and therefore are ideal for testing Newtonian dynamics in the low acceleration limit. Here, we discuss the status of an ongoing program aimed to do this test. Compared to other studies of globular clsuters, the novelty is that we trace the velocity dispersion profile of globular clusters far enough from the center to probe gravitational accelerations well below a0. In all three clusters studied so far the velocity dispersion is found to remain constant at large radii rather than follow the Keplerian falloff. On average, the flattening occurs at the radius where the cluster internal acceleration of gravity is 1.8+-0.4 x 10^{-8} cm/s/s, fully consistent with MOND predictions.Comment: Comments: To Appear in the proceeding of the "First crisis in cosmology" conference, published in the American Institute of Physiscs' proceedings series, Vol. 822. (includes 3 pages and 1 fig