Density Estimation by Monte Carlo and Quasi-Monte Carlo

Estimating the density of a continuous random variable $X$ has been studied extensively in statistics, in the setting where $n$ independent observations of $X$ are given a priori and one wishes to estimate the density from that. Popular methods include histograms and kernel density estimators. In this review paper, we are interested instead in the situation where the observations are generated by Monte Carlo simulation from a model. Then, one can take advantage of variance reduction methods such as stratification, conditional Monte Carlo, and randomized quasi-Monte Carlo (RQMC), and obtain a more accurate density estimator than with standard Monte Carlo for a given computing budget. We discuss several ways of doing this, proposed in recent papers, with a focus on methods that exploit RQMC. A first idea is to directly combine RQMC with a standard kernel density estimator. Another one is to adapt a simulation-based derivative estimation method such as smoothed perturbation analysis or the likelihood ratio method to obtain a continuous estimator of the cumulative density function (CDF), whose derivative is an unbiased estimator of the density. This can then be combined with RQMC. We summarize recent theoretical results with these approaches and give numerical illustrations of how they improve the convergence of the mean square integrated error.NSERC Discovery Grant, IVADO Grant, ERDF, ESF, EXP. 2019/0043

Variance Reduction with Array-RQMC for Tau-Leaping Simulation of Stochastic Biological and Chemical Reaction Networks

We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with $\tau$-leaping. The task is to estimate the expectation of a function of molecule copy numbers at a given future time $T$ by the sample average over $n$ sample paths, and the goal is to reduce the variance of this sample-average estimator. We find that when the method is properly applied, variance reductions by factors in the thousands can be obtained. These factors are much larger than those observed previously by other authors who tried RQMC methods for the same examples. Array-RQMC simulates an array of realizations of the Markov chain and requires a sorting function to reorder these chains according to their states, after each step. The choice of sorting function is a key ingredient for the efficiency of the method, although in our experiments, Array-RQMC was never worse than ordinary Monte Carlo, regardless of the sorting method. The expected number of reactions of each type per step also has an impact on the efficiency gain.ERDF, ESF, EXP. 2019/00432, Canada Research Chair, IVADO Research Grant, NSERC Discovery Grant RGPIN-110050

Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges more slowly than at the canonical rate of $\mathcal{O}(1/n)$. When the sample is generated from a simulation model and we have control over how this is done, we can do better. We examine an approach in which conditional Monte Carlo yields, under certain conditions, a random conditional density which is an unbiased estimator of the true density at any point. By averaging independent replications, we obtain a density estimator that converges at a faster rate than the usual ones. Moreover, combining this new type of estimator with randomized quasi-Monte Carlo to generate the samples typically brings a larger improvement on the error and convergence rate than for the usual estimators, because the new estimator is smoother as a function of the underlying uniform random numbers.IVADO Research Grant, NSERC-Canada Discorvery Grant, Canada Research Chair, Inria International Chair, ERDF, ESF, EXP. 2019/0043

A Tool for Custom Construction of QMC and RQMC Point Sets

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the s-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. We summarize what are the various Hilbert spaces, discrepancies, types of weights, figures of merit, types of constructions, and search methods supported by LatNet Builder. We briefly discuss its organization and we provide simple illustrations of what it can do.NSERC Discovery Grant, IVADO Grant, Corps des Mines Stipend, ERDF, ESF, EXP. 2019/0043

Sequences of complete human cytomegalovirus genomes from infected cell cultures and clinical specimens

We have assessed two approaches to sequencing complete human cytomegalovirus (HCMV) genomes (236 kbp) in DNA extracted from infected cell cultures (strains 3157, HAN13, HAN20 and HAN38) or clinical specimens (strains JP and 3301). The first approach involved amplifying genomes from the DNA samples as overlapping PCR products, sequencing these by the Sanger method, acquiring reads from a capillary instrument and assembling these using the Staden programs. The second approach involved generating sequence data from the DNA samples by using an Illumina Genome Analyzer (IGA), processing the filtered reads by reference-independent (de novo) assembly, utilizing the resulting sequence to direct reference-dependent assembly of the same data and finishing by limited PCR sequencing. Both approaches were successful. In particular, the investigation demonstrated the utility of IGA data for efficiently sequencing genomes from clinical samples containing as little as 3 % HCMV DNA. Analysis of the genome sequences obtained showed that each of the strains grown in cell culture was a mutant. Certain of the mutations were shared among strains from independent clinical sources, thus suggesting that they may have arisen in a common ancestor during natural infection. Moreover, one of the strains (JP) sequenced directly from a clinical specimen was mutated in two genes, one of which encodes a proposed immune-evasion function, viral interleukin-10. These observations imply that HCMV mutants exist in human infections

Primary resistance of HIV to antiretrovirals among individuals recently diagnosed at voluntary counselling and testing centres in the metropolitan region of Recife, Pernambuco

Determining the prevalence and type of antiretroviral (ARV) resistance among ARV-naïve individuals is important to assess the potential responses of these individuals to first-line regimens. The prevalence of primary resistance and the occurrence of recent infections among individuals with human immunodeficiency virus (HIV)/acquired immune deficiency syndrome (AIDS) were identified among recently diagnosed patients at five sexually transmitted disease/AIDS testing and counselling centres in the metropolitan region of Recife (RMR), Pernambuco, Brazil, between 2007-2009. One-hundred and eight samples were analysed using the Calypte® BED assay. Males predominated (56%), as did patients aged 31-50 years. Twenty-three percent presented evidence of a recent HIV infection. The median CD4+ T lymphocyte count was 408 cells/mm³ and the median viral load was 3.683 copies/mL. The prevalence of primary resistance was 4.6% (confidence interval 95% = 1-8.2%) based on criteria that excluded common polymorphisms in accordance with the surveillance drug resistance mutation criteria. The prevalence of resistance to non-nucleoside reverse transcriptase, nucleoside/nucleotide reverse transcriptase and protease inhibitors were 3.8%, 1.5% and 0.8%, respectively. Fifty-seven percent of strains were from clade B, 37.7% were clade F and 3.1% were clade C; there were no statistically significant differences with respect to resistance between clades. Recent infection tended to be more common in men (p = 0.06) and in municipalities in the south of the RMR (Jaboatão dos Guararapes and Cabo de Santo Agostinho) (p = 0.046). The high prevalence of recent infection and the high prevalence of non-B strains in this poor Brazilian region merit further attention.Laboratório Central de Saúde Pública de Pernambuco Setor de VirologiaUniversidade Federal de Pernambuco Programa de Pós-Graduação em Medicina TropicalFiocruz Centro de Pesquisa Aggeu MagalhãesCentro de Testagem e Aconselhamento Herbert de SouzaUniversidade Federal de São Paulo (UNIFESP) Laboratório de RetrovirologiaUNIFESP, Laboratório de RetrovirologiaSciEL

HIV-1 Infection in Cyprus, the Eastern Mediterranean European Frontier: A Densely Sampled Transmission Dynamics Analysis from 1986 to 2012

Since HIV-1 treatment is increasingly considered an effective preventionstrategy, it is important to study local HIV-1 epidemics to formulate tailored preventionpolicies. The prevalence of HIV-1 in Cyprus was historically low until 2005. To investigatethe shift in epidemiological trends, we studied the transmission dynamics of HIV-1 in Cyprususing a densely sampled Cypriot HIV-1 transmission cohort that included 85 percent ofHIV-1-infected individuals linked to clinical care between 1986 and 2012 based on detailedclinical, epidemiological, behavioral and HIV-1 genetic information. Subtyping andtransmission cluster reconstruction were performed using maximum likelihood and Bayesianmethods, and the transmission chain network was linked to the clinical, epidemiological andbehavioral data. The results reveal that for the main HIV-1 subtype A1 and B sub-epidemics,young and drug-naïve HIV-1-infected individuals in Cyprus are driving the dynamics of thelocal HIV-1 epidemic. The results of this study provide a better understanding of thedynamics of the HIV-1 infection in Cyprus, which may impact the development of preventionstrategies. Furthermore, this methodology for analyzing densely sampled transmissiondynamics is applicable to other geographic regions to implement effective HIV-1 preventionstrategies in local settings

Transmission of HIV drug resistance and the predicted effect on current first-line regimens in Europe

BACKGROUND: Numerous studies have shown that baseline drug resistance patterns may influence the outcome of antiretroviral therapy. Therefore guidelines recommend drug resistance testing to guide the choice of initial regimen. In addition to optimizing individual patient management, these baseline resistance data enable transmitted drug resistance (TDR) to be surveyed for public health purposes. The SPREAD-program systematically collects data to gain insight into TDR occurring in Europe since 2001. METHODS: Demographic, clinical and virological data from 4,140 antiretroviral-naive HIV-infected individuals from 26 countries who were newly diagnosed between 2008 and 2010 were analyzed. Evidence of TDR was defined using the WHO list for surveillance of drug resistance mutations. Prevalence of TDR was assessed over time by comparing the results to SPREAD data from 2002-2007. Baseline susceptibility to antiretroviral drugs was predicted using Stanford HIVdb v7.0. RESULTS: The overall prevalence of TDR did not change significantly over time and was 8.3% (95%CI 7.2-9.5) in 2008-2010. The most frequent indicators of TDR were NRTI-mutations (4.5%), followed by NNRTI-mutations (2.9%) and PI-mutations (2.0%). Baseline mutations were most predictive of reduced susceptibility to initial NNRTI-based regimens: 4.5% and 6.5% of patient isolates were predicted to have resistance to regimens containing efavirenz or rilpivirine respectively, independent of current NRTI backbones. CONCLUSIONS: Although TDR was highest for NRTIs, the impact of baseline drug resistance patterns on susceptibility was largest for NNRTIs. The prevalence of TDR assessed by epidemiological surveys does not clearly indicate to what degree susceptibility to different drug classes is affecte

Detection of a Single Identical Cytomegalovirus (CMV) Strain in Recently Seroconverted Young Women

Infection with multiple CMV strains is common in immunocompromised hosts, but its occurrence in normal hosts has not been well-studied.We analyzed CMV strains longitudinally in women who acquired CMV while enrolled in a CMV glycoprotein B (gB) vaccine trial. Sequencing of four variable genes was performed in samples collected from seroconversion and up to 34 months thereafter.199 cultured isolates from 53 women and 65 original fluids from a subset of 19 women were sequenced. 51 women were infected with one strain each without evidence for genetic drift; only two women shed multiple strains. Genetic variability among strains increased with the number of sequenced genetic loci. Nevertheless, 13 of 53 women proved to be infected with an identical CMV strain based on sequencing at all four variable genes. CMV vaccine did not alter the degree of genetic diversity amongst strains.Primary CMV infection in healthy women nearly always involves shedding of one strain that remains stable over time. Immunization with CMVgB-1 vaccine strain is not selective against specific strains. Although 75% of women harbored their unique strain, or a strain shared with only one other woman, 25% shared a single common strain, suggesting that this predominant strain with a particular combination of genetic loci is advantageous in this large urban area

HIV-1 Infection in Cyprus, the Eastern Mediterranean European Frontier: A Densely Sampled Transmission Dynamics Analysis from 1986 to 2012

Since HIV-1 treatment is increasingly considered an effective preventionstrategy, it is important to study local HIV-1 epidemics to formulate tailored preventionpolicies. The prevalence of HIV-1 in Cyprus was historically low until 2005. To investigatethe shift in epidemiological trends, we studied the transmission dynamics of HIV-1 in Cyprususing a densely sampled Cypriot HIV-1 transmission cohort that included 85 percent ofHIV-1-infected individuals linked to clinical care between 1986 and 2012 based on detailedclinical, epidemiological, behavioral and HIV-1 genetic information. Subtyping andtransmission cluster reconstruction were performed using maximum likelihood and Bayesianmethods, and the transmission chain network was linked to the clinical, epidemiological andbehavioral data. The results reveal that for the main HIV-1 subtype A1 and B sub-epidemics,young and drug-naïve HIV-1-infected individuals in Cyprus are driving the dynamics of thelocal HIV-1 epidemic. The results of this study provide a better understanding of thedynamics of the HIV-1 infection in Cyprus, which may impact the development of preventionstrategies. Furthermore, this methodology for analyzing densely sampled transmissiondynamics is applicable to other geographic regions to implement effective HIV-1 preventionstrategies in local settings