Distribution patterns of infection with multiple types of human papillomaviruses and their association with risk factors

Background: Infection with multiple types of human papillomavirus (HPV) is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1,810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical lesions and HPV by Papanicolau testing and DNA PCR detection, respectively. Principal Findings: The negative binomial distribution model used in this study showed differences between the observed and expected values within some risk factor categories analyzed. Particularly in the case of single infection and coinfection with more than 4 HPV types, observed frequencies were smaller than expected, while the number of women infected with 2 to 4 viral types were higher than expected. Data analysis according to a negative binomial regression showed an increase in the risk of acquiring more HPV types in women who were of indigenous ethnicity (+37.8%), while this risk decreased in women who had given birth more than 4 times (-31.1%), or were of mestizo (-24.6%) or black (-40.9%) ethnicity. Conclusions: According to a theoretical probability distribution, the observed number of women having either a single infection or more than 4 viral types was smaller than expected, while for those infected with 2-4 HPV types it was larger than expected. Taking into account that this study showed a higher HPV coinfection rate in the indigenous ethnicity, the role of underlying factors should be assessed in detail in future studies.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

Describing seasonal variability in the distribution of daily effective temperatures for 1985-2009 compared to 1904-1984 for De Bilt, Holland

This paper proposes a method for describing the distribution of observed temperatures on any day of the year such that the distribution and summary statistics of interest derived from the distribution vary smoothly through the year. The method removes the noise inherent in calculating summary statistics directly from the data thus easing comparisons of distributions and summary statistics between different periods. The method is demonstrated using daily effective temperatures (DET) derived from observations of temperature and wind speed at De Bilt, Holland. Distributions and summary statistics are obtained from 1985 to 2009 and compared to the period 1904–1984. A two-stage process first obtains parameters of a theoretical probability distribution, in this case the generalized extreme value (GEV) distribution, which describes the distribution of DET on any day of the year. Second, linear models describe seasonal variation in the parameters. Model predictions provide parameters of the GEV distribution, and therefore summary statistics, that vary smoothly through the year. There is evidence of an increasing mean temperature, a decrease in the variability in temperatures mainly in the winter and more positive skew, more warm days, in the summer. In the winter, the 2% point, the value below which 2% of observations are expected to fall, has risen by 1.2 °C, in the summer the 98% point has risen by 0.8 °C. Medians have risen by 1.1 and 0.9 °C in winter and summer, respectively. The method can be used to describe distributions of future climate projections and other climate variables. Further extensions to the methodology are suggested.

The exponentiated generalized inverse Gaussian distribution

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.

The beta-Birnbaum-Saunders distribution An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies For the first time based on this distribution the so-called beta-Birnbaum-Saunders distribution is proposed for fatigue life modeling Various properties of the new model including expansions for the moments moment generating function mean deviations density function of the order statistics and their moments are derived We discuss maximum likelihood estimation of the model s parameters The superiority of the new model is illustrated by means of three failure real data sets (C) 2010 Elsevier B V All rights reserved

Power flow for primary distribution networks considering uncertainty in demand and user connection

This paper presents a method for calculating the power flow in distribution networks considering uncertainties in the distribution system. Active and reactive power are used as uncertain variables and probabilistically modeled through probability distribution functions. Uncertainty about the connection of the users with the different feeders is also considered. A Monte Carlo simulation is used to generate the possible load scenarios of the users. The results of the power flow considering uncertainty are the mean values and standard deviations of the variables of interest (voltages in all nodes, active and reactive power flows, etc.), giving the user valuable information about how the network will behave under uncertainty rather than the traditional fixed values at one point in time. The method is tested using real data from a primary feeder system, and results are presented considering uncertainty in demand and also in the connection. To demonstrate the usefulness of the approach, the results are then used in a probabilistic risk analysis to identify potential problems of undervoltage in distribution systems. (C) 2012 Elsevier Ltd. All rights reserved.

Analytical and Monte Carlo approaches to evaluate probability distributions of interruption duration

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties-and, in some cases, rewards-that introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the maximum continuous interruption duration (MCID) per customer.This parameter is responsible for the majority of penalties in many electric distribution utilities. This paper describes analytical and Monte Carlo simulation approaches to evaluate probability distributions of interruption duration indices. More emphasis will be given to the development of an analytical method to assess the probability distribution associated with the parameter MCID and the correspond ng penalties. Case studies on a simple distribution network and on a real Brazilian distribution system are presented and discussed.

Variability of daily winter wind speed distribution over Northern Europe during the past millennium in regional and global climate simulations

We analyse the variability of the probability distribution of daily wind speed in wintertime over Northern and Central Europe in a series of global and regional climate simulations covering the last centuries, and in reanalysis products covering approximately the last 60 years. The focus of the study lies on identifying the link of the variations in the wind speed distribution to the regional near-surface temperature, to the meridional temperature gradient and to the North Atlantic Oscillation. Our main result is that the link between the daily wind distribution and the regional climate drivers is strongly model dependent. The global models tend to behave similarly, although they show some discrepancies. The two regional models also tend to behave similarly to each other, but surprisingly the results derived from each regional model strongly deviates from the results derived from its driving global model. In addition, considering multi-centennial timescales, we find in two global simulations a long-term tendency for the probability distribution of daily wind speed to widen through the last centuries. The cause for this widening is likely the effect of the deforestation prescribed in these simulations. We conclude that no clear systematic relationship between the mean temperature, the temperature gradient and/or the North Atlantic Oscillation, with the daily wind speed statistics can be inferred from these simulations. The understand- ing of past and future changes in the distribution of wind speeds, and thus of wind speed extremes, will require a detailed analysis of the representation of the interaction between large-scale and small-scale dynamics.

Modelled spatial and seasonal distribution of Blue Whiting (Micromesistius poutassou) larvae in the North-East Atlantic (1951 to 2005)

Blue whiting (Micromesistius poutassou, http://www.marinespecies.org/aphia.php?p=taxdetails&id=126439) is a small mesopelagic planktivorous gadoid found throughout the North-East Atlantic. This data contains the results of a model-based analysis of larvae captured by the Continuous Plankton Recorder (CPR) during the period 1951-2005. The observations are analysed using Generalised Additive Models (GAMs) of the the spatial, seasonal and interannual variation in the occurrence of larvae. The best fitting model is chosen using the Aikaike Information Criteria (AIC). The probability of occurrence in the continous plankton recorder is then normalised and converted to a probability distribution function in space (UTM projection Zone 28) and season (day of year). The best fitting model splits the distribution into two separate spawning grounds north and south of a dividing line at 53 N. The probability distribution is therefore normalised in these two regions (ie the space-time integral over each of the two regions is 1). The modelled outputs are on a UTM Zone 28 grid: however, for convenience, the latitude ("lat") and longitude ("lon") of each of these grid points are also included as a variable in the NetCDF file. The assignment of each grid point to either the Northern or Southern component (defined here as north/south of 53 N), is also included as a further variable ("component"). Finally, the day of year ("doy") is stored as the number of days elapsed from and included January 1 (ie doy=1 on January 1) - the year is thereafter divided into 180 grid points.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

Effect of data length and bin numbers on distribution entropy (DistEn) measurement in analyzing healthy aging

Complexity analysis of a given time series is executed using various measures of irregularity, the most commonly used being Approximate entropy (ApEn), Sample entropy (SampEn) and Fuzzy entropy (FuzzyEn). However, the dependence of these measures on the critical parameter of tolerance `r' leads to precarious results, owing to random selections of r. Attempts to eliminate the use of r in entropy calculations introduced a new measure of entropy namely distribution entropy (DistEn) based on the empirical probability distribution function (ePDF). DistEn completely avoids the use of a variance dependent parameter like r and replaces it by a parameter M, which corresponds to the number of bins used in the histogram to calculate it. When tested for synthetic data, M has been observed to produce a minimal effect on DistEn as compared to the effect of r on other entropy measures. Also, DistEn is said to be relatively stable with data length (N) variations, as far as synthetic data is concerned. However, these claims have not been analyzed for physiological data. Our study evaluates the effect of data length N and bin number M on the performance of DistEn using both synthetic and physiologic time series data. Synthetic logistic data of `Periodic' and `Chaotic' levels of complexity and 40 RR interval time series belonging to two groups of healthy aging population (young and elderly) have been used for the analysis. The stability and consistency of DistEn as a complexity measure as well as a classifier have been studied. Experiments prove that the parameters N and M are more influential in deciding the efficacy of DistEn performance in the case of physiologic data than synthetic data. Therefore, a generalized random selection of M for a given data length N may not always be an appropriate combination to yield good performance of DistEn for physiologic data.

Prediction of highway truck conveyance configuration under over-limit prohibition and conveyance equilibrium

Aiming at the shortage of prevailing prediction methods about highway truck conveyance configuration in over-limit freight research that transferring the goods attributed to over-limit portion to another fully loaded truck of the same configuration and developing the truck traffic volume synchronously, a new way to get accumulated probability function of truck power tonnage in basal year by highway truck classified by wheel and axle type load mass spectrum investigation was presented. Logit models were used to forecast overall highway freight diversion and single cargo tonnage diversion when the weight rules and strict of enforcement intensity of overload were changed in scheme year. Assumption that the probability distribution of single truck loadage should be consistent with the probability distribution of single goods freighted, the model describes the truck conveyance configuration in the future under strict over-limit prohibition. The model was used and tested in Highway Over-limit Research Project in Anhui by World Bank.