Free energy Sequential Monte Carlo, application to mixture modelling

We introduce a new class of Sequential Monte Carlo (SMC) methods, which we call free energy SMC. This class is inspired by free energy methods, which originate from Physics, and where one samples from a biased distribution such that a given function $\xi(\theta)$ of the state $\theta$ is forced to be uniformly distributed over a given interval. From an initial sequence of distributions $(\pi_t)$ of interest, and a particular choice of $\xi(\theta)$, a free energy SMC sampler computes sequentially a sequence of biased distributions $(\tilde{\pi}_{t})$ with the following properties: (a) the marginal distribution of $\xi(\theta)$ with respect to $\tilde{\pi}_{t}$ is approximatively uniform over a specified interval, and (b) $\tilde{\pi}_{t}$ and $\pi_{t}$ have the same conditional distribution with respect to $\xi$. We apply our methodology to mixture posterior distributions, which are highly multimodal. In the mixture context, forcing certain hyper-parameters to higher values greatly faciliates mode swapping, and makes it possible to recover a symetric output. We illustrate our approach with univariate and bivariate Gaussian mixtures and two real-world datasets.Comment: presented at "Bayesian Statistics 9" (Valencia meetings, 4-8 June 2010, Benidorm

An exotic deformation of the hyperbolic space

On the one hand, we construct a continuous family of non-isometric proper CAT(-1) spaces on which the isometry group ${\rm Isom}(\mathbf{H}^{n})$ of the real hyperbolic $n$-space acts minimally and cocompactly. This provides the first examples of non-standard CAT(0) model spaces for simple Lie groups. On the other hand, we classify all continuous non-elementary actions of ${\rm Isom}(\mathbf{H}^{n})$ on the infinite-dimensional real hyperbolic space. It turns out that they are in correspondence with the exotic model spaces that we construct.Comment: 42 pages, minor modifications, this is the final versio

On the heat redistribution of the hot transiting exoplanet WASP-18b

The energy deposition and redistribution in hot Jupiter atmospheres is not well understood currently, but is a major factor for their evolution and survival. We present a time dependent radiative transfer model for the atmosphere of WASP-18b which is a massive (10 MJup) hot Jupiter (Teq ~ 2400 K) exoplanet orbiting an F6V star with an orbital period of only 0.94 days. Our model includes a simplified parametrisation of the day-to-night energy redistribution by a modulation of the stellar heating mimicking a solid body rotation of the atmosphere. We present the cases with either no rotation at all with respect to the synchronously rotating reference frame or a fast differential rotation. The results of the model are compared to previous observations of secondary eclipses of Nymeyer et al. (2011) with the Spitzer Space Telescope. Their observed planetary flux suggests that the efficiency of heat distribution from the day-side to the night-side of the planet is extremely inefficient. Our results are consistent with the fact that such large day-side fluxes can be obtained only if there is no rotation of the atmosphere. Additionally, we infer light curves of the planet for a full orbit in the two Warm Spitzer bandpassses for the two cases of rotation and discuss the observational differences.Comment: 4 figures, accepted for publication in Icaru