Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields

We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R\to R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on R^d, d=1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is ``fixed domain'' (or ``infill'') asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat richer than in the Gaussian case (the latter is recovered when g is affine), in part because estimators of the type considered may have an asymptotic variance which is random in the limit. Broadly, when g is smooth and nonaffine, three types of limit distributions can arise, types (i), (ii) and (iii), say. Each type can be represented as a random integral. More specifically, type (i) can be represented as the integral of a certain random function with respect to Lebesgue measure; type (ii) can be represented as the integral of a second random functio

Saddlepoint approximation for moment generating functions of truncated random variables

We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approximation of passage time distributions in ion channel models which incorporate time interval omission. We derive two types of representation for the MGF of a truncated random variable. One of these representations is obtained by exponential tilting. The second type of representation, which has two versions, is referred to as an exponential convolution representation. Each representation motivates a different approximation. It turns out that each of the three approximations is extremely accurate in those cases ``to which it is suited.'' Moreover, there is a simple rule of thumb for deciding which approximation to use in a given case, and if this rule is followed, then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate.Comment: Published at http://dx.doi.org/10.1214/009053604000000689 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data

We propose a new distribution for analysing paleomagnetic directional data that is a novel transformation of the von Mises-Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalising constant in the new density is easy to compute and estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter which controls the tail-weight of the distribution. We also develop a general regression model framework that allows both the mean direction and the shape parameters of the error distribution to depend on covariates. The proposed regression procedure is shown to be equivariant with respect to the choice of coordinate system for the directional response. To illustrate, we analyse paleomagnetic directional data from the GEOMAGIA50.v3 database (Brown et al. 2015). We predict the mean direction at various geological 1 time points and show that there is significant heteroscedasticity present. It is envisaged that the regression structures and error distribution proposed here will also prove useful when covariate information is available with (i) other types of directional response data; and (ii) square-root transformed compositional data of general dimension

Network analysis of host-virus communities in bats and rodents reveals determinants of cross-species transmission.

Bats are natural reservoirs of several important emerging viruses. Cross-species transmission appears to be quite common among bats, which may contribute to their unique reservoir potential. Therefore, understanding the importance of bats as reservoirs requires examining them in a community context rather than concentrating on individual species. Here, we use a network approach to identify ecological and biological correlates of cross-species virus transmission in bats and rodents, another important host group. We show that given our current knowledge the bat viral sharing network is more connected than the rodent network, suggesting viruses may pass more easily between bat species. We identify host traits associated with important reservoir species: gregarious bats are more likely to share more viruses and bats which migrate regionally are important for spreading viruses through the network. We identify multiple communities of viral sharing within bats and rodents and highlight potential species traits that can help guide studies of novel pathogen emergence.This work was supported by the Research and Policy for Infectious Disease Dynamics (RAPIDD) program of the Science and Technology Directorate (US Department of Homeland Security) and the Fogarty International Center (National Institutes of Health). D.T.S.H. acknowledges funding from a David H. Smith post-doctoral fellowship. A.A.C. is partially funded by a Royal Society Wolfson Research Merit award, and J.L.N.W. is supported by the Alborada Trust. Thanks to Paul Cryan and Michael O'Donnell of the USGS Fort Collins Science Center for help with species distribution analyses.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1111/ele.1249

Spherical regression models with general covariates and anisotropic errors

Existing parametric regression models in the literature for response data on the unit sphere assume that the covariates have particularly simple structure, for example that they are either scalar or are themselves on the unit sphere, and/or that the error distribution is isotropic. In many practical situations such models are too inflexible. Here we develop richer para-metric spherical regression models in which the co-variates can have quite general structure (for example, they may be on the unit sphere, in Euclidean space, categorical, or some combination of these) and in which the errors are anisotropic. We consider two anisotropic error distributions — the Kent distribution and the elliptically symmetric angular Gaussian distribution — and two parametrisations of each which enable distinct ways to model how the response depends on the covariates. Various hypotheses of interest, such as the significance of particular covariates, or anisotropy of the errors, are easy to test, for example by classical likelihood ratio tests. We also introduce new model-based residuals for evaluating the fitted models. In the examples we consider, the hypothesis tests indicate strong evidence to favour the novel models over simpler existing ones

Long-Term Survival of an Urban Fruit Bat Seropositive for Ebola and Lagos Bat Viruses

Ebolaviruses (EBOV) (family Filoviridae) cause viral hemorrhagic fevers in humans and non-human primates when they spill over from their wildlife reservoir hosts with case fatality rates of up to 90%. Fruit bats may act as reservoirs of the Filoviridae. The migratory fruit bat, Eidolon helvum, is common across sub-Saharan Africa and lives in large colonies, often situated in cities. We screened sera from 262 E. helvum using indirect fluorescent tests for antibodies against EBOV subtype Zaire. We detected a seropositive bat from Accra, Ghana, and confirmed this using western blot analysis. The bat was also seropositive for Lagos bat virus, a Lyssavirus, by virus neutralization test. The bat was fitted with a radio transmitter and was last detected in Accra 13 months after release post-sampling, demonstrating long-term survival. Antibodies to filoviruses have not been previously demonstrated in E. helvum. Radio-telemetry data demonstrates long-term survival of an individual bat following exposure to viruses of families that can be highly pathogenic to other mammal species. Because E. helvum typically lives in large urban colonies and is a source of bushmeat in some regions, further studies should determine if this species forms a reservoir for EBOV from which spillover infections into the human population may occur

Fabular: regression formulas as probabilistic programming

Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R's formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.Adam Ścibior received travel support from the DARPA PPAML programme. Marcin Szymczak was supported by Microsoft Research through its PhD Scholarship Programme.This is the author accepted manuscript. The final version is available from the Association of Computer Machinery via http://dx.doi.org/10.1145/2837614.283765