Multiplicative random walk Metropolis-Hastings on the real line

In this article we propose multiplication based random walk Metropolis Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH) algorithm. This algorithm, even if simple to apply, was not studied earlier in Markov chain Monte Carlo literature. The associated kernel is shown to have standard properties like irreducibility, aperiodicity and Harris recurrence under some mild assumptions. These ensure basic convergence (ergodicity) of the kernel. Further the kernel is shown to be geometric ergodic for a large class of target densities on $\mathbb{R}$. This class even contains realistic target densities for which random walk or Langevin MH are not geometrically ergodic. Three simulation studies are given to demonstrate the mixing property and superiority of RDMH to standard MH algorithms on real line. A share-price return data is also analyzed and the results are compared with those available in the literature

Using Long-Term Volunteer Records to Examine Dormouse (Muscardinusavellanarius) Nestbox Selection.

Within ecology, there are unanswered questions about species-habitat interactions, which could potentially be resolved by a pragmatic analysis of a long-term volunteer-collected dataset. Here, we analysed 18 years of volunteer-collected data from a UK dormouse nestbox monitoring programme to determine the influence of habitat variables on nestbox choice by common dormice (Muscardinusavellanarius). We measured a range of habitat variables in a coppiced woodland in Gloucestershire, UK, and analysed these in relation to dormouse nestbox occupancy records (by dormice, other small mammals, and birds) collected by volunteers. While some characteristics of the woodland had changed over 18 years, simple transformation of the data and interpretation of the results indicated that the dataset was informative. Using stepwise regressions, multiple environmental and ecological factors were found to determine nestbox selection. Distance from the edge of the wood was the most influential (this did not change over 18 years), with boxes in the woodland interior being selected preferentially. There was a significant negative relationship with the presence of ferns (indicative of damp shady conditions). The presence of oak (a long-lived species), and the clumped structural complexity of the canopy were also important factors in the final model. There was no evidence of competition between dormice and birds or other mammals. The results provide greater understanding of artificial dormouse nest-site requirements and indicate that, in terms of habitat selection, long-term volunteer-collected datasets contribute usefully to understanding the requirements of species with an important conservation status