Translated Poisson approximation to equilibrium distributions of Markov population processes

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in Kolmogorov distance, is of the smallest order that is compatible with their having integer support. Here, an approximation in the much stronger total variation norm is established, without any loss in the asymptotic order of accuracy; the approximating distribution is a translated Poisson distribution having the same variance and (almost) the same mean. Our arguments are based on the Stein-Chen method and Dynkin's formula.Comment: 18 page

Exploiting the feller coupling for the ewens sampling formula

This is the final version of the article. It first appeared from the Institute of Mathematical Statistics via http://dx.doi.org/10.1214/15-STS53

Compound poisson approximation via information functionals

An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integer-valued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same conditional distribution given that they are non-zero, a bound on the relative entropy distance between their sum and the compound Poisson distribution is derived, based on the data-processing property of relative entropy and earlier Poisson approximation results. When the summands have arbitrary distributions, corresponding bounds are derived in terms of the total variation distance. The main technical ingredient is the introduction of two "information functionals,'' and the analysis of their properties. These information functionals play a role analogous to that of the classical Fisher information in normal approximation. Detailed comparisons are made between the resulting inequalities and related bounds

Simulating the component counts of combinatorial structures.

This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures.ADB acknowledges support from ARC grants DP150101459 and DP150103588

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Estimation of changes in the force of infection for intestinal and urogenital schistosomiasis in countries with Schistosomiasis Control Initiative-assisted programmes

The last decade has seen an expansion of national schistosomiasis control programmes in Africa based on large-scale preventative chemotherapy. In many areas this has resulted in considerable reductions in infection and morbidity levels in treated individuals. In this paper, we quantify changes in the force of infection (FOI), defined here as the per (human) host parasite establishment rate, to ascertain the impact on transmission of some of these programmes under the umbrella of the Schistosomiasis Control Initiative (SCI)

Privacy-Preserving Decentralised Singular Value Decomposition

With the proliferation of data and emerging data-driven applications, how to perform data analytical operations while respecting privacy concerns has become a very interesting research topic. With the advancement of communication and computing technologies, e.g. the FoG computing concept and its associated Edge computing technologies, it is now appealing to deploy decentralized data-driven applications. Following this trend, in this paper, we investigate privacy-preserving singular value decomposition (SVD) solutions tailored for these new computing environments. We first analyse a privacy-preserving SVD solution by Chen et al., which is based on the Paillier encryption scheme and some heuristic randomization method. We show that (1) their solution leaks statistical information to an individual player in the system; (2) their solution leaks much more information when more than one players collude. Based on the analysis, we present a new solution, which distributes the SVD results into two different players in a privacy-preserving manner. In comparison, our solution minimizes the information leakage to both individual player and colluded ones, via randomization and threshold homomorphic encryption techniques

The sign problem across the QCD phase transition

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the $U_A(1)$ anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.Comment: 9 pages and 9 fig

Developing an intervention to facilitate family communication about inherited genetic conditions, and training genetic counsellors in its delivery.

Many families experience difficulty in talking about an inherited genetic condition that affects one or more of them. There have now been a number of studies identifying the issues in detail, however few have developed interventions to assist families. The SPRinG collaborative have used the UK Medical Research Council's guidance on Developing and Evaluating Complex Interventions, to work with families and genetic counsellors (GCs) to co-design a psycho-educational intervention to facilitate family communication and promote better coping and adaptation to living with an inherited genetic condition for parents and their children (<18 years). The intervention is modelled on multi-family discussion groups (MFDGs) used in psychiatric settings. The MFDG was developed and tested over three phases. First focus groups with parents, young people, children and health professionals discussed whether MFDG was acceptable and proposed a suitable design. Using evidence and focus group data, the intervention and a training manual were developed and three GCs were trained in its delivery. Finally, a prototype MFDG was led by a family therapist and co-facilitated by the three GCs. Data analysis showed that families attending the focus groups and intervention thought MFDG highly beneficial, and the pilot sessions had a significant impact on their family' functioning. We also demonstrated that it is possible to train GCs to deliver the MFDG intervention. Further studies are now required to test the feasibility of undertaking a definitive randomised controlled trial to evaluate its effectiveness in improving family outcomes before implementing into genetic counselling practice.The National Institute of Health Research funded the study but any views expressed do not necessarily reflect those of the Authority. Funded by NIHR reference number: RP-DG-1211-10015

Real patient learning integrated in a preclinical block musculoskeletal disorders. Does it make a difference?

Although musculoskeletal disorders are the most common reason for general practitioner visits, training did not keep pace. Implementation of learning from patients with rheumatologic disorders linked together with the teaching of theoretical knowledge in the preclinical medical education might be an important step forward in the improvement of quality of care for these patients. The Leiden Medical School curriculum has implemented two non-obligatory real patient learning (RPL) practicals integrated within the preclinical block musculoskeletal disorders. This study investigates the educational effectiveness of the practicals, the expectations students have of RPL, and students’ satisfaction. Participants’ grades on the end-of-block test served as the test results of the educational effectiveness of the practicals and were compared with those of the non-participants. Qualitative data was collected by means of questionnaires generated by focus groups. The participants in practicals scored significantly higher at the end-of-block test. The expected effects of the contact with real patients concerned positive effects on cognition and skills. ‘Contextualizing of the theory’, ‘better memorizing of clinical pictures’, and ‘understanding of the impact of the disease’ were the most frequently mentioned effects of the practicals. Overall, the participants were (very) enthusiastic about this educational format. The RPL practicals integrated within a preclinical block musculoskeletal disorders are a valuable addition to the Leiden medical curriculum. This relatively limited intervention exhibits a strong effect on students’ performance in tests. Future research should be directed towards the long-term effects of this intervention