Accelerating Parallel Tempering: Quantile Tempering Algorithm (QuanTA)

Using MCMC to sample from a target distribution, $\pi(x)$ on a $d$-dimensional state space can be a difficult and computationally expensive problem. Particularly when the target exhibits multimodality, then the traditional methods can fail to explore the entire state space and this results in a bias sample output. Methods to overcome this issue include the parallel tempering algorithm which utilises an augmented state space approach to help the Markov chain traverse regions of low probability density and reach other modes. This method suffers from the curse of dimensionality which dramatically slows the transfer of mixing information from the auxiliary targets to the target of interest as $d \rightarrow \infty$. This paper introduces a novel prototype algorithm, QuanTA, that uses a Gaussian motivated transformation in an attempt to accelerate the mixing through the temperature schedule of a parallel tempering algorithm. This new algorithm is accompanied by a comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach; concluding that under weak regularity conditions the new approach gives accelerated mixing through the temperature schedule. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples

Weight-Preserving Simulated Tempering

Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for different inverse-temperature values, sometimes dramatically so. In this paper, we provide a fix to overcome this problem, by adjusting the mode weights to be preserved (i.e., constant) over different inverse-temperature settings. We then apply simulated tempering algorithms to multimodal targets using our mode weight correction. We present simulations in which our weight-preserving algorithm mixes between modes much more successfully than traditional tempering algorithms. We also prove a diffusion limit for an version of our algorithm, which shows that under appropriate assumptions, our algorithm mixes in time O(d [log d]^2)

Within-guild dietary discrimination from 3-D textural analysis of tooth microwear in insectivorous mammals

Resource exploitation and competition for food are important selective pressures in animal evolution. A number of recent investigations have focused on linkages between diversification, trophic morphology and diet in bats, partly because their roosting habits mean that for many bat species diet can be quantified relatively easily through faecal analysis. Dietary analysis in mammals is otherwise invasive, complicated, time consuming and expensive. Here we present evidence from insectivorous bats that analysis of three-dimensional (3-D) textures of tooth microwear using International Organization for Standardization (ISO) roughness parameters derived from sub-micron surface data provides an additional, powerful tool for investigation of trophic resource exploitation in mammals. Our approach, like scale-sensitive fractal analysis, offers considerable advantages over twodimensional (2-D) methods of microwear analysis, including improvements in robustness, repeatability and comparability of studies. Our results constitute the first analysis of microwear textures in carnivorous mammals based on ISO roughness parameters. They demonstrate that the method is capable of dietary discrimination, even between cryptic species with subtly different diets within trophic guilds, and even when sample sizes are small. We find significant differences in microwear textures between insectivore species whose diet contains different proportions of ‘hard’ prey (such as beetles) and ‘soft’ prey (such as moths), and multivariate analyses are able to distinguish between species with different diets based solely on their tooth microwear textures. Our results show that, compared with previous 2-D analyses of microwear in bats, ISO roughness parameters provide a much more sophisticated characterization of the nature of microwear surfaces and can yield more robust and subtle dietary discrimination. ISO-based textural analysis of tooth microwear thus has a useful role to play, complementing existing approaches, in trophic analysis of mammals, both extant and extinct

A utility based approach to information for stochastic differential equations

AbstractA Bayesian perspective is taken to quantify the amount of information learned from observing a stochastic process, Xt, on the interval [0, T] which satisfies the stochastic differential equation, dXt = S(θ, t, Xt)dt+σ(t, Xt)dBt. Information is defined as a change in expected utility when the experimenter is faced with the decision problem of reporting beliefs about the parameter of interest θ. For locally asymptotic mixed normal families we establish an asymptotic relationship between the Shannon information of the posterior and Fisher's information of the process. In particular we compute this measure for the linear case (S(θ, t, Xt) = θS(t, Xt)), Brownian motion with drift, the Ornstein-Uhlenbeck process and the Bessel process

Sustained Magnetic Responses in Temporal Cortex Reflect Instantaneous Significance of Approaching and Receding Sounds

Rising sound intensity often signals an approaching sound source and can serve as a powerful warning cue, eliciting phasic attention, perception biases and emotional responses. How the evaluation of approaching sounds unfolds over time remains elusive. Here, we capitalised on the temporal resolution of magnetoencephalograpy (MEG) to investigate in humans a dynamic encoding of perceiving approaching and receding sounds. We compared magnetic responses to intensity envelopes of complex sounds to those of white noise sounds, in which intensity change is not perceived as approaching. Sustained magnetic fields over temporal sensors tracked intensity change in complex sounds in an approximately linear fashion, an effect not seen for intensity change in white noise sounds, or for overall intensity. Hence, these fields are likely to track approach/recession, but not the apparent (instantaneous) distance of the sound source, or its intensity as such. As a likely source of this activity, the bilateral inferior temporal gyrus and right temporo-parietal junction emerged. Our results indicate that discrete temporal cortical areas parametrically encode behavioural significance in moving sound sources where the signal unfolded in a manner reminiscent of evidence accumulation. This may help an understanding of how acoustic percepts are evaluated as behaviourally relevant, where our results highlight a crucial role of cortical areas

Texturing waste: attachment and identity in every-day consumption and waste practices

Waste has often been a target of literature and policy promoting pro-environmental behaviour. However, little attention has been paid to how subjects interpret and construct waste in their daily lives. In this article we develop a synthesis of practice theory and psycho-social concepts of attachment and transitional space to explore how biographically patterned relationships and attachments to practice shape subjects' understandings of resource consumption and disposal. Deploying biographical interview data produced by the Energy Biographies Project, we illustrate how tangible, intersubjective and interdependent experiences rub up against cultural and behavioural norms, reshaping the meanings and strategies through which subjects interpret and manage waste

Monitoring carbon in electron and ion beam deposition within FIB-SEM

It is well known that carbon present in scanning electron microscopes (SEM), Focused ion beam (FIB) systems and FIB-SEMs, causes imaging artefacts and influences the quality of TEM lamellae or structures fabricated in FIB-SEMs. The severity of such effects depends not only on the quantity of carbon present but also on its bonding state. Despite this, the presence of carbon and its bonding state is not regularly monitored in FIB-SEMs. Here we demonstrated that Secondary Electron Hyperspectral Imaging (SEHI) can be implemented in different FIB-SEMs (ThermoFisher Helios G4-CXe PFIB and Helios Nanolab G3 UC) and used to observe carbon built up/removal and bonding changes resulting from electron/ion beam exposure. As well as the ability to monitor, this study also showed the capability of Plasma FIB Xe exposure to remove carbon contamination from the surface of a Ti6246 alloy without the requirement of chemical surface treatments