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It is well known that traditional Markov chain Monte Carlo (MCMC) methods can fail to effectively explore the state space for multimodal problems. Parallel tempering is a well-established population approach for such target distributions involving a collection of particles indexed by temperature. However, this method can suffer dramatically from the curse of dimensionality. In this paper we introduce an improvement on parallel tempering called QuanTA. A comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach is given. Under weak regularity conditions, QuanTA gives accelerated mixing through the temperature space. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples.
In this paper we propose a new theory and methodology to tackle the problem of unifying Monte Carlo samples from distributed densities into a single Monte Carlo draw from the target density. This surprisingly challenging problem arises in many settings (for instance, expert elicitation, multiview learning, distributed ‘big data’ problems, etc.), but to date the framework and methodology proposed in this paper (Monte Carlo fusion) is the first general approach which avoids any form of approximation error in obtaining the unified inference. In this paper we focus on the key theoretical underpinnings of this new methodology, and simple (direct) Monte Carlo interpretations of the theory. There is considerable scope to tailor the theory introduced in this paper to particular application settings (such as the big data setting), construct efficient parallelised schemes, understand the approximation and computational efficiencies of other such unification paradigms, and explore new theoretical and methodological directions.
In this paper we consider the optimal scaling of high-dimensional random walk Metropolis algorithms for densities differentiable in the Lp mean but which may be irregular at some points (such as the Laplace density, for example) and/or supported on an interval. Our main result is the weak convergence of the Markov chain (appropriately rescaled in time and space) to a Langevin diffusion process as the dimension d goes to ∞. As the log-density might be nondifferentiable, the limiting diffusion could be singular. The scaling limit is established under assumptions which are much weaker than the one used in the original derivation of Roberts et al. (1997). This result has important practical implications for the use of random walk Metropolis algorithms in Bayesian frameworks based on sparsity inducing priors.
Gurga Chiya and Tepe Marani are small, adjacent mounds located close to the town of Halabja in the southern part of the Shahrizor Plain, one of the most fertile regions of Iraqi Kurdistan. Survey and excavation at these previously unexplored sites is beginning to produce evidence for human settlement spanning the sixth to the fourth millennia, c. 5600–3300 cal. b.c. In Mesopotamian chronology this corresponds to the Late Neolithic through to Chalcolithic periods; the Halaf, Ubaid, and Uruk phases of conventional culture history. In Iraqi Kurdistan, documentation of these periods—which witnessed many important transformations in prehistoric village life—is currently very thin. Here we offer a preliminary report on the emerging results from the Shahrizor Plain, with a particular focus on the description of material culture (ceramic and lithic assemblages), in order to establish a benchmark for further research. We also provide a detailed report on botanical remains and accompanying radiocarbon dates, which allow us to place this new evidence in a wider comparative framework. A further, brief account is given of Late Bronze Age material culture from the upper layers at Gurga Chiya. We conclude with observations on the significance of the Shahrizor Plain for wider research into the later prehistory of the Middle East, and the importance of preserving and investigating its archaeological record.
We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws related to those of Brownian motion and its local time, and are based on the principle of retrospective rejection sampling. A simple illustration is provided.
We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the computer science notion of algorithm complexity. Our main result states that any weak limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate assumptions, the random-walk Metropolis algorithm in d dimensions takes O(d) iterations to converge to stationarity, while the Metropolis-adjusted Langevin algorithm takes O(d1/3) iterations to converge to stationarity.
Uranium incorporation into magnetite and its behaviour during subsequent oxidation has been investigated at high pH to determine the uranium retention mechanism(s) on formation and oxidative perturbation of magnetite in systems relevant to radioactive waste disposal. Ferrihydrite was exposed to U(VI)aq containing cement leachates (pH 10.5–13.1) and crystallization of magnetite was induced via addition of Fe(II)aq. A combination of XRD, chemical extraction and XAS techniques provided direct evidence that U(VI) was reduced and incorporated into the magnetite structure, possibly as U(V), with a significant fraction recalcitrant to oxidative remobilization. Immobilization of U(VI) by reduction and incorporation into magnetite at high pH, and with significant stability upon reoxidation, has clear and important implications for limiting uranium migration in geological disposal of radioactive wastes.
Depression is a particular problem in older people and it is important to know how it affects and is affected by smoking cessation.
To identify reciprocal, longitudinal relationships between smoking cessation and depression among older smokers.
Across four waves, covering six years (2002–2008), changes in smoking status and depression, measured using the 8-item Centre for Epidemiologic Studies Depression Scale, were assessed among recent ex-smokers and smokers (n = 2375) in the English Longitudinal Study of Ageing.
In latent growth curve analysis, smoking at baseline predicted depression caseness longitudinally and vice versa. When both processes were modelled concurrently, depression predicted continued smoking longitudinally (B(β) = 0.21 (0.27); 95% CI = 0.08–0.35) but not the other way round. This was the case irrespective of mental health history and adjusting for a range of covariates.
In older smokers, depression appears to act as an important barrier to quitting, although quitting has no long-term impact on depression.
While one of the IAU's missions is to “serve as the internationally recognized authority for assigning designations to celestial bodies and surface features on them” (†), the participation of the public in the naming of celestial objects has been a little-known, but decade-long tradition of the IAU.
This chapter first discusses various methodological concerns related to Cypriote iconography, before turning to a series of limestone images depicting a tri-corporate warrior, traditionally associated with the Greek Geryon, that appears in Cypriot sanctuaries during the Archaic period. There have been two fundamental approaches to interpreting divine images dedicated in Cypriot sanctuaries. The first approach assumes a wholesale transferal of both image and meaning from a foreign origin to the island, and the second approach focuses on local contexts for divine iconography and related rituals. In Greek art, the myth was especially popular in the sixth century BC among representations of the many exploits of Herakles, who was himself a favorite in Archaic Greece. The isolation of hybridization processes in art shifts the focus from origins and streams of influence to genesis and agency. Finally, the chapter suggests a more nuanced approach that focuses on the transmission, translation, and reception of religious iconography and the productive capacity of cultural interactions.
We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler (CMH sampler). We develop conditions under which the CMH sampler will be geometrically or uniformly ergodic. We illustrate our results by analysing a CMH sampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.
The Arctic pole of inaccessibility (API), defined as the point on the Arctic Ocean that is farthest from any land, is commonly asserted to lie at 84° 03′ N, 174° 51′ W. We show that the true position is 85° 48′ N, 176° 09′ E, over 200 km from the traditional location. The reason for this error is unknown.