Unbiased and Consistent Nested Sampling via Sequential Monte Carlo

We introduce a new class of sequential Monte Carlo methods called Nested Sampling via Sequential Monte Carlo (NS-SMC), which reframes the Nested Sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. This new framework allows convergence results to be obtained in the setting when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood estimates are unbiased. In contrast to NS, the analysis of NS-SMC does not require the (unrealistic) assumption that the simulated samples be independent. As the original NS algorithm is a special case of NS-SMC, this provides insights as to why NS seems to produce accurate estimates despite a typical violation of its assumptions. For applications of NS-SMC, we give advice on tuning MCMC kernels in an automated manner via a preliminary pilot run, and present a new method for appropriately choosing the number of MCMC repeats at each iteration. Finally, a numerical study is conducted where the performance of NS-SMC and temperature-annealed SMC is compared on several challenging and realistic problems. MATLAB code for our experiments is made available at https://github.com/LeahPrice/SMC-NS .Comment: 45 pages, some minor typographical errors fixed since last versio

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

Bayesian synthetic likelihood (BSL; Price, Drovandi, Lee, and Nott 2018) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Compared to alternative methods such as approximate Bayesian computation (ABC), BSL requires little tuning and requires less model simulations than ABC when the chosen summary statistic is high-dimensional. The original synthetic likelihood relies on a multivariate normal approximation of the intractable likelihood, where the mean and covariance are estimated by simulation. An extension of BSL considers replacing the sample covariance with a penalized covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. Finally, another extension of BSL aims to develop a more robust synthetic likelihood estimator while acknowledging there might be model misspecification. In this paper, we present the R package BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The package also includes several examples to illustrate use of the package and the utility of the methods

Penetration and early colonization in basidiospore-derived infection of Melampsora pulcherrima (Bub.) Maire on Mercurialis annua L.

SUMMARYThe early phases of basidiospore-derived infection of Melampsora pulcherrima (Bub.) Maire on the leaves of Mercurialis annua L. were studied by light microscopy, SEM and TEM. The fine morphology of the basidiospore germling penetration and intraepidermal infection structures is discussed in comparison with that of other rusts recently described. The direct penetration through the epidermal cell wall, characteristic of the rust basidiospore-derived germlings, is confirmed. The absence of an extrahyphal matrix around the intraepidermal vesicle and the presence of a collar around the vesicle neck are pointed out

Optimal experimental design for predator–prey functional response experiments

Functional response models are important in understanding predator–prey interactions. The development of functional response methodology has progressed from mechanistic models to more statistically motivated models that can account for variance and the over-dispersion commonly seen in the datasets collected from functional response experiments. However, little information seems to be available for those wishing to prepare optimal parameter estimation designs for functional response experiments. It is worth noting that optimally designed experiments may require smaller sample sizes to achieve the same statistical outcomes as non-optimally designed experiments. In this paper, we develop a model-based approach to optimal experimental design for functional response experiments in the presence of parameter uncertainty (also known as a robust optimal design approach). Further, we develop and compare new utility functions which better focus on the statistical efficiency of the designs; these utilities are generally applicable for robust optimal design in other applications (not just in functional response). The methods are illustrated using a beta-binomial functional response model for two published datasets: an experiment involving the freshwater predator Notonecta glauca (an aquatic insect) preying on Asellus aquaticus (a small crustacean), and another experiment involving a ladybird beetle (Propylea quatuordecimpunctata L.) preying on the black bean aphid (Aphis fabae Scopoli). As a by-product, we also derive necessary quantities to perform optimal design for beta-binomial regression models, which may be useful in other applications

Signs of resistance to Melampsora larici-tremulae on species of Pinus hosts of Melampsora pinitorqua: implications regarding the taxonomic relationship between the two rust fungi

Signs of resistance such as cortical necroses which occurred after artificial inoculations with Melampsora larici-tremulae on some species of the genus Pinus in the host range of M. pinitorqua were evaluated. Similar observations were carried out on P. sylvestris inoculated with two provenances of M. larici-tremulae from areas with different environmental conditions. In both experiments, the degree of resistance to M. larici-tremulae depended on how suitable environmental conditions were for both the host and the fungus. The greatest resistance to M. laricitremulae was shown by P. sylvestris.These observations could indicate that P. sylvestris is becoming a nonhost of M. larici-tremulae. The type of host-parasite interaction between some species of Pinus and M. larici-tremulae, when compared to analogous interactions between the same species of Pinus and M. pinitorqua, can shed light on the taxonomic relationship between the two rust fungi

An 800-million-solar-mass black hole in a significantly neutral Universe at redshift 7.5

Quasars are the most luminous non-transient objects known and as a result they enable studies of the Universe at the earliest cosmic epochs. Despite extensive efforts, however, the quasar ULAS J1120+0641 at z=7.09 has remained the only one known at z>7 for more than half a decade. Here we report observations of the quasar ULAS J134208.10+092838.61 (hereafter J1342+0928) at redshift z=7.54. This quasar has a bolometric luminosity of 4e13 times the luminosity of the Sun and a black hole mass of 8e8 solar masses. The existence of this supermassive black hole when the Universe was only 690 million years old---just five percent of its current age---reinforces models of early black-hole growth that allow black holes with initial masses of more than about 1e4 solar masses or episodic hyper-Eddington accretion. We see strong evidence of absorption of the spectrum of the quasar redwards of the Lyman alpha emission line (the Gunn-Peterson damping wing), as would be expected if a significant amount (more than 10 per cent) of the hydrogen in the intergalactic medium surrounding J1342+0928 is neutral. We derive a significant fraction of neutral hydrogen, although the exact fraction depends on the modelling. However, even in our most conservative analysis we find a fraction of more than 0.33 (0.11) at 68 per cent (95 per cent) probability, indicating that we are probing well within the reionization epoch of the Universe.Comment: Updated to match the final journal versio

A Model-Based Bayesian Estimation of the Rate of Evolution of VNTR Loci in Mycobacterium tuberculosis

Variable numbers of tandem repeats (VNTR) typing is widely used for studying the bacterial cause of tuberculosis. Knowledge of the rate of mutation of VNTR loci facilitates the study of the evolution and epidemiology of Mycobacterium tuberculosis. Previous studies have applied population genetic models to estimate the mutation rate, leading to estimates varying widely from around to per locus per year. Resolving this issue using more detailed models and statistical methods would lead to improved inference in the molecular epidemiology of tuberculosis. Here, we use a model-based approach that incorporates two alternative forms of a stepwise mutation process for VNTR evolution within an epidemiological model of disease transmission. Using this model in a Bayesian framework we estimate the mutation rate of VNTR in M. tuberculosis from four published data sets of VNTR profiles from Albania, Iran, Morocco and Venezuela. In the first variant, the mutation rate increases linearly with respect to repeat numbers (linear model); in the second, the mutation rate is constant across repeat numbers (constant model). We find that under the constant model, the mean mutation rate per locus is (95% CI: ,)and under the linear model, the mean mutation rate per locus per repeat unit is (95% CI: ,). These new estimates represent a high rate of mutation at VNTR loci compared to previous estimates. To compare the two models we use posterior predictive checks to ascertain which of the two models is better able to reproduce the observed data. From this procedure we find that the linear model performs better than the constant model. The general framework we use allows the possibility of extending the analysis to more complex models in the future

A Survey of Bayesian Statistical Approaches for Big Data

The modern era is characterised as an era of information or Big Data. This has motivated a huge literature on new methods for extracting information and insights from these data. A natural question is how these approaches differ from those that were available prior to the advent of Big Data. We present a review of published studies that present Bayesian statistical approaches specifically for Big Data and discuss the reported and perceived benefits of these approaches. We conclude by addressing the question of whether focusing only on improving computational algorithms and infrastructure will be enough to face the challenges of Big Data