Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.Comment: To be published in the proceedings of MCMQMC 201

Defining standards in colorectal optimisation: a Delphi study protocol to achieve international consensus on key standards for colorectal surgery prehabilitation

Introduction Prehabilitation in colorectal surgery is evolving and may minimise postoperative morbidity and mortality. With many different healthcare professionals contributing to the prehabilitation literature, there is significant variation in reported primary endpoints that restricts comparison. In addition, there has been limited work on patient-related outcome measures suggesting that patients with colorectal cancer needs and issues are being overlooked. The Defining Standards in Colorectal Optimisation Study aims to achieve international consensus from all stakeholders on key standards to provide a framework for reporting future prehabilitation research. Methods and analysis A systematic review will identify key standards reported in trials of prehabilitation in colorectal surgery. Standards that are important to patients will be identified by a patient and public involvement (PPI) event. The longlist of standards generated from the systematic review and PPI event will be used to develop a three-round online Delphi process. This will engage all stakeholders (healthcare professionals and patients) both nationally and internationally. The results of the Delphi will be followed by a face-to-face interactive consensus meeting that will define the final standards for prehabilitation for elective colorectal surgery. Ethics and dissemination The University of Glasgow College of Medical, Veterinary and Life Sciences Ethics Committee has approved this protocol, which is registered as a study (200190120) with the Core Outcome Measures in Effectiveness Trials Initiative. Publication of the standards developed by all stakeholders will increase the potential for comparative research that advances understanding of the clinical application of prehabilitation. PROSPERO registration number CRD42019120381

Developing a core outcome set for fistulising perianal Crohn's disease

OBJECTIVE: Lack of standardised outcomes hampers effective analysis and comparison of data when comparing treatments in fistulising perianal Crohn's disease (pCD). Development of a standardised set of outcomes would resolve these issues. This study provides the definitive core outcome set (COS) for fistulising pCD. DESIGN: Candidate outcomes were generated through a systematic review and patient interviews. Consensus was established via a three-round Delphi process using a 9-point Likert scale based on how important they felt it was in determining treatment success culminating in a final consensus meeting. Stakeholders were recruited nationally and grouped into three panels (surgeons and radiologists, gastroenterologists and IBD specialist nurses, and patients). Participants received feedback fromtheir panel(in the second round) andall participants(in the third round) to allow refinement of their scores. RESULTS: A total of 295 outcomes were identified from systematic reviews and interviews that were categorised into 92 domains. 187 stakeholders (response rate 78.5%) prioritised 49 outcomes through a three-round Delphi study.The final consensus meeting of 41 experts and patients generated agreement on an eight domain COS. The COS comprised three patient-reported outcome domains (quality of life, incontinence and a combined score of patient priorities) and five clinician-reported outcome domains (perianal disease activity, development of new perianal abscess/sepsis, new/recurrent fistula, unplanned surgery and faecal diversion). CONCLUSION: A fistulising pCD COS has been produced by all key stakeholders. Application of the COS will reduce heterogeneity in outcome reporting, thereby facilitating more meaningful comparisons between treatments, data synthesis and ultimately benefit patient care

Legacy of COVID‐19 – the opportunity to enhance surgical services for patients with colorectal disease

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Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates

A Simulated Annealing Approach to Approximate Bayes Computations

Approximate Bayes Computations (ABC) are used for parameter inference when the likelihood function of the model is expensive to evaluate but relatively cheap to sample from. In particle ABC, an ensemble of particles in the product space of model outputs and parameters is propagated in such a way that its output marginal approaches a delta function at the data and its parameter marginal approaches the posterior distribution. Inspired by Simulated Annealing, we present a new class of particle algorithms for ABC, based on a sequence of Metropolis kernels, associated with a decreasing sequence of tolerances w.r.t. the data. Unlike other algorithms, our class of algorithms is not based on importance sampling. Hence, it does not suffer from a loss of effective sample size due to re-sampling. We prove convergence under a condition on the speed at which the tolerance is decreased. Furthermore, we present a scheme that adapts the tolerance and the jump distribution in parameter space according to some mean-fields of the ensemble, which preserves the statistical independence of the particles, in the limit of infinite sample size. This adaptive scheme aims at converging as close as possible to the correct result with as few system updates as possible via minimizing the entropy production in the system. The performance of this new class of algorithms is compared against two other recent algorithms on two toy examples.Comment: 20 pages, 2 figure

Developing a core outcome set for fistulising perianal Crohn’s disease

Objective Lack of standardised outcomes hampers effective analysis and comparison of data when comparing treatments in fistulising perianal Crohn’s disease (pCD). Development of a standardised set of outcomes would resolve these issues. This study provides the definitive core outcome set (COS) for fistulising pCD. Design Candidate outcomes were generated through a systematic review and patient interviews. Consensus was established via a three-round Delphi process using a 9-point Likert scale based on how important they felt it was in determining treatment success culminating in a final consensus meeting. Stakeholders were recruited nationally and grouped into three panels (surgeons and radiologists, gastroenterologists and IBD specialist nurses, and patients). Participants received feedback from their panel (in the second round) and all participants (in the third round) to allow refinement of their scores. Results A total of 295 outcomes were identified from systematic reviews and interviews that were categorised into 92 domains. 187 stakeholders (response rate 78.5%) prioritised 49 outcomes through a three-round Delphi study. The final consensus meeting of 41 experts and patients generated agreement on an eight domain COS. The COS comprised three patient-reported outcome domains (quality of life, incontinence and a combined score of patient priorities) and five clinician-reported outcome domains (perianal disease activity, development of new perianal abscess/sepsis, new/recurrent fistula, unplanned surgery and faecal diversion). Conclusion A fistulising pCD COS has been produced by all key stakeholders. Application of the COS will reduce heterogeneity in outcome reporting, thereby facilitating more meaningful comparisons between treatments, data synthesis and ultimately benefit patient care

Genome-wide fine-scale recombination rate variation in Drosophila melanogaster

Estimating fine-scale recombination maps of Drosophila from population genomic data is a challenging problem, in particular because of the high background recombination rate. In this paper, a new computational method is developed to address this challenge. Through an extensive simulation study, it is demonstrated that the method allows more accurate inference, and exhibits greater robustness to the effects of natural selection and noise, compared to a well-used previous method developed for studying fine-scale recombination rate variation in the human genome. As an application, a genome-wide analysis of genetic variation data is performed for two Drosophila melanogaster populations, one from North America (Raleigh, USA) and the other from Africa (Gikongoro, Rwanda). It is shown that fine-scale recombination rate variation is widespread throughout the D. melanogaster genome, across all chromosomes and in both populations. At the fine-scale, a conservative, systematic search for evidence of recombination hotspots suggests the existence of a handful of putative hotspots each with at least a tenfold increase in intensity over the background rate. A wavelet analysis is carried out to compare the estimated recombination maps in the two populations and to quantify the extent to which recombination rates are conserved. In general, similarity is observed at very broad scales, but substantial differences are seen at fine scales. The average recombination rate of the X chromosome appears to be higher than that of the autosomes in both populations, and this pattern is much more pronounced in the African population than the North American population. The correlation between various genomic features—including recombination rates, diversity, divergence, GC content, gene content, and sequence quality—is examined using the wavelet analysis, and it is shown that the most notable difference between D. melanogaster and humans is in the correlation between recombination and diversity

Inferring Human Colonization History Using a Copying Model

Genome-wide scans of genetic variation can potentially provide detailed information on how modern humans colonized the world but require new methods of analysis. We introduce a statistical approach that uses Single Nucleotide Polymorphism (SNP) data to identify sharing of chromosomal segments between populations and uses the pattern of sharing to reconstruct a detailed colonization scenario. We apply our model to the SNP data for the 53 populations of the Human Genome Diversity Project described in Conrad et al. (Nature Genetics 38,1251-60, 2006). Our results are consistent with the consensus view of a single “Out-of-Africa” bottleneck and serial dilution of diversity during global colonization, including a prominent East Asian bottleneck. They also suggest novel details including: (1) the most northerly East Asian population in the sample (Yakut) has received a significant genetic contribution from the ancestors of the most northerly European one (Orcadian). (2) Native South Americans have received ancestry from a source closely related to modern North-East Asians (Mongolians and Oroquen) that is distinct from the sources for native North Americans, implying multiple waves of migration into the Americas. A detailed depiction of the peopling of the world is available in animated form

Time-frequency scaling transformation of the phonocardiogram based of the matching pursuit method.

International audienceA time-frequency scaling transformation based on the matching pursuit (MP) method is developed for the phonocardiogram (PCG). The MP method decomposes a signal into a series of time-frequency atoms by using an iterative process. The modification of the time scale of the PCG can be performed without perceptible change in its spectral characteristics. It is also possible to modify the frequency scale without changing the temporal properties. The technique has been tested on 11 PCG's containing heart sounds and different murmurs. A scaling/inverse-scaling procedure was used for quantitative evaluation of the scaling performance. Both the spectrogram and a MP-based Wigner distribution were used for visual comparison in the time-frequency domain. The results showed that the technique is suitable and effective for the time-frequency scale transformation of both the transient property of the heart sounds and the more complex random property of the murmurs. It is also shown that the effectiveness of the method is strongly related to the optimization of the parameters used for the decomposition of the signals