Efficient random variable generation: ratio of uniforms and polar rejection sampling

Monte Carlo techniques, which require the generation of samples from some target density, are often the only alternative for performing Bayesian inference. Two classic sampling techniques to draw independent samples are the ratio of uniforms (RoU) and rejection sampling (RS). An efficient sampling algorithm is proposed combining the RoU and polar RS (i.e. RS inside a sector of a circle using polar coordinates). Its efficiency is shown in drawing samples from truncated Cauchy and Gaussian random variables, which have many important applications in signal processing and communications. RESUMEN. Método eficiente para generar algunas variables aleatorias de uso común en procesado de señal y comunicaciones (por ejemplo, Gaussianas o Cauchy truncadas) mediante la combinación de dos técnicas: "ratio of uniforms" y "rejection sampling".

Almost rejectionless sampling from Nakagami-m distributions (m ≥ 1)

The Nakagami-m distribution is widely used for the simulation of fading channels in wireless communications. A novel, simple and extremely efficient acceptance-rejection algorithm is introduced for the generation of independent Nakagami-m random variables. The proposed method uses another Nakagami density with a half-integer value of the fading parameter, mp ¼ n/2 ≤ m, as proposal function, from which samples can be drawn exactly and easily. This novel rejection technique is able to work with arbitrary values of m ≥ 1, average path energy, V, and provides a higher acceptance rate than all currently available methods. RESUMEN. Método extremadamente eficiente para generar variables aleatorias de Nakagami (utilizadas para modelar el desvanecimiento en canales de comunicaciones móviles) basado en "rejection sampling".

Conditioning of stochastic 3-D fracture networks to hydrological and geophysical data

The geometry and connectivity of fractures exert a strong influence on the flow and transport properties of fracture networks. We present a novel approach to stochastically generate three-dimensional discrete networks of connected fractures that are conditioned to hydrological and geophysical data. A hierarchical rejection sampling algorithm is used to draw realizations from the posterior probability density function at different conditioning levels. The method is applied to a well-studied granitic formation using data acquired within two boreholes located 6 m apart. The prior models include 27 fractures with their geometry (position and orientation) bounded by information derived from single-hole ground-penetrating radar (GPR) data acquired during saline tracer tests and optical televiewer logs. Eleven cross-hole hydraulic connections between fractures in neighboring boreholes and the order in which the tracer arrives at different fractures are used for conditioning. Furthermore, the networks are conditioned to the observed relative hydraulic importance of the different hydraulic connections by numerically simulating the flow response. Among the conditioning data considered, constraints on the relative flow contributions were the most effective in determining the variability among the network realizations. Nevertheless, we find that the posterior model space is strongly determined by the imposed prior bounds. Strong prior bounds were derived from GPR measurements and helped to make the approach computationally feasible. We analyze a set of 230 posterior realizations that reproduce all data given their uncertainties assuming the same uniform transmissivity in all fractures. The posterior models provide valuable statistics on length scales and density of connected fractures, as well as their connectivity. In an additional analysis, effective transmissivity estimates of the posterior realizations indicate a strong influence of the DFN structure, in that it induces large variations of equivalent transmissivities between realizations. The transmissivity estimates agree well with previous estimates at the site based on pumping, flowmeter and temperature data.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations.

BACKGROUND: The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. RESULTS: Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. CONCLUSION: ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

Background The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. Results Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. Conclusion ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm. to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker. demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.

Independent doubly Adaptive Rejection Metropolis Sampling

Adaptive Rejection Metropolis Sampling (ARMS) is a wellknown MCMC scheme for generating samples from onedimensional target distributions. ARMS is widely used within Gibbs sampling, where automatic and fast samplers are often needed to draw from univariate full-conditional densities. In this work, we propose an alternative adaptive algorithm (IA2RMS) that overcomes the main drawback of ARMS (an uncomplete adaptation of the proposal in some cases), speeding up the convergence of the chain to the target. Numerical results show that IA2RMS outperforms the standard ARMS, providing a correlation among samples close to zero.

A retrospective analysis of mycophenolic acid and cyclosporin concentrations with acute rejection in renal transplant recipients

Objectives: Although monitoring of cyclosporin (CsA) is standard clinical practice postrenal transplantation. mycophenolic acid (MPA) concentrations are not routinely measured. There is evidence that a relationship exists between MPA area under the concentration-time curve (AUC) and rejection. In this study, a retrospective analysis was undertaken of 27 adult renal transplant recipients. Methods: Patients received CsA and MPA therapy and had a four-point MPA AUC investigation. The relationship between MPA AUC performed in the first week after transplantation, as well as median trough cyclosporin concentrations, and clinical outcomes in the first month posttransplant were evaluated. Results: A total of 12 patients experienced biopsy proven rejection (44.4%) and 4 patients had gastrointestinal adverse events (14.8%). A statistically significant relationship was observed between the incidence of biopsy proven rejection and both MPA AUC (p = 0.02) and median trough CsA concentration (p = 0.008). No relationship between trough MPA concentration and rejection was observed (p = 0.21). Only 3 of 11 (27%) patients with an MPA AUC > 30 mg.h/L and a median trough CsA > 175 mug/L experienced acute rejection, compared with a 56% incidence of rejection for the remaining 16 patients. Patients who experienced adverse gastrointestinal events had significantly lower MPA AUC (p = 0.04), but median trough CsA concentrations were not significantly different (p = 0.24). Further, 3 of these 4 patients had rejection episodes. Conclusions: in addition to standard CsA monitoring, we propose further investigation of the use of a 4-point sampling strategy to predict MPA AUC in the first week posttransplant, which may facilitate optimization of mycophenolate mofetil dose at a rime when patients are most vulnerable to acute rejection. (C) 2001 The Canadian Society of Clinical Chemists. All rights reserved.

Free-breathing T2 mapping at 3T for the monitoring of cardiac allograft rejection: initial results

rejection can lead to loss of function. Histological reading of endomyocardial biopsy remains the "gold standard" for guiding immunosuppression, despite its methodological limitations (sampling error and interobserver variability). The measurement of the T2 relaxation time has been suggested for detection of allograft rejection, on the pathophysiological basis that the T2 relaxation time prolongs with local edema resulting from acute allograft rejection. Using breath-held cardiac magnetic resonance T2 mapping at 1.5 T, Usman et al. (CircCardiovascImaging2012) detected moderate allograft rejection (grade 2R, ISHLT 2004). With modern immunosuppression grade 2R rejection has become a rare event, but the need remains for a technique that permits the discrimination of absent (grade 0R) and mild rejection (grade 1R). We therefore investigated whether an increase of magnetic field strength to 3T and the use of real-time navigator-gated respiration compensation allow for an increase in the sensitivity of T2 relaxation time detection that is necessary to achieve this discrimination. Methods: Eighteen patients received EMB (Tan et al., ArchPatholLabMed2007) and cardiac T2 mapping on the same day. Reading of T2 maps was blinded to the histological results. For final analysis, 3 cases with known 2R rejection at the time of T2 mapping were added, yielding 21 T2 mapping sessions. A respiration-navigator-gated radial gradient-recalled-echo pulse sequence (resolution 1.17 mm2, matrix 2562, trigger time 3 heartbeats, T2 preparation duration TET2 Prep = 60/30/0 ms) was applied to obtain 3 short-axis T2 maps (van Heeswijk et al., JACCCardiovascImaging2012), which were segmented according to AHA guidelines (Cerqueira et al, Circulation2001). The highest segmental T2 values were grouped according to histological rejection grade and differences were analyzed by Student's t-test, except for the non-blinded cases with 2R rejection. The degree of discrimination was determined using the Spearman's ranked correlation test. Results: The high-quality T2 maps allowed for visual differentiation of the rejection degrees (Figure 1), and the correlation of T2 mapping with the histological grade of acute cellular rejection was significant (Spearman's r = 0.56, p = 0.007). The 0R (n = 15) and 1R (n = 3) degrees demonstrated significantly different T2 values (46.9 ± 5.0 and 54.3 ± 3.0 ms, p = 0.02, Figure 2). Cases with 2R rejection showed clear T2 elevation (T2 = 60.3 ± 16.2 ms). Conclusions: This pilot study demonstrates that non-invasive free-breathing cardiac T2 mapping at 3T discriminates between no and mild cardiac allograft rejection. Confirmation of these encouraging results in a larger cohort should consider a study able to show equivalency or superiority of T2 mapping.

Efficient sampling from truncated bivariate Gaussians via Box-Muller transformation

Many practical simulation tasks demand procedures to draw samples efficiently from multivariate truncated Gaussian distributions. In this work, we introduce a novel rejection approach, based on the Box-Muller transformation, to generate samples from a truncated bivariate Gaussian density with an arbitrary support. Furthermore, for an important class of support regions the new method allows us to achieve exact sampling, thus becoming the most efficient approach possible. RESUMEN. Método específico para generar muestras de manera eficiente de Gaussianas bidimensionales truncadas con cualquier zona de truncamiento basado en la transformación de Box-Muller.

Sampling times for monitoring tacrolimus in stable adult liver transplant recipients

The aim of this study was to determine the most informative sampling time(s) providing a precise prediction of tacrolimus area under the concentration-time curve (AUC). Fifty-four concentration-time profiles of tacrolimus from 31 adult liver transplant recipients were analyzed. Each profile contained 5 tacrolimus whole-blood concentrations (predose and 1, 2, 4, and 6 or 8 hours postdose), measured using liquid chromatography-tandem mass spectrometry. The concentration at 6 hours was interpolated for each profile, and 54 values of AUC(0-6) were calculated using the trapezoidal rule. The best sampling times were then determined using limited sampling strategies and sensitivity analysis. Linear mixed-effects modeling was performed to estimate regression coefficients of equations incorporating each concentration-time point (C0, C1, C2, C4, interpolated C5, and interpolated C6) as a predictor of AUC(0-6). Predictive performance was evaluated by assessment of the mean error (ME) and root mean square error (RMSE). Limited sampling strategy (LSS) equations with C2, C4, and C5 provided similar results for prediction of AUC(0-6) (R-2 = 0.869, 0.844, and 0.832, respectively). These 3 time points were superior to C0 in the prediction of AUC. The ME was similar for all time points; the RMSE was smallest for C2, C4, and C5. The highest sensitivity index was determined to be 4.9 hours postdose at steady state, suggesting that this time point provides the most information about the AUC(0-12). The results from limited sampling strategies and sensitivity analysis supported the use of a single blood sample at 5 hours postdose as a predictor of both AUC(0-6) and AUC(0-12). A jackknife procedure was used to evaluate the predictive performance of the model, and this demonstrated that collecting a sample at 5 hours after dosing could be considered as the optimal sampling time for predicting AUC(0-6).

Human Herpesvirus-6 And Cytomegalovirus Dna In Liver Donor Biopsies And Their Correlation With Hla Matches And Acute Cellular Rejection.

Herpesvirus reactivation is common after liver transplantation. Analyze the presence of cytomegalovirus (HCMV) and human herpesvirus-6 (HHV-6) DNA in liver donor biopsies, seeking to better understand issues involving human donor leukocyte antigens (HLA)-A, B and DR, as well as correlations with acute cellular rejection. Fifty-nine liver transplantation patients were investigated for the presence of HCMV and HHV-6 DNA in liver donor biopsies, using the Nested-PCR technique. The clinical donor information and HLA matches were obtained from the São Paulo State Transplant System. The recipients' records regarding acute cellular rejection were studied. Seven (11.8%) biopsies were positive for HCMV DNA and 29 (49%) were positive for HHV-6 DNA. In 14 donors with HLA-DR 15 nine had HHV-6 DNA positive liver biopsy with a tendency for significant association (p=0.09), 22 recipients developed acute cellular rejection and 9/22 were positive for HLA-DR 15 (p=0.03; χ(2)=4.51), which was statistically significant in univariate analysis and showed a tendency after multivariate analysis (p=0.08). HHV-6 DNA was prevalent in liver donors studied as well as HLA-DR 15. These findings suggest that patients with HLA-DR 15 in liver donor biopsies develop more rejection after liver transplantation.

Temporal variation of the phytoplankton community at short sampling intervals in the Mundaú reservoir, Northeastern Brazil

The aim of this study was to determine how abiotic factors drive the phytoplankton community in a water supply reservoir within short sampling intervals. Samples were collected at the subsurface (0.1 m) and bottom of limnetic (8 m) and littoral (2 m) zones in both the dry and rainy seasons. The following abiotic variables were analyzed: water temperature, dissolved oxygen, electrical conductivity, total dissolved solids, turbidity, pH, total nitrogen, nitrite, nitrate, total phosphorus, total dissolved phosphorus and orthophosphate. Phytoplankton biomass was determined from biovolume values. The role abiotic variables play in the dynamics of phytoplankton species was determined by means of Canonical Correspondence Analysis. Algae biomass ranged from 1.17×10(4) to 9.21×10(4) µg.L-1; cyanobacteria had biomass values ranging from 1.07×10(4) to 8.21×10(4) µg.L-1. High availability of phosphorous, nitrogen limitation, alkaline pH and thermal stability all favored cyanobacteria blooms, particularly during the dry season. Temperature, pH, total phosphorous and turbidity were key factors in characterizing the phytoplankton community between sampling times and stations. Of the species studied, Cylindrospermopsis raciborskii populations were dominant in the phytoplankton in both the dry and rainy seasons. We conclude that the phytoplankton was strongly influenced by abiotic variables, particularly in relation to seasonal distribution patterns.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Some factors complicate comparisons between linkage maps from different studies. This problem can be resolved if measures of precision, such as confidence intervals and frequency distributions, are associated with markers. We examined the precision of distances and ordering of microsatellite markers in the consensus linkage maps of chromosomes 1, 3 and 4 from two F 2 reciprocal Brazilian chicken populations, using bootstrap sampling. Single and consensus maps were constructed. The consensus map was compared with the International Consensus Linkage Map and with the whole genome sequence. Some loci showed segregation distortion and missing data, but this did not affect the analyses negatively. Several inversions and position shifts were detected, based on 95% confidence intervals and frequency distributions of loci. Some discrepancies in distances between loci and in ordering were due to chance, whereas others could be attributed to other effects, including reciprocal crosses, sampling error of the founder animals from the two populations, F(2) population structure, number of and distance between microsatellite markers, number of informative meioses, loci segregation patterns, and sex. In the Brazilian consensus GGA1, locus LEI1038 was in a position closer to the true genome sequence than in the International Consensus Map, whereas for GGA3 and GGA4, no such differences were found. Extending these analyses to the remaining chromosomes should facilitate comparisons and the integration of several available genetic maps, allowing meta-analyses for map construction and quantitative trait loci (QTL) mapping. The precision of the estimates of QTL positions and their effects would be increased with such information.