Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

Curve crossing for the reflected Levy process at zero and infinity

Let $R_{t}=\sup_{0\leq s\leq t}X_{s}-X_{t}$ be a Levy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for $R_{t}$ is finite, is given. We also discuss the almost sure finiteness of $\limsup_{t\to 0}R_{t}/t^{\kappa}$, for each $\kappa\geq 0$.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Costing conservation: an expert appraisal of the pollinator habitat benefits of England’s entry level stewardship

Pollination services provided by insects play a key role in English crop production and wider ecology. Despite growing evidence of the negative effects of habitat loss on pollinator populations, limited policy support is available to reverse this pressure. One measure that may provide beneficial habitat to pollinators is England’s entry level stewardship agri-environment scheme. This study uses a novel expert survey to develop weights for a range of models which adjust the balance of Entry Level Stewardship options within the current area of spending. The annual costs of establishing and maintaining these option compositions were estimated at £59.3–£12.4 M above current expenditure. Although this produced substantial reduction in private cost:benefit ratios, the benefits of the scheme to pollinator habitat rose by 7–140 %; significantly increasing the public cost:benefit ratio. This study demonstrates that the scheme has significant untapped potential to provide good quality habitat for pollinators across England, even within existing expenditure. The findings should open debate on the costs and benefits of specific entry level stewardship management options and how these can be enhanced to benefit both participants and biodiversity more equitably.

Periodic auroral events at the high-latitude convection reversal in the 16 MLT region

Combined optical and radar observations of two breakup-like auroral events near the polar cap boundary, within 74–76° MLAT and 1210 – 1240 UT (roughly 1540 – 1610 MLT) on 9 Jan. 1989 are reported. A two-component structure of the auroral phenomenon is indicated, with a local intensification of the pre-existing arc as well as a separate, tailward moving discrete auroral event on the poleward side of the background aurora, close to the reversal between well-defined zones of sunward and tailward ion flows. The all-sky TV observations do not indicate a connection between the two components, which also show different optical spectral composition. The 16 MLT background arc is located on sunward convecting field lines, as opposed to the 12–14 MLT auroral emission observed on this day. Although the magnetospheric plasma source (s) of the 16 MLT events are not easily identified from these ground-based data alone, it is suggested that the lower and higher latitude components, may map to the plasma sheet boundary layer and along open field lines to the magnetopause boundary, respectively. The events occur at the time of enhancements of westward ionospheric ion flow and corresponding eastward electrojet current south of 74° MLAT. Thus, they seem to be very significant events, involving periodic (10 min period), tailward moving filaments of field-aligned current/discrete auroral emission at the 16 MLT polar cap boundary.

RE1 silencing transcription factor/neuron-restrictive silencing factor regulates expansion of adult mouse subventricular zone-derived neural stem/progenitor cells in vitro

Adult neural stem cell (aNSC) activity is tuned by external stimuli through the recruitment of transcription factors. This study examines the RE1 silencing transcription factor (REST) in neural stem/progenitor cells isolated from the subventricular zone of adult mouse brain and provides the first extensive characterization of REST-mediated control of the cellular and molecular properties. This study shows that REST knockdown affects the capacity of progenitor cells to generate neurospheres, reduces cell proliferation, and triggers cell differentiation despite the presence of growth factors. Genome- and transcriptome-wide analyses show that REST binding sites are significantly enriched in genes associated with synaptic transmission and nervous system development and function. Seeking candidate regulators of aNSC function, this study identifies a member of the bone morphogenetic protein (BMP) family, BMP6, the mRNA and protein of which increased after REST knockdown. The results of this study extend previous findings, demonstrating a reciprocal control of REST expression by BMPs. Administration of exogenous BMP6 inhibits aNSC proliferation and induces the expression of the astrocytic marker glial fibrillary acidic protein, highlighting its antimitogenic and prodifferentiative effects. This study suggests that BMP6 produced in a REST-regulated manner together with other signals can contribute to regulation of NSC maintenance and fate. © 2015 Wiley Periodicals, Inc.

Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

An endogenous regulator of inflammation, resolvin E1, modulates osteoclast differentiation and bone resorption

Background and purpose: The inflammation-resolving lipid mediator resolvin E1 (RvE1) effectively stops inflammation-induced bone loss in vivo in experimental periodontitis. It was of interest to determine whether RvE1 has direct actions on osteoclast (OC) development and bone resorption. Experimental approach: Primary OC cultures derived from mouse bone marrow were treated with RvE1 and analysed for OC differentiation, cell survival and bone substrate resorption. Receptor binding was measured using radiolabelled RvE1. Nuclear factor (NF)-kappa B activation and Akt phosphorylation were determined with western blotting. Lipid mediator production was assessed with liquid chromatography tandem mass spectrometry. Key results: OC growth and resorption pit formation were markedly decreased in the presence of RvE1. OC differentiation was inhibited by RvE1 as demonstrated by decreased number of multinuclear OC, a delay in the time course of OC development and attenuation of receptor activator of NF-kappa B ligand-induced nuclear translocation of the p50 subunit of NF-kappa B. OC survival and apoptosis were not altered by RvE1. Messenger RNA for both receptors of RvE1, ChemR23 and BLT(1) is expressed in OC cultures. Leukotriene B(4) (LTB(4)) competed with [(3)H] RvE1 binding on OC cell membrane preparations, and the LTB(4) antagonist U75302 prevented RvE1 inhibition of OC growth, indicating that BLT(1) mediates RvE1 actions on OC. Primary OC synthesized the RvE1 precursor 18R-hydroxy-eicosapentaenoic acid and LTB(4). Co-incubation of OC with peripheral blood neutrophils resulted in transcellular RvE1 biosynthesis. Conclusions and implications: These results indicate that RvE1 inhibits OC growth and bone resorption by interfering with OC differentiation. The bone-sparing actions of RvE1 are in addition to inflammation resolution, a direct action in bone remodelling.

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