Modeling motor vehicle crashes using Poisson-gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter.

PubMed

Lord, Dominique

2006-07-01

There has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution; when crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the "low mean problem" (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies and should, therefore, be reliably estimated. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of an unreliably estimated dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used by transportation safety modelers for estimating the dispersion parameter of Poisson-gamma models were evaluated: the method of moments, the weighted regression, and the maximum likelihood method. In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes unreliably estimated increases significantly as the sample mean and sample size decrease. Consequently, the results show that an unreliably estimated dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with an unreliable dispersion parameter for modeling motor vehicle crashes.

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.

PubMed

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

Bayesian inference on multiscale models for poisson intensity estimation: applications to photon-limited image denoising.

PubMed

Lefkimmiatis, Stamatios; Maragos, Petros; Papandreou, George

2009-08-01

We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data.

PubMed

Sepúlveda, Nuno; Campino, Susana G; Assefa, Samuel A; Sutherland, Colin J; Pain, Arnab; Clark, Taane G

2013-02-26

The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data.

Characterizing the performance of the Conway-Maxwell Poisson generalized linear model.

PubMed

Francis, Royce A; Geedipally, Srinivas Reddy; Guikema, Seth D; Dhavala, Soma Sekhar; Lord, Dominique; LaRocca, Sarah

2012-01-01

Count data are pervasive in many areas of risk analysis; deaths, adverse health outcomes, infrastructure system failures, and traffic accidents are all recorded as count events, for example. Risk analysts often wish to estimate the probability distribution for the number of discrete events as part of doing a risk assessment. Traditional count data regression models of the type often used in risk assessment for this problem suffer from limitations due to the assumed variance structure. A more flexible model based on the Conway-Maxwell Poisson (COM-Poisson) distribution was recently proposed, a model that has the potential to overcome the limitations of the traditional model. However, the statistical performance of this new model has not yet been fully characterized. This article assesses the performance of a maximum likelihood estimation method for fitting the COM-Poisson generalized linear model (GLM). The objectives of this article are to (1) characterize the parameter estimation accuracy of the MLE implementation of the COM-Poisson GLM, and (2) estimate the prediction accuracy of the COM-Poisson GLM using simulated data sets. The results of the study indicate that the COM-Poisson GLM is flexible enough to model under-, equi-, and overdispersed data sets with different sample mean values. The results also show that the COM-Poisson GLM yields accurate parameter estimates. The COM-Poisson GLM provides a promising and flexible approach for performing count data regression. © 2011 Society for Risk Analysis.

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution

PubMed Central

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section. PMID:28983398

Paretian Poisson Processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2008-05-01

Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ` Paretian Poisson processes'. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks.

PubMed

Reis, Matthias; Kromer, Justus A; Klipp, Edda

2018-01-20

Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription-translation network and Bateman's model from nuclear physics. For both examples, multimodality was previously not reported.

On the fractal characterization of Paretian Poisson processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo I.; Sokolov, Igor M.

2012-06-01

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

Background stratified Poisson regression analysis of cohort data.

PubMed

Richardson, David B; Langholz, Bryan

2012-03-01

Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models.

Multi-Parameter Linear Least-Squares Fitting to Poisson Data One Count at a Time

NASA Technical Reports Server (NTRS)

Wheaton, W.; Dunklee, A.; Jacobson, A.; Ling, J.; Mahoney, W.; Radocinski, R.

1993-01-01

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multi-component linear model, with underlying physical count rates or fluxes which are to be estimated from the data.

Analysis of overdispersed count data: application to the Human Papillomavirus Infection in Men (HIM) Study.

PubMed

Lee, J-H; Han, G; Fulp, W J; Giuliano, A R

2012-06-01

The Poisson model can be applied to the count of events occurring within a specific time period. The main feature of the Poisson model is the assumption that the mean and variance of the count data are equal. However, this equal mean-variance relationship rarely occurs in observational data. In most cases, the observed variance is larger than the assumed variance, which is called overdispersion. Further, when the observed data involve excessive zero counts, the problem of overdispersion results in underestimating the variance of the estimated parameter, and thus produces a misleading conclusion. We illustrated the use of four models for overdispersed count data that may be attributed to excessive zeros. These are Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial models. The example data in this article deal with the number of incidents involving human papillomavirus infection. The four models resulted in differing statistical inferences. The Poisson model, which is widely used in epidemiology research, underestimated the standard errors and overstated the significance of some covariates.

Eruption patterns of the chilean volcanoes Villarrica, Llaima, and Tupungatito

NASA Astrophysics Data System (ADS)

Muñoz, Miguel

1983-09-01

The historical eruption records of three Chilean volcanoes have been subjected to many statistical tests, and none have been found to differ significantly from random, or Poissonian, behaviour. The statistical analysis shows rough conformity with the descriptions determined from the eruption rate functions. It is possible that a constant eruption rate describes the activity of Villarrica; Llaima and Tupungatito present complex eruption rate patterns that appear, however, to have no statistical significance. Questions related to loading and extinction processes and to the existence of shallow secondary magma chambers to which magma is supplied from a deeper system are also addressed. The analysis and the computation of the serial correlation coefficients indicate that the three series may be regarded as stationary renewal processes. None of the test statistics indicates rejection of the Poisson hypothesis at a level less than 5%, but the coefficient of variation for the eruption series at Llaima is significantly different from the value expected for a Poisson process. Also, the estimates of the normalized spectrum of the counting process for the three series suggest a departure from the random model, but the deviations are not found to be significant at the 5% level. Kolmogorov-Smirnov and chi-squared test statistics, applied directly to ascertaining to which probability P the random Poisson model fits the data, indicate that there is significant agreement in the case of Villarrica ( P=0.59) and Tupungatito ( P=0.3). Even though the P-value for Llaima is a marginally significant 0.1 (which is equivalent to rejecting the Poisson model at the 90% confidence level), the series suggests that nonrandom features are possibly present in the eruptive activity of this volcano.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data

PubMed Central

2013-01-01

Background The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. Results Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. Conclusions In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data. PMID:23442253

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

PubMed

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

PubMed Central

Neti, Prasad V.S.V.; Howell, Roger W.

2010-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log-normal (LN) distribution function (J Nucl Med. 2006;47:1049–1058) with the aid of autoradiography. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analysis of these earlier data. Methods The measured distributions of α-particle tracks per cell were subjected to statistical tests with Poisson, LN, and Poisson-lognormal (P-LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL of 210Po-citrate. When cells were exposed to 67 kBq/mL, the P-LN distribution function gave a better fit; however, the underlying activity distribution remained log-normal. Conclusion The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:18483086

Log Normal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of Alpha Particle Track Autoradiography

PubMed Central

Neti, Prasad V.S.V.; Howell, Roger W.

2008-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log normal distribution function (J Nucl Med 47, 6 (2006) 1049-1058) with the aid of an autoradiographic approach. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analyses of these data. Methods The measured distributions of alpha particle tracks per cell were subjected to statistical tests with Poisson (P), log normal (LN), and Poisson – log normal (P – LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL 210Po-citrate. When cells were exposed to 67 kBq/mL, the P – LN distribution function gave a better fit, however, the underlying activity distribution remained log normal. Conclusions The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:16741316

Evolving Scale-Free Networks by Poisson Process: Modeling and Degree Distribution.

PubMed

Feng, Minyu; Qu, Hong; Yi, Zhang; Xie, Xiurui; Kurths, Jurgen

2016-05-01

Since the great mathematician Leonhard Euler initiated the study of graph theory, the network has been one of the most significant research subject in multidisciplinary. In recent years, the proposition of the small-world and scale-free properties of complex networks in statistical physics made the network science intriguing again for many researchers. One of the challenges of the network science is to propose rational models for complex networks. In this paper, in order to reveal the influence of the vertex generating mechanism of complex networks, we propose three novel models based on the homogeneous Poisson, nonhomogeneous Poisson and birth death process, respectively, which can be regarded as typical scale-free networks and utilized to simulate practical networks. The degree distribution and exponent are analyzed and explained in mathematics by different approaches. In the simulation, we display the modeling process, the degree distribution of empirical data by statistical methods, and reliability of proposed networks, results show our models follow the features of typical complex networks. Finally, some future challenges for complex systems are discussed.

Understanding poisson regression.

PubMed

Hayat, Matthew J; Higgins, Melinda

2014-04-01

Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

Evolutionary inference via the Poisson Indel Process.

PubMed

Bouchard-Côté, Alexandre; Jordan, Michael I

2013-01-22

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

Evolutionary inference via the Poisson Indel Process

PubMed Central

Bouchard-Côté, Alexandre; Jordan, Michael I.

2013-01-01

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114–124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments. PMID:23275296

A new multivariate zero-adjusted Poisson model with applications to biomedicine.

PubMed

Liu, Yin; Tian, Guo-Liang; Tang, Man-Lai; Yuen, Kam Chuen

2018-05-25

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, ) cannot be used to fit multivariate count data with excess zero-vectors; (ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases; (iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Poisson regression models outperform the geometrical model in estimating the peak-to-trough ratio of seasonal variation: a simulation study.

PubMed

Christensen, A L; Lundbye-Christensen, S; Dethlefsen, C

2011-12-01

Several statistical methods of assessing seasonal variation are available. Brookhart and Rothman [3] proposed a second-order moment-based estimator based on the geometrical model derived by Edwards [1], and reported that this estimator is superior in estimating the peak-to-trough ratio of seasonal variation compared with Edwards' estimator with respect to bias and mean squared error. Alternatively, seasonal variation may be modelled using a Poisson regression model, which provides flexibility in modelling the pattern of seasonal variation and adjustments for covariates. Based on a Monte Carlo simulation study three estimators, one based on the geometrical model, and two based on log-linear Poisson regression models, were evaluated in regards to bias and standard deviation (SD). We evaluated the estimators on data simulated according to schemes varying in seasonal variation and presence of a secular trend. All methods and analyses in this paper are available in the R package Peak2Trough[13]. Applying a Poisson regression model resulted in lower absolute bias and SD for data simulated according to the corresponding model assumptions. Poisson regression models had lower bias and SD for data simulated to deviate from the corresponding model assumptions than the geometrical model. This simulation study encourages the use of Poisson regression models in estimating the peak-to-trough ratio of seasonal variation as opposed to the geometrical model. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Time distributions of solar energetic particle events: Are SEPEs really random?

NASA Astrophysics Data System (ADS)

Jiggens, P. T. A.; Gabriel, S. B.

2009-10-01

Solar energetic particle events (SEPEs) can exhibit flux increases of several orders of magnitude over background levels and have always been considered to be random in nature in statistical models with no dependence of any one event on the occurrence of previous events. We examine whether this assumption of randomness in time is correct. Engineering modeling of SEPEs is important to enable reliable and efficient design of both Earth-orbiting and interplanetary spacecraft and future manned missions to Mars and the Moon. All existing engineering models assume that the frequency of SEPEs follows a Poisson process. We present analysis of the event waiting times using alternative distributions described by Lévy and time-dependent Poisson processes and compared these with the usual Poisson distribution. The results show significant deviation from a Poisson process and indicate that the underlying physical processes might be more closely related to a Lévy-type process, suggesting that there is some inherent “memory” in the system. Inherent Poisson assumptions of stationarity and event independence are investigated, and it appears that they do not hold and can be dependent upon the event definition used. SEPEs appear to have some memory indicating that events are not completely random with activity levels varying even during solar active periods and are characterized by clusters of events. This could have significant ramifications for engineering models of the SEP environment, and it is recommended that current statistical engineering models of the SEP environment should be modified to incorporate long-term event dependency and short-term system memory.

Marginalized zero-inflated Poisson models with missing covariates.

PubMed

Benecha, Habtamu K; Preisser, John S; Divaris, Kimon; Herring, Amy H; Das, Kalyan

2018-05-11

Unlike zero-inflated Poisson regression, marginalized zero-inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school-based fluoride mouthrinse program. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Analyzing hospitalization data: potential limitations of Poisson regression.

PubMed

Weaver, Colin G; Ravani, Pietro; Oliver, Matthew J; Austin, Peter C; Quinn, Robert R

2015-08-01

Poisson regression is commonly used to analyze hospitalization data when outcomes are expressed as counts (e.g. number of days in hospital). However, data often violate the assumptions on which Poisson regression is based. More appropriate extensions of this model, while available, are rarely used. We compared hospitalization data between 206 patients treated with hemodialysis (HD) and 107 treated with peritoneal dialysis (PD) using Poisson regression and compared results from standard Poisson regression with those obtained using three other approaches for modeling count data: negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression. We examined the appropriateness of each model and compared the results obtained with each approach. During a mean 1.9 years of follow-up, 183 of 313 patients (58%) were never hospitalized (indicating an excess of 'zeros'). The data also displayed overdispersion (variance greater than mean), violating another assumption of the Poisson model. Using four criteria, we determined that the NB and ZINB models performed best. According to these two models, patients treated with HD experienced similar hospitalization rates as those receiving PD {NB rate ratio (RR): 1.04 [bootstrapped 95% confidence interval (CI): 0.49-2.20]; ZINB summary RR: 1.21 (bootstrapped 95% CI 0.60-2.46)}. Poisson and ZIP models fit the data poorly and had much larger point estimates than the NB and ZINB models [Poisson RR: 1.93 (bootstrapped 95% CI 0.88-4.23); ZIP summary RR: 1.84 (bootstrapped 95% CI 0.88-3.84)]. We found substantially different results when modeling hospitalization data, depending on the approach used. Our results argue strongly for a sound model selection process and improved reporting around statistical methods used for modeling count data. © The Author 2015. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

Leptospirosis disease mapping with standardized morbidity ratio and Poisson-Gamma model: An analysis of Leptospirosis disease in Kelantan, Malaysia

NASA Astrophysics Data System (ADS)

Che Awang, Aznida; Azah Samat, Nor

2017-09-01

Leptospirosis is a disease caused by the infection of pathogenic species from the genus of Leptospira. Human can be infected by the leptospirosis from direct or indirect exposure to the urine of infected animals. The excretion of urine from the animal host that carries pathogenic Leptospira causes the soil or water to be contaminated. Therefore, people can become infected when they are exposed to contaminated soil and water by cut on the skin as well as open wound. It also can enter the human body by mucous membrane such nose, eyes and mouth, for example by splashing contaminated water or urine into the eyes or swallowing contaminated water or food. Currently, there is no vaccine available for the prevention or treatment of leptospirosis disease but this disease can be treated if it is diagnosed early to avoid any complication. The disease risk mapping is important in a way to control and prevention of disease. Using a good choice of statistical model will produce a good disease risk map. Therefore, the aim of this study is to estimate the relative risk for leptospirosis disease based initially on the most common statistic used in disease mapping called Standardized Morbidity Ratio (SMR) and Poisson-gamma model. This paper begins by providing a review of the SMR method and Poisson-gamma model, which we then applied to leptospirosis data of Kelantan, Malaysia. Both results are displayed and compared using graph, tables and maps. The result shows that the second method Poisson-gamma model produces better relative risk estimates compared to the SMR method. This is because the Poisson-gamma model can overcome the drawback of SMR where the relative risk will become zero when there is no observed leptospirosis case in certain regions. However, the Poisson-gamma model also faced problems where the covariate adjustment for this model is difficult and no possibility for allowing spatial correlation between risks in neighbouring areas. The problems of this model have motivated many researchers to introduce other alternative methods for estimating the risk.

Weather variability and the incidence of cryptosporidiosis: comparison of time series poisson regression and SARIMA models.

PubMed

Hu, Wenbiao; Tong, Shilu; Mengersen, Kerrie; Connell, Des

2007-09-01

Few studies have examined the relationship between weather variables and cryptosporidiosis in Australia. This paper examines the potential impact of weather variability on the transmission of cryptosporidiosis and explores the possibility of developing an empirical forecast system. Data on weather variables, notified cryptosporidiosis cases, and population size in Brisbane were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics for the period of January 1, 1996-December 31, 2004, respectively. Time series Poisson regression and seasonal auto-regression integrated moving average (SARIMA) models were performed to examine the potential impact of weather variability on the transmission of cryptosporidiosis. Both the time series Poisson regression and SARIMA models show that seasonal and monthly maximum temperature at a prior moving average of 1 and 3 months were significantly associated with cryptosporidiosis disease. It suggests that there may be 50 more cases a year for an increase of 1 degrees C maximum temperature on average in Brisbane. Model assessments indicated that the SARIMA model had better predictive ability than the Poisson regression model (SARIMA: root mean square error (RMSE): 0.40, Akaike information criterion (AIC): -12.53; Poisson regression: RMSE: 0.54, AIC: -2.84). Furthermore, the analysis of residuals shows that the time series Poisson regression appeared to violate a modeling assumption, in that residual autocorrelation persisted. The results of this study suggest that weather variability (particularly maximum temperature) may have played a significant role in the transmission of cryptosporidiosis. A SARIMA model may be a better predictive model than a Poisson regression model in the assessment of the relationship between weather variability and the incidence of cryptosporidiosis.

Parameter Estimation in Astronomy with Poisson-Distributed Data. 1; The (CHI)2(gamma) Statistic

NASA Technical Reports Server (NTRS)

Mighell, Kenneth J.

1999-01-01

Applying the standard weighted mean formula, [Sigma (sub i)n(sub i)ssigma(sub i, sup -2)], to determine the weighted mean of data, n(sub i), drawn from a Poisson distribution, will, on average, underestimate the true mean by approx. 1 for all true mean values larger than approx.3 when the common assumption is made that the error of the i th observation is sigma(sub i) = max square root of n(sub i), 1).This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques which use the modified Neyman'chi(sub 2) statistic, chi(sup 2, sub N) equivalent Sigma(sub i)((n(sub i) - y(sub i)(exp 2)) / max(n(sub i), 1), to compare Poisson - distributed data with model values, y(sub i), will typically predict a total number of counts that underestimates the true total by about 1 count per bin. Based on my finding that weighted mean of data drawn from a Poisson distribution can be determined using the formula [Sigma(sub i)[n(sub i) + min(n(sub i), 1)](n(sub i) + 1)(exp -1)] / [Sigma(sub i)(n(sub i) + 1)(exp -1))], I propose that a new chi(sub 2) statistic, chi(sup 2, sub gamma) equivalent, should always be used to analyze Poisson- distributed data in preference to the modified Neyman's chi(exp 2) statistic. I demonstrated the power and usefulness of,chi(sub gamma, sup 2) minimization by using two statistical fitting techniques and five chi(exp 2) statistics to analyze simulated X-ray power - low 15 - channel spectra with large and small counts per bin. I show that chi(sub gamma, sup 2) minimization with the Levenberg - Marquardt or Powell's method can produce excellent results (mean slope errors approx. less than 3%) with spectra having as few as 25 total counts.

Fuzzy classifier based support vector regression framework for Poisson ratio determination

NASA Astrophysics Data System (ADS)

Asoodeh, Mojtaba; Bagheripour, Parisa

2013-09-01

Poisson ratio is considered as one of the most important rock mechanical properties of hydrocarbon reservoirs. Determination of this parameter through laboratory measurement is time, cost, and labor intensive. Furthermore, laboratory measurements do not provide continuous data along the reservoir intervals. Hence, a fast, accurate, and inexpensive way of determining Poisson ratio which produces continuous data over the whole reservoir interval is desirable. For this purpose, support vector regression (SVR) method based on statistical learning theory (SLT) was employed as a supervised learning algorithm to estimate Poisson ratio from conventional well log data. SVR is capable of accurately extracting the implicit knowledge contained in conventional well logs and converting the gained knowledge into Poisson ratio data. Structural risk minimization (SRM) principle which is embedded in the SVR structure in addition to empirical risk minimization (EMR) principle provides a robust model for finding quantitative formulation between conventional well log data and Poisson ratio. Although satisfying results were obtained from an individual SVR model, it had flaws of overestimation in low Poisson ratios and underestimation in high Poisson ratios. These errors were eliminated through implementation of fuzzy classifier based SVR (FCBSVR). The FCBSVR significantly improved accuracy of the final prediction. This strategy was successfully applied to data from carbonate reservoir rocks of an Iranian Oil Field. Results indicated that SVR predicted Poisson ratio values are in good agreement with measured values.

Poisson Regression Analysis of Illness and Injury Surveillance Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frome E.L., Watkins J.P., Ellis E.D.

2012-12-12

The Department of Energy (DOE) uses illness and injury surveillance to monitor morbidity and assess the overall health of the work force. Data collected from each participating site include health events and a roster file with demographic information. The source data files are maintained in a relational data base, and are used to obtain stratified tables of health event counts and person time at risk that serve as the starting point for Poisson regression analysis. The explanatory variables that define these tables are age, gender, occupational group, and time. Typical response variables of interest are the number of absences duemore » to illness or injury, i.e., the response variable is a count. Poisson regression methods are used to describe the effect of the explanatory variables on the health event rates using a log-linear main effects model. Results of fitting the main effects model are summarized in a tabular and graphical form and interpretation of model parameters is provided. An analysis of deviance table is used to evaluate the importance of each of the explanatory variables on the event rate of interest and to determine if interaction terms should be considered in the analysis. Although Poisson regression methods are widely used in the analysis of count data, there are situations in which over-dispersion occurs. This could be due to lack-of-fit of the regression model, extra-Poisson variation, or both. A score test statistic and regression diagnostics are used to identify over-dispersion. A quasi-likelihood method of moments procedure is used to evaluate and adjust for extra-Poisson variation when necessary. Two examples are presented using respiratory disease absence rates at two DOE sites to illustrate the methods and interpretation of the results. In the first example the Poisson main effects model is adequate. In the second example the score test indicates considerable over-dispersion and a more detailed analysis attributes the over-dispersion to extra-Poisson variation. The R open source software environment for statistical computing and graphics is used for analysis. Additional details about R and the data that were used in this report are provided in an Appendix. Information on how to obtain R and utility functions that can be used to duplicate results in this report are provided.« less

Statistical properties of several models of fractional random point processes

NASA Astrophysics Data System (ADS)

Bendjaballah, C.

2011-08-01

Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.

Limitations of Poisson statistics in describing radioactive decay.

PubMed

Sitek, Arkadiusz; Celler, Anna M

2015-12-01

The assumption that nuclear decays are governed by Poisson statistics is an approximation. This approximation becomes unjustified when data acquisition times longer than or even comparable with the half-lives of the radioisotope in the sample are considered. In this work, the limits of the Poisson-statistics approximation are investigated. The formalism for the statistics of radioactive decay based on binomial distribution is derived. The theoretical factor describing the deviation of variance of the number of decays predicated by the Poisson distribution from the true variance is defined and investigated for several commonly used radiotracers such as (18)F, (15)O, (82)Rb, (13)N, (99m)Tc, (123)I, and (201)Tl. The variance of the number of decays estimated using the Poisson distribution is significantly different than the true variance for a 5-minute observation time of (11)C, (15)O, (13)N, and (82)Rb. Durations of nuclear medicine studies often are relatively long; they may be even a few times longer than the half-lives of some short-lived radiotracers. Our study shows that in such situations the Poisson statistics is unsuitable and should not be applied to describe the statistics of the number of decays in radioactive samples. However, the above statement does not directly apply to counting statistics at the level of event detection. Low sensitivities of detectors which are used in imaging studies make the Poisson approximation near perfect. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Large Occurrence Patterns of New Zealand Deep Earthquakes: Characterization by Use of a Switching Poisson Model

NASA Astrophysics Data System (ADS)

Shaochuan, Lu; Vere-Jones, David

2011-10-01

The paper studies the statistical properties of deep earthquakes around North Island, New Zealand. We first evaluate the catalogue coverage and completeness of deep events according to cusum (cumulative sum) statistics and earlier literature. The epicentral, depth, and magnitude distributions of deep earthquakes are then discussed. It is worth noting that strong grouping effects are observed in the epicentral distribution of these deep earthquakes. Also, although the spatial distribution of deep earthquakes does not change, their occurrence frequencies vary from time to time, active in one period, relatively quiescent in another. The depth distribution of deep earthquakes also hardly changes except for events with focal depth less than 100 km. On the basis of spatial concentration we partition deep earthquakes into several groups—the Taupo-Bay of Plenty group, the Taranaki group, and the Cook Strait group. Second-order moment analysis via the two-point correlation function reveals only very small-scale clustering of deep earthquakes, presumably limited to some hot spots only. We also suggest that some models usually used for shallow earthquakes fit deep earthquakes unsatisfactorily. Instead, we propose a switching Poisson model for the occurrence patterns of deep earthquakes. The goodness-of-fit test suggests that the time-varying activity is well characterized by a switching Poisson model. Furthermore, detailed analysis carried out on each deep group by use of switching Poisson models reveals similar time-varying behavior in occurrence frequencies in each group.

Statistical modeling of storm-level Kp occurrences

USGS Publications Warehouse

Remick, K.J.; Love, J.J.

2006-01-01

We consider the statistical modeling of the occurrence in time of large Kp magnetic storms as a Poisson process, testing whether or not relatively rare, large Kp events can be considered to arise from a stochastic, sequential, and memoryless process. For a Poisson process, the wait times between successive events occur statistically with an exponential density function. Fitting an exponential function to the durations between successive large Kp events forms the basis of our analysis. Defining these wait times by calculating the differences between times when Kp exceeds a certain value, such as Kp ??? 5, we find the wait-time distribution is not exponential. Because large storms often have several periods with large Kp values, their occurrence in time is not memoryless; short duration wait times are not independent of each other and are often clumped together in time. If we remove same-storm large Kp occurrences, the resulting wait times are very nearly exponentially distributed and the storm arrival process can be characterized as Poisson. Fittings are performed on wait time data for Kp ??? 5, 6, 7, and 8. The mean wait times between storms exceeding such Kp thresholds are 7.12, 16.55, 42.22, and 121.40 days respectively.

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

NASA Technical Reports Server (NTRS)

Erkmen, Baris I.; Moision, Bruce E.

2010-01-01

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Risk Estimation for Lung Cancer in Libya: Analysis Based on Standardized Morbidity Ratio, Poisson-Gamma Model, BYM Model and Mixture Model

PubMed

Alhdiri, Maryam Ahmed; Samat, Nor Azah; Mohamed, Zulkifley

2017-03-01

Cancer is the most rapidly spreading disease in the world, especially in developing countries, including Libya. Cancer represents a significant burden on patients, families, and their societies. This disease can be controlled if detected early. Therefore, disease mapping has recently become an important method in the fields of public health research and disease epidemiology. The correct choice of statistical model is a very important step to producing a good map of a disease. Libya was selected to perform this work and to examine its geographical variation in the incidence of lung cancer. The objective of this paper is to estimate the relative risk for lung cancer. Four statistical models to estimate the relative risk for lung cancer and population censuses of the study area for the time period 2006 to 2011 were used in this work. They are initially known as Standardized Morbidity Ratio, which is the most popular statistic, which used in the field of disease mapping, Poisson-gamma model, which is one of the earliest applications of Bayesian methodology, Besag, York and Mollie (BYM) model and Mixture model. As an initial step, this study begins by providing a review of all proposed models, which we then apply to lung cancer data in Libya. Maps, tables and graph, goodness-of-fit (GOF) were used to compare and present the preliminary results. This GOF is common in statistical modelling to compare fitted models. The main general results presented in this study show that the Poisson-gamma model, BYM model, and Mixture model can overcome the problem of the first model (SMR) when there is no observed lung cancer case in certain districts. Results show that the Mixture model is most robust and provides better relative risk estimates across a range of models. Creative Commons Attribution License

Risk Estimation for Lung Cancer in Libya: Analysis Based on Standardized Morbidity Ratio, Poisson-Gamma Model, BYM Model and Mixture Model

PubMed Central

Alhdiri, Maryam Ahmed; Samat, Nor Azah; Mohamed, Zulkifley

2017-01-01

Cancer is the most rapidly spreading disease in the world, especially in developing countries, including Libya. Cancer represents a significant burden on patients, families, and their societies. This disease can be controlled if detected early. Therefore, disease mapping has recently become an important method in the fields of public health research and disease epidemiology. The correct choice of statistical model is a very important step to producing a good map of a disease. Libya was selected to perform this work and to examine its geographical variation in the incidence of lung cancer. The objective of this paper is to estimate the relative risk for lung cancer. Four statistical models to estimate the relative risk for lung cancer and population censuses of the study area for the time period 2006 to 2011 were used in this work. They are initially known as Standardized Morbidity Ratio, which is the most popular statistic, which used in the field of disease mapping, Poisson-gamma model, which is one of the earliest applications of Bayesian methodology, Besag, York and Mollie (BYM) model and Mixture model. As an initial step, this study begins by providing a review of all proposed models, which we then apply to lung cancer data in Libya. Maps, tables and graph, goodness-of-fit (GOF) were used to compare and present the preliminary results. This GOF is common in statistical modelling to compare fitted models. The main general results presented in this study show that the Poisson-gamma model, BYM model, and Mixture model can overcome the problem of the first model (SMR) when there is no observed lung cancer case in certain districts. Results show that the Mixture model is most robust and provides better relative risk estimates across a range of models. PMID:28440974

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of thismore » object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.« less

Comment on: 'A Poisson resampling method for simulating reduced counts in nuclear medicine images'.

PubMed

de Nijs, Robin

2015-07-21

In order to be able to calculate half-count images from already acquired data, White and Lawson published their method based on Poisson resampling. They verified their method experimentally by measurements with a Co-57 flood source. In this comment their results are reproduced and confirmed by a direct numerical simulation in Matlab. Not only Poisson resampling, but also two direct redrawing methods were investigated. Redrawing methods were based on a Poisson and a Gaussian distribution. Mean, standard deviation, skewness and excess kurtosis half-count/full-count ratios were determined for all methods, and compared to the theoretical values for a Poisson distribution. Statistical parameters showed the same behavior as in the original note and showed the superiority of the Poisson resampling method. Rounding off before saving of the half count image had a severe impact on counting statistics for counts below 100. Only Poisson resampling was not affected by this, while Gaussian redrawing was less affected by it than Poisson redrawing. Poisson resampling is the method of choice, when simulating half-count (or less) images from full-count images. It simulates correctly the statistical properties, also in the case of rounding off of the images.

Quantum statistics of Raman scattering model with Stokes mode generation

NASA Technical Reports Server (NTRS)

Tanatar, Bilal; Shumovsky, Alexander S.

1994-01-01

The model describing three coupled quantum oscillators with decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. Due to the Manley-Rowe relations the problem of exact eigenvalues and eigenstates is reduced to the calculation of new orthogonal polynomials defined both by the difference and differential equations. The quantum statistical properties are examined in the case when initially: the Stokes mode is in the vacuum state; the Rayleigh mode is in the number state; and the vibration mode is in the number of or squeezed states. The collapses and revivals are obtained for different initial conditions as well as the change in time the sub-Poisson distribution by the super-Poisson distribution and vice versa.

Universal Poisson Statistics of mRNAs with Complex Decay Pathways.

PubMed

Thattai, Mukund

2016-01-19

Messenger RNA (mRNA) dynamics in single cells are often modeled as a memoryless birth-death process with a constant probability per unit time that an mRNA molecule is synthesized or degraded. This predicts a Poisson steady-state distribution of mRNA number, in close agreement with experiments. This is surprising, since mRNA decay is known to be a complex process. The paradox is resolved by realizing that the Poisson steady state generalizes to arbitrary mRNA lifetime distributions. A mapping between mRNA dynamics and queueing theory highlights an identifiability problem: a measured Poisson steady state is consistent with a large variety of microscopic models. Here, I provide a rigorous and intuitive explanation for the universality of the Poisson steady state. I show that the mRNA birth-death process and its complex decay variants all take the form of the familiar Poisson law of rare events, under a nonlinear rescaling of time. As a corollary, not only steady-states but also transients are Poisson distributed. Deviations from the Poisson form occur only under two conditions, promoter fluctuations leading to transcriptional bursts or nonindependent degradation of mRNA molecules. These results place severe limits on the power of single-cell experiments to probe microscopic mechanisms, and they highlight the need for single-molecule measurements. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

A random-censoring Poisson model for underreported data.

PubMed

de Oliveira, Guilherme Lopes; Loschi, Rosangela Helena; Assunção, Renato Martins

2017-12-30

A major challenge when monitoring risks in socially deprived areas of under developed countries is that economic, epidemiological, and social data are typically underreported. Thus, statistical models that do not take the data quality into account will produce biased estimates. To deal with this problem, counts in suspected regions are usually approached as censored information. The censored Poisson model can be considered, but all censored regions must be precisely known a priori, which is not a reasonable assumption in most practical situations. We introduce the random-censoring Poisson model (RCPM) which accounts for the uncertainty about both the count and the data reporting processes. Consequently, for each region, we will be able to estimate the relative risk for the event of interest as well as the censoring probability. To facilitate the posterior sampling process, we propose a Markov chain Monte Carlo scheme based on the data augmentation technique. We run a simulation study comparing the proposed RCPM with 2 competitive models. Different scenarios are considered. RCPM and censored Poisson model are applied to account for potential underreporting of early neonatal mortality counts in regions of Minas Gerais State, Brazil, where data quality is known to be poor. Copyright © 2017 John Wiley & Sons, Ltd.

Poisson mixture model for measurements using counting.

PubMed

Miller, Guthrie; Justus, Alan; Vostrotin, Vadim; Dry, Donald; Bertelli, Luiz

2010-03-01

Starting with the basic Poisson statistical model of a counting measurement process, 'extraPoisson' variance or 'overdispersion' are included by assuming that the Poisson parameter representing the mean number of counts itself comes from another distribution. The Poisson parameter is assumed to be given by the quantity of interest in the inference process multiplied by a lognormally distributed normalising coefficient plus an additional lognormal background that might be correlated with the normalising coefficient (shared uncertainty). The example of lognormal environmental background in uranium urine data is discussed. An additional uncorrelated background is also included. The uncorrelated background is estimated from a background count measurement using Bayesian arguments. The rather complex formulas are validated using Monte Carlo. An analytical expression is obtained for the probability distribution of gross counts coming from the uncorrelated background, which allows straightforward calculation of a classical decision level in the form of a gross-count alarm point with a desired false-positive rate. The main purpose of this paper is to derive formulas for exact likelihood calculations in the case of various kinds of backgrounds.

Influence of the nucleus area distribution on the survival fraction after charged particles broad beam irradiation.

PubMed

Wéra, A-C; Barazzuol, L; Jeynes, J C G; Merchant, M J; Suzuki, M; Kirkby, K J

2014-08-07

It is well known that broad beam irradiation with heavy ions leads to variation in the number of hit(s) received by each cell as the distribution of particles follows the Poisson statistics. Although the nucleus area will determine the number of hit(s) received for a given dose, variation amongst its irradiated cell population is generally not considered. In this work, we investigate the effect of the nucleus area's distribution on the survival fraction. More specifically, this work aims to explain the deviation, or tail, which might be observed in the survival fraction at high irradiation doses. For this purpose, the nucleus area distribution was added to the beam Poisson statistics and the Linear-Quadratic model in order to fit the experimental data. As shown in this study, nucleus size variation, and the associated Poisson statistics, can lead to an upward survival trend after broad beam irradiation. The influence of the distribution parameters (mean area and standard deviation) was studied using a normal distribution, along with the Linear-Quadratic model parameters (α and β). Finally, the model proposed here was successfully tested to the survival fraction of LN18 cells irradiated with a 85 keV µm(- 1) carbon ion broad beam for which the distribution in the area of the nucleus had been determined.

Punctuated equilibrium dynamics in human communications

NASA Astrophysics Data System (ADS)

Peng, Dan; Han, Xiao-Pu; Wei, Zong-Wen; Wang, Bing-Hong

2015-10-01

A minimal model based on network incorporating individual interactions is proposed to study the non-Poisson statistical properties of human behavior: individuals in system interact with their neighbors, the probability of an individual acting correlates to its activity, and all the individuals involved in action will change their activities randomly. The model reproduces varieties of spatial-temporal patterns observed in empirical studies of human daily communications, providing insight into various human activities and embracing a range of realistic social interacting systems, particularly, intriguing bimodal phenomenon. This model bridges priority queueing theory and punctuated equilibrium dynamics, and our modeling and analysis is likely to shed light on non-Poisson phenomena in many complex systems.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

From Loss of Memory to Poisson.

ERIC Educational Resources Information Center

Johnson, Bruce R.

1983-01-01

A way of presenting the Poisson process and deriving the Poisson distribution for upper-division courses in probability or mathematical statistics is presented. The main feature of the approach lies in the formulation of Poisson postulates with immediate intuitive appeal. (MNS)

Wigner surmises and the two-dimensional homogeneous Poisson point process.

PubMed

Sakhr, Jamal; Nieminen, John M

2006-04-01

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.

Super-stable Poissonian structures

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

In this paper we characterize classes of Poisson processes whose statistical structures are super-stable. We consider a flow generated by a one-dimensional ordinary differential equation, and an ensemble of particles ‘surfing’ the flow. The particles start from random initial positions, and are propagated along the flow by stochastic ‘wave processes’ with general statistics and general cross correlations. Setting the initial positions to be Poisson processes, we characterize the classes of Poisson processes that render the particles’ positions—at all times, and invariantly with respect to the wave processes—statistically identical to their initial positions. These Poisson processes are termed ‘super-stable’ and facilitate the generalization of the notion of stationary distributions far beyond the realm of Markov dynamics.

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance.

PubMed

Poplová, Michaela; Sovka, Pavel; Cifra, Michal

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal.

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance

PubMed Central

Poplová, Michaela; Sovka, Pavel

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal. PMID:29216207

Statistical mapping of count survey data

USGS Publications Warehouse

Royle, J. Andrew; Link, W.A.; Sauer, J.R.; Scott, J. Michael; Heglund, Patricia J.; Morrison, Michael L.; Haufler, Jonathan B.; Wall, William A.

2002-01-01

We apply a Poisson mixed model to the problem of mapping (or predicting) bird relative abundance from counts collected from the North American Breeding Bird Survey (BBS). The model expresses the logarithm of the Poisson mean as a sum of a fixed term (which may depend on habitat variables) and a random effect which accounts for remaining unexplained variation. The random effect is assumed to be spatially correlated, thus providing a more general model than the traditional Poisson regression approach. Consequently, the model is capable of improved prediction when data are autocorrelated. Moreover, formulation of the mapping problem in terms of a statistical model facilitates a wide variety of inference problems which are cumbersome or even impossible using standard methods of mapping. For example, assessment of prediction uncertainty, including the formal comparison of predictions at different locations, or through time, using the model-based prediction variance is straightforward under the Poisson model (not so with many nominally model-free methods). Also, ecologists may generally be interested in quantifying the response of a species to particular habitat covariates or other landscape attributes. Proper accounting for the uncertainty in these estimated effects is crucially dependent on specification of a meaningful statistical model. Finally, the model may be used to aid in sampling design, by modifying the existing sampling plan in a manner which minimizes some variance-based criterion. Model fitting under this model is carried out using a simulation technique known as Markov Chain Monte Carlo. Application of the model is illustrated using Mourning Dove (Zenaida macroura) counts from Pennsylvania BBS routes. We produce both a model-based map depicting relative abundance, and the corresponding map of prediction uncertainty. We briefly address the issue of spatial sampling design under this model. Finally, we close with some discussion of mapping in relation to habitat structure. Although our models were fit in the absence of habitat information, the resulting predictions show a strong inverse relation with a map of forest cover in the state, as expected. Consequently, the results suggest that the correlated random effect in the model is broadly representing ecological variation, and that BBS data may be generally useful for studying bird-habitat relationships, even in the presence of observer errors and other widely recognized deficiencies of the BBS.

Random matrices and the New York City subway system

NASA Astrophysics Data System (ADS)

Jagannath, Aukosh; Trogdon, Thomas

2017-09-01

We analyze subway arrival times in the New York City subway system. We find regimes where the gaps between trains are well modeled by (unitarily invariant) random matrix statistics and Poisson statistics. The departure from random matrix statistics is captured by the value of the Coulomb potential along the subway route. This departure becomes more pronounced as trains make more stops.

Football goal distributions and extremal statistics

NASA Astrophysics Data System (ADS)

Greenhough, J.; Birch, P. C.; Chapman, S. C.; Rowlands, G.

2002-12-01

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored are too heavy-tailed to be fitted over their entire ranges by Poisson or negative binomial distributions which would be expected for uncorrelated processes. Log-normal distributions cannot include zero scores and here we find that the PDFs are consistent with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71-2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.

Statistical description of non-Gaussian samples in the F2 layer of the ionosphere during heliogeophysical disturbances

NASA Astrophysics Data System (ADS)

Sergeenko, N. P.

2017-11-01

An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2- foF2( t) were subjected to statistical processing. For the obtained samples {δ foF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δ foF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δ foF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov's criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P 0.7-0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δ foF2}.

Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969-2007.

PubMed

Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo

2015-08-01

Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Predictors of the number of under-five malnourished children in Bangladesh: application of the generalized poisson regression model

PubMed Central

2013-01-01

Background Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and (ii) to find some predictors of this outcome variable. Methods The data is extracted from the Bangladesh Demographic and Health Survey (BDHS) 2007. Briefly, this survey employs a nationally representative sample which is based on a two-stage stratified sample of households. A total of 4,460 under-five children is analysed using various statistical techniques namely Chi-square test and GPR model. Results The GPR model (as compared to the standard Poisson regression and negative Binomial regression) is found to be justified to study the above-mentioned outcome variable because of its under-dispersion (variance < mean) property. Our study also identify several significant predictors of the outcome variable namely mother’s education, father’s education, wealth index, sanitation status, source of drinking water, and total number of children ever born to a woman. Conclusions Consistencies of our findings in light of many other studies suggest that the GPR model is an ideal alternative of other statistical models to analyse the number of under-five malnourished children in a family. Strategies based on significant predictors may improve the nutritional status of children in Bangladesh. PMID:23297699

A dictionary learning approach for Poisson image deblurring.

PubMed

Ma, Liyan; Moisan, Lionel; Yu, Jian; Zeng, Tieyong

2013-07-01

The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a maximum a posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patch-based sparse representation prior over a learned dictionary, the pixel-based total variation regularization term and a data-fidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio value and the method noise, the proposed algorithm outperforms state-of-the-art methods.

Fitting statistical distributions to sea duck count data: implications for survey design and abundance estimation

USGS Publications Warehouse

Zipkin, Elise F.; Leirness, Jeffery B.; Kinlan, Brian P.; O'Connell, Allan F.; Silverman, Emily D.

2014-01-01

Determining appropriate statistical distributions for modeling animal count data is important for accurate estimation of abundance, distribution, and trends. In the case of sea ducks along the U.S. Atlantic coast, managers want to estimate local and regional abundance to detect and track population declines, to define areas of high and low use, and to predict the impact of future habitat change on populations. In this paper, we used a modified marked point process to model survey data that recorded flock sizes of Common eiders, Long-tailed ducks, and Black, Surf, and White-winged scoters. The data come from an experimental aerial survey, conducted by the United States Fish & Wildlife Service (USFWS) Division of Migratory Bird Management, during which east-west transects were flown along the Atlantic Coast from Maine to Florida during the winters of 2009–2011. To model the number of flocks per transect (the points), we compared the fit of four statistical distributions (zero-inflated Poisson, zero-inflated geometric, zero-inflated negative binomial and negative binomial) to data on the number of species-specific sea duck flocks that were recorded for each transect flown. To model the flock sizes (the marks), we compared the fit of flock size data for each species to seven statistical distributions: positive Poisson, positive negative binomial, positive geometric, logarithmic, discretized lognormal, zeta and Yule–Simon. Akaike’s Information Criterion and Vuong’s closeness tests indicated that the negative binomial and discretized lognormal were the best distributions for all species for the points and marks, respectively. These findings have important implications for estimating sea duck abundances as the discretized lognormal is a more skewed distribution than the Poisson and negative binomial, which are frequently used to model avian counts; the lognormal is also less heavy-tailed than the power law distributions (e.g., zeta and Yule–Simon), which are becoming increasingly popular for group size modeling. Choosing appropriate statistical distributions for modeling flock size data is fundamental to accurately estimating population summaries, determining required survey effort, and assessing and propagating uncertainty through decision-making processes.

pyblocxs: Bayesian Low-Counts X-ray Spectral Analysis in Sherpa

NASA Astrophysics Data System (ADS)

Siemiginowska, A.; Kashyap, V.; Refsdal, B.; van Dyk, D.; Connors, A.; Park, T.

2011-07-01

Typical X-ray spectra have low counts and should be modeled using the Poisson distribution. However, χ2 statistic is often applied as an alternative and the data are assumed to follow the Gaussian distribution. A variety of weights to the statistic or a binning of the data is performed to overcome the low counts issues. However, such modifications introduce biases or/and a loss of information. Standard modeling packages such as XSPEC and Sherpa provide the Poisson likelihood and allow computation of rudimentary MCMC chains, but so far do not allow for setting a full Bayesian model. We have implemented a sophisticated Bayesian MCMC-based algorithm to carry out spectral fitting of low counts sources in the Sherpa environment. The code is a Python extension to Sherpa and allows to fit a predefined Sherpa model to high-energy X-ray spectral data and other generic data. We present the algorithm and discuss several issues related to the implementation, including flexible definition of priors and allowing for variations in the calibration information.

The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction

PubMed Central

Williamson, Ross S.; Sahani, Maneesh; Pillow, Jonathan W.

2015-01-01

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron’s probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as “single-spike information” to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex. PMID:25831448

Quantification of integrated HIV DNA by repetitive-sampling Alu-HIV PCR on the basis of poisson statistics.

PubMed

De Spiegelaere, Ward; Malatinkova, Eva; Lynch, Lindsay; Van Nieuwerburgh, Filip; Messiaen, Peter; O'Doherty, Una; Vandekerckhove, Linos

2014-06-01

Quantification of integrated proviral HIV DNA by repetitive-sampling Alu-HIV PCR is a candidate virological tool to monitor the HIV reservoir in patients. However, the experimental procedures and data analysis of the assay are complex and hinder its widespread use. Here, we provide an improved and simplified data analysis method by adopting binomial and Poisson statistics. A modified analysis method on the basis of Poisson statistics was used to analyze the binomial data of positive and negative reactions from a 42-replicate Alu-HIV PCR by use of dilutions of an integration standard and on samples of 57 HIV-infected patients. Results were compared with the quantitative output of the previously described Alu-HIV PCR method. Poisson-based quantification of the Alu-HIV PCR was linearly correlated with the standard dilution series, indicating that absolute quantification with the Poisson method is a valid alternative for data analysis of repetitive-sampling Alu-HIV PCR data. Quantitative outputs of patient samples assessed by the Poisson method correlated with the previously described Alu-HIV PCR analysis, indicating that this method is a valid alternative for quantifying integrated HIV DNA. Poisson-based analysis of the Alu-HIV PCR data enables absolute quantification without the need of a standard dilution curve. Implementation of the CI estimation permits improved qualitative analysis of the data and provides a statistical basis for the required minimal number of technical replicates. © 2014 The American Association for Clinical Chemistry.

An examination of sources of sensitivity of consumer surplus estimates in travel cost models.

PubMed

Blaine, Thomas W; Lichtkoppler, Frank R; Bader, Timothy J; Hartman, Travis J; Lucente, Joseph E

2015-03-15

We examine sensitivity of estimates of recreation demand using the Travel Cost Method (TCM) to four factors. Three of the four have been routinely and widely discussed in the TCM literature: a) Poisson verses negative binomial regression; b) application of Englin correction to account for endogenous stratification; c) truncation of the data set to eliminate outliers. A fourth issue we address has not been widely modeled: the potential effect on recreation demand of the interaction between income and travel cost. We provide a straightforward comparison of all four factors, analyzing the impact of each on regression parameters and consumer surplus estimates. Truncation has a modest effect on estimates obtained from the Poisson models but a radical effect on the estimates obtained by way of the negative binomial. Inclusion of an income-travel cost interaction term generally produces a more conservative but not a statistically significantly different estimate of consumer surplus in both Poisson and negative binomial models. It also generates broader confidence intervals. Application of truncation, the Englin correction and the income-travel cost interaction produced the most conservative estimates of consumer surplus and eliminated the statistical difference between the Poisson and the negative binomial. Use of the income-travel cost interaction term reveals that for visitors who face relatively low travel costs, the relationship between income and travel demand is negative, while it is positive for those who face high travel costs. This provides an explanation of the ambiguities on the findings regarding the role of income widely observed in the TCM literature. Our results suggest that policies that reduce access to publicly owned resources inordinately impact local low income recreationists and are contrary to environmental justice. Copyright © 2014 Elsevier Ltd. All rights reserved.

Population activity statistics dissect subthreshold and spiking variability in V1.

PubMed

Bányai, Mihály; Koman, Zsombor; Orbán, Gergő

2017-07-01

Response variability, as measured by fluctuating responses upon repeated performance of trials, is a major component of neural responses, and its characterization is key to interpret high dimensional population recordings. Response variability and covariability display predictable changes upon changes in stimulus and cognitive or behavioral state, providing an opportunity to test the predictive power of models of neural variability. Still, there is little agreement on which model to use as a building block for population-level analyses, and models of variability are often treated as a subject of choice. We investigate two competing models, the doubly stochastic Poisson (DSP) model assuming stochasticity at spike generation, and the rectified Gaussian (RG) model tracing variability back to membrane potential variance, to analyze stimulus-dependent modulation of both single-neuron and pairwise response statistics. Using a pair of model neurons, we demonstrate that the two models predict similar single-cell statistics. However, DSP and RG models have contradicting predictions on the joint statistics of spiking responses. To test the models against data, we build a population model to simulate stimulus change-related modulations in pairwise response statistics. We use single-unit data from the primary visual cortex (V1) of monkeys to show that while model predictions for variance are qualitatively similar to experimental data, only the RG model's predictions are compatible with joint statistics. These results suggest that models using Poisson-like variability might fail to capture important properties of response statistics. We argue that membrane potential-level modeling of stochasticity provides an efficient strategy to model correlations. NEW & NOTEWORTHY Neural variability and covariability are puzzling aspects of cortical computations. For efficient decoding and prediction, models of information encoding in neural populations hinge on an appropriate model of variability. Our work shows that stimulus-dependent changes in pairwise but not in single-cell statistics can differentiate between two widely used models of neuronal variability. Contrasting model predictions with neuronal data provides hints on the noise sources in spiking and provides constraints on statistical models of population activity. Copyright © 2017 the American Physiological Society.

Human dynamics scaling characteristics for aerial inbound logistics operation

NASA Astrophysics Data System (ADS)

Wang, Qing; Guo, Jin-Li

2010-05-01

In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions - that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models.

Coupling Poisson rectangular pulse and multiplicative microcanonical random cascade models to generate sub-daily precipitation timeseries

NASA Astrophysics Data System (ADS)

Pohle, Ina; Niebisch, Michael; Müller, Hannes; Schümberg, Sabine; Zha, Tingting; Maurer, Thomas; Hinz, Christoph

2018-07-01

To simulate the impacts of within-storm rainfall variabilities on fast hydrological processes, long precipitation time series with high temporal resolution are required. Due to limited availability of observed data such time series are typically obtained from stochastic models. However, most existing rainfall models are limited in their ability to conserve rainfall event statistics which are relevant for hydrological processes. Poisson rectangular pulse models are widely applied to generate long time series of alternating precipitation events durations and mean intensities as well as interstorm period durations. Multiplicative microcanonical random cascade (MRC) models are used to disaggregate precipitation time series from coarse to fine temporal resolution. To overcome the inconsistencies between the temporal structure of the Poisson rectangular pulse model and the MRC model, we developed a new coupling approach by introducing two modifications to the MRC model. These modifications comprise (a) a modified cascade model ("constrained cascade") which preserves the event durations generated by the Poisson rectangular model by constraining the first and last interval of a precipitation event to contain precipitation and (b) continuous sigmoid functions of the multiplicative weights to consider the scale-dependency in the disaggregation of precipitation events of different durations. The constrained cascade model was evaluated in its ability to disaggregate observed precipitation events in comparison to existing MRC models. For that, we used a 20-year record of hourly precipitation at six stations across Germany. The constrained cascade model showed a pronounced better agreement with the observed data in terms of both the temporal pattern of the precipitation time series (e.g. the dry and wet spell durations and autocorrelations) and event characteristics (e.g. intra-event intermittency and intensity fluctuation within events). The constrained cascade model also slightly outperformed the other MRC models with respect to the intensity-frequency relationship. To assess the performance of the coupled Poisson rectangular pulse and constrained cascade model, precipitation events were stochastically generated by the Poisson rectangular pulse model and then disaggregated by the constrained cascade model. We found that the coupled model performs satisfactorily in terms of the temporal pattern of the precipitation time series, event characteristics and the intensity-frequency relationship.

A superstatistical model of metastasis and cancer survival

NASA Astrophysics Data System (ADS)

Leon Chen, L.; Beck, Christian

2008-05-01

We introduce a superstatistical model for the progression statistics of malignant cancer cells. The metastatic cascade is modeled as a complex nonequilibrium system with several macroscopic pathways and inverse-chi-square distributed parameters of the underlying Poisson processes. The predictions of the model are in excellent agreement with observed survival-time probability distributions of breast cancer patients.

Fractional models of seismoacoustic and electromagnetic activity

NASA Astrophysics Data System (ADS)

Shevtsov, Boris; Sheremetyeva, Olga

2017-10-01

Statistical models of the seismoacoustic and electromagnetic activity caused by deformation disturbances are considered on the basis of compound Poisson process and its fractional generalizations. Wave representations of these processes are used too. It is discussed five regimes of deformation activity and their role in understanding of the earthquakes precursors nature.

Differential expression analysis for RNAseq using Poisson mixed models

PubMed Central

Sun, Shiquan; Hood, Michelle; Scott, Laura; Peng, Qinke; Mukherjee, Sayan; Tung, Jenny

2017-01-01

Abstract Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html. PMID:28369632

Sparsity-based Poisson denoising with dictionary learning.

PubMed

Giryes, Raja; Elad, Michael

2014-12-01

The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging, and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive-independent identically distributed. Gaussian noise, for which many effective algorithms are available. However, in a low-SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. Salmon et al took this route, proposing a patch-based exponential image representation model based on Gaussian mixture model, leading to state-of-the-art results. In this paper, we propose to harness sparse-representation modeling to the image patches, adopting the same exponential idea. Our scheme uses a greedy pursuit with boot-strapping-based stopping condition and dictionary learning within the denoising process. The reconstruction performance of the proposed scheme is competitive with leading methods in high SNR and achieving state-of-the-art results in cases of low SNR.

Poisson property of the occurrence of flip-flops in a model membrane.

PubMed

Arai, Noriyoshi; Akimoto, Takuma; Yamamoto, Eiji; Yasui, Masato; Yasuoka, Kenji

2014-02-14

How do lipid molecules in membranes perform a flip-flop? The flip-flops of lipid molecules play a crucial role in the formation and flexibility of membranes. However, little has been determined about the behavior of flip-flops, either experimentally, or in molecular dynamics simulations. Here, we provide numerical results of the flip-flops of model lipid molecules in a model membrane and investigate the statistical properties, using millisecond-order coarse-grained molecular simulations (dissipative particle dynamics). We find that there are three different ways of flip-flops, which can be clearly characterized by their paths on the free energy surface. Furthermore, we found that the probability of the number of the flip-flops is well fitted by the Poisson distribution, and the probability density function for the inter-occurrence times of flip-flops coincides with that of the forward recurrence times. These results indicate that the occurrence of flip-flops is a Poisson process, which will play an important role in the flexibilities of membranes.

IMFIT: A FAST, FLEXIBLE NEW PROGRAM FOR ASTRONOMICAL IMAGE FITTING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Erwin, Peter; Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München

2015-02-01

I describe a new, open-source astronomical image-fitting program called IMFIT, specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. A key characteristic of the program is an object-oriented design that allows new types of image components (two-dimensional surface-brightness functions) to be easily written and added to the program. Image functions provided with IMFIT include the usual suspects for galaxy decompositions (Sérsic, exponential, Gaussian), along with Core-Sérsic and broken-exponential profiles, elliptical rings, and three components that perform line-of-sight integration through three-dimensional luminosity-density models of disks and rings seen at arbitrary inclinations. Available minimization algorithmsmore » include Levenberg-Marquardt, Nelder-Mead simplex, and Differential Evolution, allowing trade-offs between speed and decreased sensitivity to local minima in the fit landscape. Minimization can be done using the standard χ{sup 2} statistic (using either data or model values to estimate per-pixel Gaussian errors, or else user-supplied error images) or Poisson-based maximum-likelihood statistics; the latter approach is particularly appropriate for cases of Poisson data in the low-count regime. I show that fitting low-signal-to-noise ratio galaxy images using χ{sup 2} minimization and individual-pixel Gaussian uncertainties can lead to significant biases in fitted parameter values, which are avoided if a Poisson-based statistic is used; this is true even when Gaussian read noise is present.« less

Replication of Cancellation Orders Using First-Passage Time Theory in Foreign Currency Market

NASA Astrophysics Data System (ADS)

Boilard, Jean-François; Kanazawa, Kiyoshi; Takayasu, Hideki; Takayasu, Misako

Our research focuses on the annihilation dynamics of limit orders in a spot foreign currency market for various currency pairs. We analyze the cancellation order distribution conditioned on the normalized distance from the mid-price; where the normalized distance is defined as the final distance divided by the initial distance. To reproduce real data, we introduce two simple models that assume the market price moves randomly and cancellation occurs either after fixed time t or following the Poisson process. Results of our model qualitatively reproduce basic statistical properties of cancellation orders of the data when limit orders are cancelled according to the Poisson process. We briefly discuss implication of our findings in the construction of more detailed microscopic models.

A statistical approach for inferring the 3D structure of the genome.

PubMed

Varoquaux, Nelle; Ay, Ferhat; Noble, William Stafford; Vert, Jean-Philippe

2014-06-15

Recent technological advances allow the measurement, in a single Hi-C experiment, of the frequencies of physical contacts among pairs of genomic loci at a genome-wide scale. The next challenge is to infer, from the resulting DNA-DNA contact maps, accurate 3D models of how chromosomes fold and fit into the nucleus. Many existing inference methods rely on multidimensional scaling (MDS), in which the pairwise distances of the inferred model are optimized to resemble pairwise distances derived directly from the contact counts. These approaches, however, often optimize a heuristic objective function and require strong assumptions about the biophysics of DNA to transform interaction frequencies to spatial distance, and thereby may lead to incorrect structure reconstruction. We propose a novel approach to infer a consensus 3D structure of a genome from Hi-C data. The method incorporates a statistical model of the contact counts, assuming that the counts between two loci follow a Poisson distribution whose intensity decreases with the physical distances between the loci. The method can automatically adjust the transfer function relating the spatial distance to the Poisson intensity and infer a genome structure that best explains the observed data. We compare two variants of our Poisson method, with or without optimization of the transfer function, to four different MDS-based algorithms-two metric MDS methods using different stress functions, a non-metric version of MDS and ChromSDE, a recently described, advanced MDS method-on a wide range of simulated datasets. We demonstrate that the Poisson models reconstruct better structures than all MDS-based methods, particularly at low coverage and high resolution, and we highlight the importance of optimizing the transfer function. On publicly available Hi-C data from mouse embryonic stem cells, we show that the Poisson methods lead to more reproducible structures than MDS-based methods when we use data generated using different restriction enzymes, and when we reconstruct structures at different resolutions. A Python implementation of the proposed method is available at http://cbio.ensmp.fr/pastis. © The Author 2014. Published by Oxford University Press.

Efficient statistical mapping of avian count data

USGS Publications Warehouse

Royle, J. Andrew; Wikle, C.K.

2005-01-01

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.

Comparison of INAR(1)-Poisson model and Markov prediction model in forecasting the number of DHF patients in west java Indonesia

NASA Astrophysics Data System (ADS)

Ahdika, Atina; Lusiyana, Novyan

2017-02-01

World Health Organization (WHO) noted Indonesia as the country with the highest dengue (DHF) cases in Southeast Asia. There are no vaccine and specific treatment for DHF. One of the efforts which can be done by both government and resident is doing a prevention action. In statistics, there are some methods to predict the number of DHF cases to be used as the reference to prevent the DHF cases. In this paper, a discrete time series model, INAR(1)-Poisson model in specific, and Markov prediction model are used to predict the number of DHF patients in West Java Indonesia. The result shows that MPM is the best model since it has the smallest value of MAE (mean absolute error) and MAPE (mean absolute percentage error).

The Galactic Isotropic γ-ray Background and Implications for Dark Matter

NASA Astrophysics Data System (ADS)

Campbell, Sheldon S.; Kwa, Anna; Kaplinghat, Manoj

2018-06-01

We present an analysis of the radial angular profile of the galacto-isotropic (GI) γ-ray flux-the statistically uniform flux in angular annuli centred on the Galactic centre. Two different approaches are used to measure the GI flux profile in 85 months of Fermi-LAT data: the BDS statistical method which identifies spatial correlations, and a new Poisson ordered-pixel method which identifies non-Poisson contributions. Both methods produce similar GI flux profiles. The GI flux profile is well-described by an existing model of bremsstrahlung, π0 production, inverse Compton scattering, and the isotropic background. Discrepancies with data in our full-sky model are not present in the GI component, and are therefore due to mis-modelling of the non-GI emission. Dark matter annihilation constraints based solely on the observed GI profile are close to the thermal WIMP cross section below 100 GeV, for fixed models of the dark matter density profile and astrophysical γ-ray foregrounds. Refined measurements of the GI profile are expected to improve these constraints by a factor of a few.

Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data.

PubMed

Rakitzis, Athanasios C; Castagliola, Philippe; Maravelakis, Petros E

2018-02-01

In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.

Application of spatial Poisson process models to air mass thunderstorm rainfall

NASA Technical Reports Server (NTRS)

Eagleson, P. S.; Fennessy, N. M.; Wang, Qinliang; Rodriguez-Iturbe, I.

1987-01-01

Eight years of summer storm rainfall observations from 93 stations in and around the 154 sq km Walnut Gulch catchment of the Agricultural Research Service, U.S. Department of Agriculture, in Arizona are processed to yield the total station depths of 428 storms. Statistical analysis of these random fields yields the first two moments, the spatial correlation and variance functions, and the spatial distribution of total rainfall for each storm. The absolute and relative worth of three Poisson models are evaluated by comparing their prediction of the spatial distribution of storm rainfall with observations from the second half of the sample. The effect of interstorm parameter variation is examined.

Testing prediction methods: Earthquake clustering versus the Poisson model

USGS Publications Warehouse

Michael, A.J.

1997-01-01

Testing earthquake prediction methods requires statistical techniques that compare observed success to random chance. One technique is to produce simulated earthquake catalogs and measure the relative success of predicting real and simulated earthquakes. The accuracy of these tests depends on the validity of the statistical model used to simulate the earthquakes. This study tests the effect of clustering in the statistical earthquake model on the results. Three simulation models were used to produce significance levels for a VLF earthquake prediction method. As the degree of simulated clustering increases, the statistical significance drops. Hence, the use of a seismicity model with insufficient clustering can lead to overly optimistic results. A successful method must pass the statistical tests with a model that fully replicates the observed clustering. However, a method can be rejected based on tests with a model that contains insufficient clustering. U.S. copyright. Published in 1997 by the American Geophysical Union.

The influence of processor focus on speckle correlation statistics for a Shuttle imaging radar scene of Hurricane Josephine

NASA Technical Reports Server (NTRS)

Tilley, David G.

1988-01-01

The surface wave field produced by Hurricane Josephine was imaged by the L-band SAR aboard the Challenger on October 12, 1984. Exponential trends found in the two-dimensional autocorrelations of speckled image data support an equilibrium theory model of sea surface hydrodynamics. The notions of correlated specular reflection, surface coherence, optimal Doppler parameterization and spatial resolution are discussed within the context of a Poisson-Rayleigh statistical model of the SAR imaging process.

A Model Comparison for Count Data with a Positively Skewed Distribution with an Application to the Number of University Mathematics Courses Completed

ERIC Educational Resources Information Center

Liou, Pey-Yan

2009-01-01

The current study examines three regression models: OLS (ordinary least square) linear regression, Poisson regression, and negative binomial regression for analyzing count data. Simulation results show that the OLS regression model performed better than the others, since it did not produce more false statistically significant relationships than…

Differential expression analysis for RNAseq using Poisson mixed models.

PubMed

Sun, Shiquan; Hood, Michelle; Scott, Laura; Peng, Qinke; Mukherjee, Sayan; Tung, Jenny; Zhou, Xiang

2017-06-20

Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Statistical distributions of earthquake numbers: consequence of branching process

NASA Astrophysics Data System (ADS)

Kagan, Yan Y.

2010-03-01

We discuss various statistical distributions of earthquake numbers. Previously, we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson, geometric, logarithmic and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three distributions above can be considered special cases of the NBD. In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/moment-frequency relation and the NBD of earthquake counts in large time/space windows, as well as the dependence of the NBD parameters on the magnitude threshold (magnitude of an earthquake catalogue completeness). We discuss applying these distributions, especially the NBD, to approximate event numbers in earthquake catalogues. There are many different representations of the NBD. Most can be traced either to the Pascal distribution or to the mixture of the Poisson distribution with the gamma law. We discuss advantages and drawbacks of both representations for statistical analysis of earthquake catalogues. We also consider applying the NBD to earthquake forecasts and describe the limits of the application for the given equations. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrence, the NBD has two parameters. The second parameter can be used to characterize clustering or overdispersion of a process. We determine the parameter values and their uncertainties for several local and global catalogues, and their subdivisions in various time intervals, magnitude thresholds, spatial windows, and tectonic categories. The theoretical model of how the clustering parameter depends on the corner (maximum) magnitude can be used to predict future earthquake number distribution in regions where very large earthquakes have not yet occurred.

A semi-nonparametric Poisson regression model for analyzing motor vehicle crash data.

PubMed

Ye, Xin; Wang, Ke; Zou, Yajie; Lord, Dominique

2018-01-01

This paper develops a semi-nonparametric Poisson regression model to analyze motor vehicle crash frequency data collected from rural multilane highway segments in California, US. Motor vehicle crash frequency on rural highway is a topic of interest in the area of transportation safety due to higher driving speeds and the resultant severity level. Unlike the traditional Negative Binomial (NB) model, the semi-nonparametric Poisson regression model can accommodate an unobserved heterogeneity following a highly flexible semi-nonparametric (SNP) distribution. Simulation experiments are conducted to demonstrate that the SNP distribution can well mimic a large family of distributions, including normal distributions, log-gamma distributions, bimodal and trimodal distributions. Empirical estimation results show that such flexibility offered by the SNP distribution can greatly improve model precision and the overall goodness-of-fit. The semi-nonparametric distribution can provide a better understanding of crash data structure through its ability to capture potential multimodality in the distribution of unobserved heterogeneity. When estimated coefficients in empirical models are compared, SNP and NB models are found to have a substantially different coefficient for the dummy variable indicating the lane width. The SNP model with better statistical performance suggests that the NB model overestimates the effect of lane width on crash frequency reduction by 83.1%.

Generation of Non-Homogeneous Poisson Processes by Thinning: Programming Considerations and Comparision with Competing Algorithms.

DTIC Science & Technology

1978-12-01

Poisson processes . The method is valid for Poisson processes with any given intensity function. The basic thinning algorithm is modified to exploit several refinements which reduce computer execution time by approximately one-third. The basic and modified thinning programs are compared with the Poisson decomposition and gap-statistics algorithm, which is easily implemented for Poisson processes with intensity functions of the form exp(a sub 0 + a sub 1t + a sub 2 t-squared. The thinning programs are competitive in both execution

Study of photon correlation techniques for processing of laser velocimeter signals

NASA Technical Reports Server (NTRS)

Mayo, W. T., Jr.

1977-01-01

The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.

A spatial scan statistic for compound Poisson data.

PubMed

Rosychuk, Rhonda J; Chang, Hsing-Ming

2013-12-20

The topic of spatial cluster detection gained attention in statistics during the late 1980s and early 1990s. Effort has been devoted to the development of methods for detecting spatial clustering of cases and events in the biological sciences, astronomy and epidemiology. More recently, research has examined detecting clusters of correlated count data associated with health conditions of individuals. Such a method allows researchers to examine spatial relationships of disease-related events rather than just incident or prevalent cases. We introduce a spatial scan test that identifies clusters of events in a study region. Because an individual case may have multiple (repeated) events, we base the test on a compound Poisson model. We illustrate our method for cluster detection on emergency department visits, where individuals may make multiple disease-related visits. Copyright © 2013 John Wiley & Sons, Ltd.

Statistical guides to estimating the number of undiscovered mineral deposits: an example with porphyry copper deposits

USGS Publications Warehouse

Singer, Donald A.; Menzie, W.D.; Cheng, Qiuming; Bonham-Carter, G. F.

2005-01-01

Estimating numbers of undiscovered mineral deposits is a fundamental part of assessing mineral resources. Some statistical tools can act as guides to low variance, unbiased estimates of the number of deposits. The primary guide is that the estimates must be consistent with the grade and tonnage models. Another statistical guide is the deposit density (i.e., the number of deposits per unit area of permissive rock in well-explored control areas). Preliminary estimates and confidence limits of the number of undiscovered deposits in a tract of given area may be calculated using linear regression and refined using frequency distributions with appropriate parameters. A Poisson distribution leads to estimates having lower relative variances than the regression estimates and implies a random distribution of deposits. Coefficients of variation are used to compare uncertainties of negative binomial, Poisson, or MARK3 empirical distributions that have the same expected number of deposits as the deposit density. Statistical guides presented here allow simple yet robust estimation of the number of undiscovered deposits in permissive terranes. 

Yes, the GIGP Really Does Work--And Is Workable!

ERIC Educational Resources Information Center

Burrell, Quentin L.; Fenton, Michael R.

1993-01-01

Discusses the generalized inverse Gaussian-Poisson (GIGP) process for informetric modeling. Negative binomial distribution is discussed, construction of the GIGP process is explained, zero-truncated GIGP is considered, and applications of the process with journals, library circulation statistics, and database index terms are described. (50…

The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded.

PubMed

Nakagawa, Shinichi; Johnson, Paul C D; Schielzeth, Holger

2017-09-01

The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called [Formula: see text] for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments. © 2017 The Author(s).

Statistical error in simulations of Poisson processes: Example of diffusion in solids

NASA Astrophysics Data System (ADS)

Nilsson, Johan O.; Leetmaa, Mikael; Vekilova, Olga Yu.; Simak, Sergei I.; Skorodumova, Natalia V.

2016-08-01

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations.

Discrete Model for the Structure and Strength of Cementitious Materials

NASA Astrophysics Data System (ADS)

Balopoulos, Victor D.; Archontas, Nikolaos; Pantazopoulou, Stavroula J.

2017-12-01

Cementitious materials are characterized by brittle behavior in direct tension and by transverse dilatation (due to microcracking) under compression. Microcracking causes increasingly larger transverse strains and a phenomenological Poisson's ratio that gradually increases to about ν =0.5 and beyond, at the limit point in compression. This behavior is due to the underlying structure of cementitious pastes which is simulated here with a discrete physical model. The computational model is generic, assembled from a statistically generated, continuous network of flaky dendrites consisting of cement hydrates that emanate from partially hydrated cement grains. In the actual amorphous material, the dendrites constitute the solid phase of the cement gel and interconnect to provide the strength and stiffness against load. The idealized dendrite solid is loaded in compression and tension to compute values for strength and Poisson's effects. Parametric studies are conducted, to calibrate the statistical parameters of the discrete model with the physical and mechanical characteristics of the material, so that the familiar experimental trends may be reproduced. The model provides a framework for the study of the mechanical behavior of the material under various states of stress and strain and can be used to model the effects of additives (e.g., fibers) that may be explicitly simulated in the discrete structure.

Identification of a Class of Filtered Poisson Processes.

DTIC Science & Technology

1981-01-01

LD-A135 371 IDENTIFICATION OF A CLASS OF FILERED POISSON PROCESSES I AU) NORTH CAROLINA UNIV AT CHAPEL HIL DEPT 0F STATISTICS D DE RRUC ET AL 1981...STNO&IO$ !tt ~ 4.s " . , ".7" -L N ~ TITLE :IDENTIFICATION OF A CLASS OF FILTERED POISSON PROCESSES Authors : DE BRUCQ Denis - GUALTIEROTTI Antonio...filtered Poisson processes is intro- duced : the amplitude has a law which is spherically invariant and the filter is real, linear and causal. It is shown

Poisson filtering of laser ranging data

NASA Technical Reports Server (NTRS)

Ricklefs, Randall L.; Shelus, Peter J.

1993-01-01

The filtering of data in a high noise, low signal strength environment is a situation encountered routinely in lunar laser ranging (LLR) and, to a lesser extent, in artificial satellite laser ranging (SLR). The use of Poisson statistics as one of the tools for filtering LLR data is described first in a historical context. The more recent application of this statistical technique to noisy SLR data is also described.

Yield modeling of acoustic charge transport transversal filters

NASA Technical Reports Server (NTRS)

Kenney, J. S.; May, G. S.; Hunt, W. D.

1995-01-01

This paper presents a yield model for acoustic charge transport transversal filters. This model differs from previous IC yield models in that it does not assume that individual failures of the nondestructive sensing taps necessarily cause a device failure. A redundancy in the number of taps included in the design is explained. Poisson statistics are used to describe the tap failures, weighted over a uniform defect density distribution. A representative design example is presented. The minimum number of taps needed to realize the filter is calculated, and tap weights for various numbers of redundant taps are calculated. The critical area for device failure is calculated for each level of redundancy. Yield is predicted for a range of defect densities and redundancies. To verify the model, a Monte Carlo simulation is performed on an equivalent circuit model of the device. The results of the yield model are then compared to the Monte Carlo simulation. Better than 95% agreement was obtained for the Poisson model with redundant taps ranging from 30% to 150% over the minimum.

Poisson Mixture Regression Models for Heart Disease Prediction.

PubMed

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

PubMed Central

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

Segmentation algorithm for non-stationary compound Poisson processes. With an application to inventory time series of market members in a financial market

NASA Astrophysics Data System (ADS)

Tóth, B.; Lillo, F.; Farmer, J. D.

2010-11-01

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algorithm outperforms the original one for regime switching models of compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.

Poisson-process generalization for the trading waiting-time distribution in a double-auction mechanism

NASA Astrophysics Data System (ADS)

Cincotti, Silvano; Ponta, Linda; Raberto, Marco; Scalas, Enrico

2005-05-01

In this paper, empirical analyses and computational experiments are presented on high-frequency data for a double-auction (book) market. Main objective of the paper is to generalize the order waiting time process in order to properly model such empirical evidences. The empirical study is performed on the best bid and best ask data of 7 U.S. financial markets, for 30-stock time series. In particular, statistical properties of trading waiting times have been analyzed and quality of fits is evaluated by suitable statistical tests, i.e., comparing empirical distributions with theoretical models. Starting from the statistical studies on real data, attention has been focused on the reproducibility of such results in an artificial market. The computational experiments have been performed within the Genoa Artificial Stock Market. In the market model, heterogeneous agents trade one risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market orders depending on their budget constraints. The price is cleared by means of a limit order book. The order generation is modelled with a renewal process. Based on empirical trading estimation, the distribution of waiting times between two consecutive orders is modelled by a mixture of exponential processes. Results show that the empirical waiting-time distribution can be considered as a generalization of a Poisson process. Moreover, the renewal process can approximate real data and implementation on the artificial stocks market can reproduce the trading activity in a realistic way.

Low Dose PET Image Reconstruction with Total Variation Using Alternating Direction Method.

PubMed

Yu, Xingjian; Wang, Chenye; Hu, Hongjie; Liu, Huafeng

2016-01-01

In this paper, a total variation (TV) minimization strategy is proposed to overcome the problem of sparse spatial resolution and large amounts of noise in low dose positron emission tomography (PET) imaging reconstruction. Two types of objective function were established based on two statistical models of measured PET data, least-square (LS) TV for the Gaussian distribution and Poisson-TV for the Poisson distribution. To efficiently obtain high quality reconstructed images, the alternating direction method (ADM) is used to solve these objective functions. As compared with the iterative shrinkage/thresholding (IST) based algorithms, the proposed ADM can make full use of the TV constraint and its convergence rate is faster. The performance of the proposed approach is validated through comparisons with the expectation-maximization (EM) method using synthetic and experimental biological data. In the comparisons, the results of both LS-TV and Poisson-TV are taken into consideration to find which models are more suitable for PET imaging, in particular low-dose PET. To evaluate the results quantitatively, we computed bias, variance, and the contrast recovery coefficient (CRC) and drew profiles of the reconstructed images produced by the different methods. The results show that both Poisson-TV and LS-TV can provide a high visual quality at a low dose level. The bias and variance of the proposed LS-TV and Poisson-TV methods are 20% to 74% less at all counting levels than those of the EM method. Poisson-TV gives the best performance in terms of high-accuracy reconstruction with the lowest bias and variance as compared to the ground truth (14.3% less bias and 21.9% less variance). In contrast, LS-TV gives the best performance in terms of the high contrast of the reconstruction with the highest CRC.

Low Dose PET Image Reconstruction with Total Variation Using Alternating Direction Method

PubMed Central

Yu, Xingjian; Wang, Chenye; Hu, Hongjie; Liu, Huafeng

2016-01-01

In this paper, a total variation (TV) minimization strategy is proposed to overcome the problem of sparse spatial resolution and large amounts of noise in low dose positron emission tomography (PET) imaging reconstruction. Two types of objective function were established based on two statistical models of measured PET data, least-square (LS) TV for the Gaussian distribution and Poisson-TV for the Poisson distribution. To efficiently obtain high quality reconstructed images, the alternating direction method (ADM) is used to solve these objective functions. As compared with the iterative shrinkage/thresholding (IST) based algorithms, the proposed ADM can make full use of the TV constraint and its convergence rate is faster. The performance of the proposed approach is validated through comparisons with the expectation-maximization (EM) method using synthetic and experimental biological data. In the comparisons, the results of both LS-TV and Poisson-TV are taken into consideration to find which models are more suitable for PET imaging, in particular low-dose PET. To evaluate the results quantitatively, we computed bias, variance, and the contrast recovery coefficient (CRC) and drew profiles of the reconstructed images produced by the different methods. The results show that both Poisson-TV and LS-TV can provide a high visual quality at a low dose level. The bias and variance of the proposed LS-TV and Poisson-TV methods are 20% to 74% less at all counting levels than those of the EM method. Poisson-TV gives the best performance in terms of high-accuracy reconstruction with the lowest bias and variance as compared to the ground truth (14.3% less bias and 21.9% less variance). In contrast, LS-TV gives the best performance in terms of the high contrast of the reconstruction with the highest CRC. PMID:28005929

Differences in passenger car and large truck involved crash frequencies at urban signalized intersections: an exploratory analysis.

PubMed

Dong, Chunjiao; Clarke, David B; Richards, Stephen H; Huang, Baoshan

2014-01-01

The influence of intersection features on safety has been examined extensively because intersections experience a relatively large proportion of motor vehicle conflicts and crashes. Although there are distinct differences between passenger cars and large trucks-size, operating characteristics, dimensions, and weight-modeling crash counts across vehicle types is rarely addressed. This paper develops and presents a multivariate regression model of crash frequencies by collision vehicle type using crash data for urban signalized intersections in Tennessee. In addition, the performance of univariate Poisson-lognormal (UVPLN), multivariate Poisson (MVP), and multivariate Poisson-lognormal (MVPLN) regression models in establishing the relationship between crashes, traffic factors, and geometric design of roadway intersections is investigated. Bayesian methods are used to estimate the unknown parameters of these models. The evaluation results suggest that the MVPLN model possesses most of the desirable statistical properties in developing the relationships. Compared to the UVPLN and MVP models, the MVPLN model better identifies significant factors and predicts crash frequencies. The findings suggest that traffic volume, truck percentage, lighting condition, and intersection angle significantly affect intersection safety. Important differences in car, car-truck, and truck crash frequencies with respect to various risk factors were found to exist between models. The paper provides some new or more comprehensive observations that have not been covered in previous studies. Copyright © 2013 Elsevier Ltd. All rights reserved.

Post-stratification sampling in small area estimation (SAE) model for unemployment rate estimation by Bayes approach

NASA Astrophysics Data System (ADS)

Hanike, Yusrianti; Sadik, Kusman; Kurnia, Anang

2016-02-01

This research implemented unemployment rate in Indonesia that based on Poisson distribution. It would be estimated by modified the post-stratification and Small Area Estimation (SAE) model. Post-stratification was one of technique sampling that stratified after collected survey data. It's used when the survey data didn't serve for estimating the interest area. Interest area here was the education of unemployment which separated in seven category. The data was obtained by Labour Employment National survey (Sakernas) that's collected by company survey in Indonesia, BPS, Statistic Indonesia. This company served the national survey that gave too small sample for level district. Model of SAE was one of alternative to solved it. According the problem above, we combined this post-stratification sampling and SAE model. This research gave two main model of post-stratification sampling. Model I defined the category of education was the dummy variable and model II defined the category of education was the area random effect. Two model has problem wasn't complied by Poisson assumption. Using Poisson-Gamma model, model I has over dispersion problem was 1.23 solved to 0.91 chi square/df and model II has under dispersion problem was 0.35 solved to 0.94 chi square/df. Empirical Bayes was applied to estimate the proportion of every category education of unemployment. Using Bayesian Information Criteria (BIC), Model I has smaller mean square error (MSE) than model II.

[Statistical (Poisson) motor unit number estimation. Methodological aspects and normal results in the extensor digitorum brevis muscle of healthy subjects].

PubMed

Murga Oporto, L; Menéndez-de León, C; Bauzano Poley, E; Núñez-Castaín, M J

Among the differents techniques for motor unit number estimation (MUNE) there is the statistical one (Poisson), in which the activation of motor units is carried out by electrical stimulation and the estimation performed by means of a statistical analysis based on the Poisson s distribution. The study was undertaken in order to realize an approximation to the MUNE Poisson technique showing a coprehensible view of its methodology and also to obtain normal results in the extensor digitorum brevis muscle (EDB) from a healthy population. One hundred fourteen normal volunteers with age ranging from 10 to 88 years were studied using the MUNE software contained in a Viking IV system. The normal subjects were divided into two age groups (10 59 and 60 88 years). The EDB MUNE from all them was 184 49. Both, the MUNE and the amplitude of the compound muscle action potential (CMAP) were significantly lower in the older age group (p< 0.0001), showing the MUNE a better correlation with age than CMAP amplitude ( 0.5002 and 0.4142, respectively p< 0.0001). Statistical MUNE method is an important way for the assessment to the phisiology of the motor unit. The value of MUNE correlates better with the neuromuscular aging process than CMAP amplitude does.

A stochastic-dynamic model for global atmospheric mass field statistics

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.; Kalnay-Rivas, E.

1981-01-01

A model that yields the spatial correlation structure of atmospheric mass field forecast errors was developed. The model is governed by the potential vorticity equation forced by random noise. Expansion in spherical harmonics and correlation function was computed analytically using the expansion coefficients. The finite difference equivalent was solved using a fast Poisson solver and the correlation function was computed using stratified sampling of the individual realization of F(omega) and hence of phi(omega). A higher order equation for gamma was derived and solved directly in finite differences by two successive applications of the fast Poisson solver. The methods were compared for accuracy and efficiency and the third method was chosen as clearly superior. The results agree well with the latitude dependence of observed atmospheric correlation data. The value of the parameter c sub o which gives the best fit to the data is close to the value expected from dynamical considerations.

Sojourning with the Homogeneous Poisson Process.

PubMed

Liu, Piaomu; Peña, Edsel A

2016-01-01

In this pedagogical article, distributional properties, some surprising, pertaining to the homogeneous Poisson process (HPP), when observed over a possibly random window, are presented. Properties of the gap-time that covered the termination time and the correlations among gap-times of the observed events are obtained. Inference procedures, such as estimation and model validation, based on event occurrence data over the observation window, are also presented. We envision that through the results in this paper, a better appreciation of the subtleties involved in the modeling and analysis of recurrent events data will ensue, since the HPP is arguably one of the simplest among recurrent event models. In addition, the use of the theorem of total probability, Bayes theorem, the iterated rules of expectation, variance and covariance, and the renewal equation could be illustrative when teaching distribution theory, mathematical statistics, and stochastic processes at both the undergraduate and graduate levels. This article is targeted towards both instructors and students.

Evaluation and comparison of statistical methods for early temporal detection of outbreaks: A simulation-based study

PubMed Central

Le Strat, Yann

2017-01-01

The objective of this paper is to evaluate a panel of statistical algorithms for temporal outbreak detection. Based on a large dataset of simulated weekly surveillance time series, we performed a systematic assessment of 21 statistical algorithms, 19 implemented in the R package surveillance and two other methods. We estimated false positive rate (FPR), probability of detection (POD), probability of detection during the first week, sensitivity, specificity, negative and positive predictive values and F1-measure for each detection method. Then, to identify the factors associated with these performance measures, we ran multivariate Poisson regression models adjusted for the characteristics of the simulated time series (trend, seasonality, dispersion, outbreak sizes, etc.). The FPR ranged from 0.7% to 59.9% and the POD from 43.3% to 88.7%. Some methods had a very high specificity, up to 99.4%, but a low sensitivity. Methods with a high sensitivity (up to 79.5%) had a low specificity. All methods had a high negative predictive value, over 94%, while positive predictive values ranged from 6.5% to 68.4%. Multivariate Poisson regression models showed that performance measures were strongly influenced by the characteristics of time series. Past or current outbreak size and duration strongly influenced detection performances. PMID:28715489

Photon statistics in scintillation crystals

NASA Astrophysics Data System (ADS)

Bora, Vaibhav Joga Singh

Scintillation based gamma-ray detectors are widely used in medical imaging, high-energy physics, astronomy and national security. Scintillation gamma-ray detectors are eld-tested, relatively inexpensive, and have good detection eciency. Semi-conductor detectors are gaining popularity because of their superior capability to resolve gamma-ray energies. However, they are relatively hard to manufacture and therefore, at this time, not available in as large formats and much more expensive than scintillation gamma-ray detectors. Scintillation gamma-ray detectors consist of: a scintillator, a material that emits optical (scintillation) photons when it interacts with ionization radiation, and an optical detector that detects the emitted scintillation photons and converts them into an electrical signal. Compared to semiconductor gamma-ray detectors, scintillation gamma-ray detectors have relatively poor capability to resolve gamma-ray energies. This is in large part attributed to the "statistical limit" on the number of scintillation photons. The origin of this statistical limit is the assumption that scintillation photons are either Poisson distributed or super-Poisson distributed. This statistical limit is often dened by the Fano factor. The Fano factor of an integer-valued random process is dened as the ratio of its variance to its mean. Therefore, a Poisson process has a Fano factor of one. The classical theory of light limits the Fano factor of the number of photons to a value greater than or equal to one (Poisson case). However, the quantum theory of light allows for Fano factors to be less than one. We used two methods to look at the correlations between two detectors looking at same scintillation pulse to estimate the Fano factor of the scintillation photons. The relationship between the Fano factor and the correlation between the integral of the two signals detected was analytically derived, and the Fano factor was estimated using the measurements for SrI2:Eu, YAP:Ce and CsI:Na. We also found an empirical relationship between the Fano factor and the covariance as a function of time between two detectors looking at the same scintillation pulse. This empirical model was used to estimate the Fano factor of LaBr3:Ce and YAP:Ce using the experimentally measured timing-covariance. The estimates of the Fano factor from the time-covariance results were consistent with the estimates of the correlation between the integral signals. We found scintillation light from some scintillators to be sub-Poisson. For the same mean number of total scintillation photons, sub-Poisson light has lower noise. We then conducted a simulation study to investigate whether this low-noise sub-Poisson light can be used to improve spatial resolution. We calculated the Cramer-Rao bound for dierent detector geometries, position of interactions and Fano factors. The Cramer-Rao calculations were veried by generating simulated data and estimating the variance of the maximum likelihood estimator. We found that the Fano factor has no impact on the spatial resolution in gamma-ray imaging systems.

Statistical shape analysis using 3D Poisson equation--A quantitatively validated approach.

PubMed

Gao, Yi; Bouix, Sylvain

2016-05-01

Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures. Copyright © 2016 Elsevier B.V. All rights reserved.

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping

PubMed Central

2011-01-01

Background Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level. Results In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing. Conclusions Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset. PMID:21978359

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping.

PubMed

Hampton, Kristen H; Serre, Marc L; Gesink, Dionne C; Pilcher, Christopher D; Miller, William C

2011-10-06

Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level. In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing. Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset.

Spectral statistics of random geometric graphs

NASA Astrophysics Data System (ADS)

Dettmann, C. P.; Georgiou, O.; Knight, G.

2017-04-01

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.

Nonlocal Poisson-Fermi model for ionic solvent.

PubMed

Xie, Dexuan; Liu, Jinn-Liang; Eisenberg, Bob

2016-07-01

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

A scan statistic for binary outcome based on hypergeometric probability model, with an application to detecting spatial clusters of Japanese encephalitis.

PubMed

Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong

2013-01-01

As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors

NASA Astrophysics Data System (ADS)

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α , the appropriate FRCG model has the effective range d =b2/N =α2/N , for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors.

PubMed

Pandey, Akhilesh; Kumar, Avanish; Puri, Sanjay

2017-11-01

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

A test of inflated zeros for Poisson regression models.

PubMed

He, Hua; Zhang, Hui; Ye, Peng; Tang, Wan

2017-01-01

Excessive zeros are common in practice and may cause overdispersion and invalidate inference when fitting Poisson regression models. There is a large body of literature on zero-inflated Poisson models. However, methods for testing whether there are excessive zeros are less well developed. The Vuong test comparing a Poisson and a zero-inflated Poisson model is commonly applied in practice. However, the type I error of the test often deviates seriously from the nominal level, rendering serious doubts on the validity of the test in such applications. In this paper, we develop a new approach for testing inflated zeros under the Poisson model. Unlike the Vuong test for inflated zeros, our method does not require a zero-inflated Poisson model to perform the test. Simulation studies show that when compared with the Vuong test our approach not only better at controlling type I error rate, but also yield more power.

A stochastical event-based continuous time step rainfall generator based on Poisson rectangular pulse and microcanonical random cascade models

NASA Astrophysics Data System (ADS)

Pohle, Ina; Niebisch, Michael; Zha, Tingting; Schümberg, Sabine; Müller, Hannes; Maurer, Thomas; Hinz, Christoph

2017-04-01

Rainfall variability within a storm is of major importance for fast hydrological processes, e.g. surface runoff, erosion and solute dissipation from surface soils. To investigate and simulate the impacts of within-storm variabilities on these processes, long time series of rainfall with high resolution are required. Yet, observed precipitation records of hourly or higher resolution are in most cases available only for a small number of stations and only for a few years. To obtain long time series of alternating rainfall events and interstorm periods while conserving the statistics of observed rainfall events, the Poisson model can be used. Multiplicative microcanonical random cascades have been widely applied to disaggregate rainfall time series from coarse to fine temporal resolution. We present a new coupling approach of the Poisson rectangular pulse model and the multiplicative microcanonical random cascade model that preserves the characteristics of rainfall events as well as inter-storm periods. In the first step, a Poisson rectangular pulse model is applied to generate discrete rainfall events (duration and mean intensity) and inter-storm periods (duration). The rainfall events are subsequently disaggregated to high-resolution time series (user-specified, e.g. 10 min resolution) by a multiplicative microcanonical random cascade model. One of the challenges of coupling these models is to parameterize the cascade model for the event durations generated by the Poisson model. In fact, the cascade model is best suited to downscale rainfall data with constant time step such as daily precipitation data. Without starting from a fixed time step duration (e.g. daily), the disaggregation of events requires some modifications of the multiplicative microcanonical random cascade model proposed by Olsson (1998): Firstly, the parameterization of the cascade model for events of different durations requires continuous functions for the probabilities of the multiplicative weights, which we implemented through sigmoid functions. Secondly, the branching of the first and last box is constrained to preserve the rainfall event durations generated by the Poisson rectangular pulse model. The event-based continuous time step rainfall generator has been developed and tested using 10 min and hourly rainfall data of four stations in North-Eastern Germany. The model performs well in comparison to observed rainfall in terms of event durations and mean event intensities as well as wet spell and dry spell durations. It is currently being tested using data from other stations across Germany and in different climate zones. Furthermore, the rainfall event generator is being applied in modelling approaches aimed at understanding the impact of rainfall variability on hydrological processes. Reference Olsson, J.: Evaluation of a scaling cascade model for temporal rainfall disaggregation, Hydrology and Earth System Sciences, 2, 19.30

Incorporating signal-dependent noise for hyperspectral target detection

NASA Astrophysics Data System (ADS)

Morman, Christopher J.; Meola, Joseph

2015-05-01

The majority of hyperspectral target detection algorithms are developed from statistical data models employing stationary background statistics or white Gaussian noise models. Stationary background models are inaccurate as a result of two separate physical processes. First, varying background classes often exist in the imagery that possess different clutter statistics. Many algorithms can account for this variability through the use of subspaces or clustering techniques. The second physical process, which is often ignored, is a signal-dependent sensor noise term. For photon counting sensors that are often used in hyperspectral imaging systems, sensor noise increases as the measured signal level increases as a result of Poisson random processes. This work investigates the impact of this sensor noise on target detection performance. A linear noise model is developed describing sensor noise variance as a linear function of signal level. The linear noise model is then incorporated for detection of targets using data collected at Wright Patterson Air Force Base.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

PubMed

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

NASA Astrophysics Data System (ADS)

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Fractional properties of geophysical field variability on the example of hydrochemical parameters

NASA Astrophysics Data System (ADS)

Shevtsov, Boris; Shevtsova, Olga

2017-10-01

Using the properties of compound Poisson process and its fractional generalizations, statistical models of geophysical fields variability are considered on an example of hydrochemical parameters system. These models are universal to describe objects of different nature and allow us to explain various pulsing regime. Manifestations of non-conservatism in hydrochemical parameters system and the advantages of the system approach in the description of geophysical fields variability are discussed.

Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis.

PubMed

Armstrong, Ben G; Gasparrini, Antonio; Tobias, Aurelio

2014-11-24

The time stratified case cross-over approach is a popular alternative to conventional time series regression for analysing associations between time series of environmental exposures (air pollution, weather) and counts of health outcomes. These are almost always analyzed using conditional logistic regression on data expanded to case-control (case crossover) format, but this has some limitations. In particular adjusting for overdispersion and auto-correlation in the counts is not possible. It has been established that a Poisson model for counts with stratum indicators gives identical estimates to those from conditional logistic regression and does not have these limitations, but it is little used, probably because of the overheads in estimating many stratum parameters. The conditional Poisson model avoids estimating stratum parameters by conditioning on the total event count in each stratum, thus simplifying the computing and increasing the number of strata for which fitting is feasible compared with the standard unconditional Poisson model. Unlike the conditional logistic model, the conditional Poisson model does not require expanding the data, and can adjust for overdispersion and auto-correlation. It is available in Stata, R, and other packages. By applying to some real data and using simulations, we demonstrate that conditional Poisson models were simpler to code and shorter to run than are conditional logistic analyses and can be fitted to larger data sets than possible with standard Poisson models. Allowing for overdispersion or autocorrelation was possible with the conditional Poisson model but when not required this model gave identical estimates to those from conditional logistic regression. Conditional Poisson regression models provide an alternative to case crossover analysis of stratified time series data with some advantages. The conditional Poisson model can also be used in other contexts in which primary control for confounding is by fine stratification.

Photon counting statistics analysis of biophotons from hands.

PubMed

Jung, Hyun-Hee; Woo, Won-Myung; Yang, Joon-Mo; Choi, Chunho; Lee, Jonghan; Yoon, Gilwon; Yang, Jong S; Soh, Kwang-Sup

2003-05-01

The photon counting statistics of biophotons emitted from hands is studied with a view to test its agreement with the Poisson distribution. The moments of observed probability up to seventh order have been evaluated. The moments of biophoton emission from hands are in good agreement while those of dark counts of photomultiplier tube show large deviations from the theoretical values of Poisson distribution. The present results are consistent with the conventional delta-value analysis of the second moment of probability.

[Use of multiple regression models in observational studies (1970-2013) and requirements of the STROBE guidelines in Spanish scientific journals].

PubMed

Real, J; Cleries, R; Forné, C; Roso-Llorach, A; Martínez-Sánchez, J M

In medicine and biomedical research, statistical techniques like logistic, linear, Cox and Poisson regression are widely known. The main objective is to describe the evolution of multivariate techniques used in observational studies indexed in PubMed (1970-2013), and to check the requirements of the STROBE guidelines in the author guidelines in Spanish journals indexed in PubMed. A targeted PubMed search was performed to identify papers that used logistic linear Cox and Poisson models. Furthermore, a review was also made of the author guidelines of journals published in Spain and indexed in PubMed and Web of Science. Only 6.1% of the indexed manuscripts included a term related to multivariate analysis, increasing from 0.14% in 1980 to 12.3% in 2013. In 2013, 6.7, 2.5, 3.5, and 0.31% of the manuscripts contained terms related to logistic, linear, Cox and Poisson regression, respectively. On the other hand, 12.8% of journals author guidelines explicitly recommend to follow the STROBE guidelines, and 35.9% recommend the CONSORT guideline. A low percentage of Spanish scientific journals indexed in PubMed include the STROBE statement requirement in the author guidelines. Multivariate regression models in published observational studies such as logistic regression, linear, Cox and Poisson are increasingly used both at international level, as well as in journals published in Spanish. Copyright © 2015 Sociedad Española de Médicos de Atención Primaria (SEMERGEN). Publicado por Elsevier España, S.L.U. All rights reserved.

Nonlinear Poisson Equation for Heterogeneous Media

PubMed Central

Hu, Langhua; Wei, Guo-Wei

2012-01-01

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. PMID:22947937

The non-equilibrium allele frequency spectrum in a Poisson random field framework.

PubMed

Kaj, Ingemar; Mugal, Carina F

2016-10-01

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics. Copyright © 2016 Elsevier Inc. All rights reserved.

On performance of parametric and distribution-free models for zero-inflated and over-dispersed count responses.

PubMed

Tang, Wan; Lu, Naiji; Chen, Tian; Wang, Wenjuan; Gunzler, Douglas David; Han, Yu; Tu, Xin M

2015-10-30

Zero-inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero-inflated count responses. These models extend the Poisson and negative binomial (NB) to address excessive zeros in the count response. By adding a degenerate distribution centered at 0 and interpreting it as describing a non-risk group in the population, the ZIP (ZINB) models a two-component population mixture. As in applications of Poisson and NB, the key difference between ZIP and ZINB is the allowance for overdispersion by the ZINB in its NB component in modeling the count response for the at-risk group. Overdispersion arising in practice too often does not follow the NB, and applications of ZINB to such data yield invalid inference. If sources of overdispersion are known, other parametric models may be used to directly model the overdispersion. Such models too are subject to assumed distributions. Further, this approach may not be applicable if information about the sources of overdispersion is unavailable. In this paper, we propose a distribution-free alternative and compare its performance with these popular parametric models as well as a moment-based approach proposed by Yu et al. [Statistics in Medicine 2013; 32: 2390-2405]. Like the generalized estimating equations, the proposed approach requires no elaborate distribution assumptions. Compared with the approach of Yu et al., it is more robust to overdispersed zero-inflated responses. We illustrate our approach with both simulated and real study data. Copyright © 2015 John Wiley & Sons, Ltd.

[Geographical distribution of mortality caused by stomach, trachea, bronchi and lung malignant tumors in Chile].

PubMed

Icaza N, M Gloria; Núñez F, M Loreto; Torres A, Francisco J; Díaz S, Nora L; Várela G, David E

2007-11-01

Maps have played a critical role in public health since 1855, when John Snow associated a cholera outbreak with contaminated water source in London. After cardiovascular diseases, cancer is the second leading cause of death in Chile. Cancer was responsible for 22.7% of all deaths in 1997-2004 period. To describe the geographical distribution of stomach, trachea, bronchi and lung cancer mortality. Mortality statistics for the years 1997-2004, published by the National Statistics Institute and Chilean Ministry of Health, were used. The standardized mortality ratio (SMR) for sex and age quinquennium was calculated for 341 counties in the country. A hierarchical Bayesian analysis of Poisson regression models for SMR was performed. The maps were developed using adjusted SMR (or smoothed) by the Poisson model. There is an excess mortality caused by stomach cancer in south central Chile, from Teno to Valdivia. There is an excess mortality caused by trachea, bronchi and lung cancer in northern Chile, from Copiapó to Iquique. The geographical analysis of mortality caused by cancer shows cluster of counties with an excess risk. These areas should be considered for health care decision making and resource allocation.

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

NASA Astrophysics Data System (ADS)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

Earthquake number forecasts testing

NASA Astrophysics Data System (ADS)

Kagan, Yan Y.

2017-10-01

We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness and kurtosis both tend to zero for large earthquake rates: for the Gaussian law, these values are identically zero. A calculation of the NBD skewness and kurtosis levels based on the values of the first two statistical moments of the distribution, shows rapid increase of these upper moments levels. However, the observed catalogue values of skewness and kurtosis are rising even faster. This means that for small time intervals, the earthquake number distribution is even more heavy-tailed than the NBD predicts. Therefore for small time intervals, we propose using empirical number distributions appropriately smoothed for testing forecasted earthquake numbers.

Modeling the number of car theft using Poisson regression

NASA Astrophysics Data System (ADS)

Zulkifli, Malina; Ling, Agnes Beh Yen; Kasim, Maznah Mat; Ismail, Noriszura

2016-10-01

Regression analysis is the most popular statistical methods used to express the relationship between the variables of response with the covariates. The aim of this paper is to evaluate the factors that influence the number of car theft using Poisson regression model. This paper will focus on the number of car thefts that occurred in districts in Peninsular Malaysia. There are two groups of factor that have been considered, namely district descriptive factors and socio and demographic factors. The result of the study showed that Bumiputera composition, Chinese composition, Other ethnic composition, foreign migration, number of residence with the age between 25 to 64, number of employed person and number of unemployed person are the most influence factors that affect the car theft cases. These information are very useful for the law enforcement department, insurance company and car owners in order to reduce and limiting the car theft cases in Peninsular Malaysia.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

A stochastic model for stationary dynamics of prices in real estate markets. A case of random intensity for Poisson moments of prices changes

NASA Astrophysics Data System (ADS)

Rusakov, Oleg; Laskin, Michael

2017-06-01

We consider a stochastic model of changes of prices in real estate markets. We suppose that in a book of prices the changes happen in points of jumps of a Poisson process with a random intensity, i.e. moments of changes sequently follow to a random process of the Cox process type. We calculate cumulative mathematical expectations and variances for the random intensity of this point process. In the case that the process of random intensity is a martingale the cumulative variance has a linear grows. We statistically process a number of observations of real estate prices and accept hypotheses of a linear grows for estimations as well for cumulative average, as for cumulative variance both for input and output prises that are writing in the book of prises.

Validation of Statistical Models for Estimating Hospitalization Associated with Influenza and Other Respiratory Viruses

PubMed Central

Chan, King-Pan; Chan, Kwok-Hung; Wong, Wilfred Hing-Sang; Peiris, J. S. Malik; Wong, Chit-Ming

2011-01-01

Background Reliable estimates of disease burden associated with respiratory viruses are keys to deployment of preventive strategies such as vaccination and resource allocation. Such estimates are particularly needed in tropical and subtropical regions where some methods commonly used in temperate regions are not applicable. While a number of alternative approaches to assess the influenza associated disease burden have been recently reported, none of these models have been validated with virologically confirmed data. Even fewer methods have been developed for other common respiratory viruses such as respiratory syncytial virus (RSV), parainfluenza and adenovirus. Methods and Findings We had recently conducted a prospective population-based study of virologically confirmed hospitalization for acute respiratory illnesses in persons <18 years residing in Hong Kong Island. Here we used this dataset to validate two commonly used models for estimation of influenza disease burden, namely the rate difference model and Poisson regression model, and also explored the applicability of these models to estimate the disease burden of other respiratory viruses. The Poisson regression models with different link functions all yielded estimates well correlated with the virologically confirmed influenza associated hospitalization, especially in children older than two years. The disease burden estimates for RSV, parainfluenza and adenovirus were less reliable with wide confidence intervals. The rate difference model was not applicable to RSV, parainfluenza and adenovirus and grossly underestimated the true burden of influenza associated hospitalization. Conclusion The Poisson regression model generally produced satisfactory estimates in calculating the disease burden of respiratory viruses in a subtropical region such as Hong Kong. PMID:21412433

Monitoring Poisson observations using combined applications of Shewhart and EWMA charts

NASA Astrophysics Data System (ADS)

Abujiya, Mu'azu Ramat

2017-11-01

The Shewhart and exponentially weighted moving average (EWMA) charts for nonconformities are the most widely used procedures of choice for monitoring Poisson observations in modern industries. Individually, the Shewhart EWMA charts are only sensitive to large and small shifts, respectively. To enhance the detection abilities of the two schemes in monitoring all kinds of shifts in Poisson count data, this study examines the performance of combined applications of the Shewhart, and EWMA Poisson control charts. Furthermore, the study proposes modifications based on well-structured statistical data collection technique, ranked set sampling (RSS), to detect shifts in the mean of a Poisson process more quickly. The relative performance of the proposed Shewhart-EWMA Poisson location charts is evaluated in terms of the average run length (ARL), standard deviation of the run length (SDRL), median run length (MRL), average ratio ARL (ARARL), average extra quadratic loss (AEQL) and performance comparison index (PCI). Consequently, all the new Poisson control charts based on RSS method are generally more superior than most of the existing schemes for monitoring Poisson processes. The use of these combined Shewhart-EWMA Poisson charts is illustrated with an example to demonstrate the practical implementation of the design procedure.

Statistical methods for investigating quiescence and other temporal seismicity patterns

USGS Publications Warehouse

Matthews, M.V.; Reasenberg, P.A.

1988-01-01

We propose a statistical model and a technique for objective recognition of one of the most commonly cited seismicity patterns:microearthquake quiescence. We use a Poisson process model for seismicity and define a process with quiescence as one with a particular type of piece-wise constant intensity function. From this model, we derive a statistic for testing stationarity against a 'quiescence' alternative. The large-sample null distribution of this statistic is approximated from simulated distributions of appropriate functionals applied to Brownian bridge processes. We point out the restrictiveness of the particular model we propose and of the quiescence idea in general. The fact that there are many point processes which have neither constant nor quiescent rate functions underscores the need to test for and describe nonuniformity thoroughly. We advocate the use of the quiescence test in conjunction with various other tests for nonuniformity and with graphical methods such as density estimation. ideally these methods may promote accurate description of temporal seismicity distributions and useful characterizations of interesting patterns. ?? 1988 Birkha??user Verlag.

Accounting for rate instability and spatial patterns in the boundary analysis of cancer mortality maps

PubMed Central

Goovaerts, Pierre

2006-01-01

Boundary analysis of cancer maps may highlight areas where causative exposures change through geographic space, the presence of local populations with distinct cancer incidences, or the impact of different cancer control methods. Too often, such analysis ignores the spatial pattern of incidence or mortality rates and overlooks the fact that rates computed from sparsely populated geographic entities can be very unreliable. This paper proposes a new methodology that accounts for the uncertainty and spatial correlation of rate data in the detection of significant edges between adjacent entities or polygons. Poisson kriging is first used to estimate the risk value and the associated standard error within each polygon, accounting for the population size and the risk semivariogram computed from raw rates. The boundary statistic is then defined as half the absolute difference between kriged risks. Its reference distribution, under the null hypothesis of no boundary, is derived through the generation of multiple realizations of the spatial distribution of cancer risk values. This paper presents three types of neutral models generated using methods of increasing complexity: the common random shuffle of estimated risk values, a spatial re-ordering of these risks, or p-field simulation that accounts for the population size within each polygon. The approach is illustrated using age-adjusted pancreatic cancer mortality rates for white females in 295 US counties of the Northeast (1970–1994). Simulation studies demonstrate that Poisson kriging yields more accurate estimates of the cancer risk and how its value changes between polygons (i.e. boundary statistic), relatively to the use of raw rates or local empirical Bayes smoother. When used in conjunction with spatial neutral models generated by p-field simulation, the boundary analysis based on Poisson kriging estimates minimizes the proportion of type I errors (i.e. edges wrongly declared significant) while the frequency of these errors is predicted well by the p-value of the statistical test. PMID:19023455

Nonlinear Poisson equation for heterogeneous media.

PubMed

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Bayesian dynamic modeling of time series of dengue disease case counts.

PubMed

Martínez-Bello, Daniel Adyro; López-Quílez, Antonio; Torres-Prieto, Alexander

2017-07-01

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model's short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health.

The Nonhomogeneous Poisson Process for Fast Radio Burst Rates

DOE PAGES

Lawrence, Earl; Wiel, Scott Vander; Law, Casey; ...

2017-08-30

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model dependence of the rate on both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patternsmore » and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 587 events per sky per day above a flux of 1 Jy (95% CI: 272, 924) and a flux power-law index of 0:91 (95% CI: 0.57, 1.25).« less

Modeling Count Outcomes from HIV Risk Reduction Interventions: A Comparison of Competing Statistical Models for Count Responses

PubMed Central

Xia, Yinglin; Morrison-Beedy, Dianne; Ma, Jingming; Feng, Changyong; Cross, Wendi; Tu, Xin

2012-01-01

Modeling count data from sexual behavioral outcomes involves many challenges, especially when the data exhibit a preponderance of zeros and overdispersion. In particular, the popular Poisson log-linear model is not appropriate for modeling such outcomes. Although alternatives exist for addressing both issues, they are not widely and effectively used in sex health research, especially in HIV prevention intervention and related studies. In this paper, we discuss how to analyze count outcomes distributed with excess of zeros and overdispersion and introduce appropriate model-fit indices for comparing the performance of competing models, using data from a real study on HIV prevention intervention. The in-depth look at these common issues arising from studies involving behavioral outcomes will promote sound statistical analyses and facilitate research in this and other related areas. PMID:22536496

Clustering, randomness and regularity in cloud fields. I - Theoretical considerations. II - Cumulus cloud fields

NASA Technical Reports Server (NTRS)

Weger, R. C.; Lee, J.; Zhu, Tianri; Welch, R. M.

1992-01-01

The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.

Fractional poisson--a simple dose-response model for human norovirus.

PubMed

Messner, Michael J; Berger, Philip; Nappier, Sharon P

2014-10-01

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation.

PubMed

Gustafsson, Leif; Sternad, Mikael

2007-10-01

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

Statistical modeling of dental unit water bacterial test kit performance.

PubMed

Cohen, Mark E; Harte, Jennifer A; Stone, Mark E; O'Connor, Karen H; Coen, Michael L; Cullum, Malford E

2007-01-01

While it is important to monitor dental water quality, it is unclear whether in-office test kits provide bacterial counts comparable to the gold standard method (R2A). Studies were conducted on specimens with known bacterial concentrations, and from dental units, to evaluate test kit accuracy across a range of bacterial types and loads. Colony forming units (CFU) were counted for samples from each source, using R2A and two types of test kits, and conformity to Poisson distribution expectations was evaluated. Poisson regression was used to test for effects of source and device, and to estimate rate ratios for kits relative to R2A. For all devices, distributions were Poisson for low CFU/mL when only beige-pigmented bacteria were considered. For higher counts, R2A remained Poisson, but kits exhibited over-dispersion. Both kits undercounted relative to R2A, but the degree of undercounting was reasonably stable. Kits did not grow pink-pigmented bacteria from dental-unit water identified as Methylobacterium rhodesianum. Only one of the test kits provided results with adequate reliability at higher bacterial concentrations. Undercount bias could be estimated for this device and used to adjust test kit results. Insensitivity to methylobacteria spp. is problematic.

Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoneking, M.R.; Den Hartog, D.J.

1996-06-01

The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimatesmore » for the fit parameters. They compare this method with a {chi}{sup 2}-minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than {approximately}20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers.« less

Datamining approaches for modeling tumor control probability.

PubMed

Naqa, Issam El; Deasy, Joseph O; Mu, Yi; Huang, Ellen; Hope, Andrew J; Lindsay, Patricia E; Apte, Aditya; Alaly, James; Bradley, Jeffrey D

2010-11-01

Tumor control probability (TCP) to radiotherapy is determined by complex interactions between tumor biology, tumor microenvironment, radiation dosimetry, and patient-related variables. The complexity of these heterogeneous variable interactions constitutes a challenge for building predictive models for routine clinical practice. We describe a datamining framework that can unravel the higher order relationships among dosimetric dose-volume prognostic variables, interrogate various radiobiological processes, and generalize to unseen data before when applied prospectively. Several datamining approaches are discussed that include dose-volume metrics, equivalent uniform dose, mechanistic Poisson model, and model building methods using statistical regression and machine learning techniques. Institutional datasets of non-small cell lung cancer (NSCLC) patients are used to demonstrate these methods. The performance of the different methods was evaluated using bivariate Spearman rank correlations (rs). Over-fitting was controlled via resampling methods. Using a dataset of 56 patients with primary NCSLC tumors and 23 candidate variables, we estimated GTV volume and V75 to be the best model parameters for predicting TCP using statistical resampling and a logistic model. Using these variables, the support vector machine (SVM) kernel method provided superior performance for TCP prediction with an rs=0.68 on leave-one-out testing compared to logistic regression (rs=0.4), Poisson-based TCP (rs=0.33), and cell kill equivalent uniform dose model (rs=0.17). The prediction of treatment response can be improved by utilizing datamining approaches, which are able to unravel important non-linear complex interactions among model variables and have the capacity to predict on unseen data for prospective clinical applications.

On the Spike Train Variability Characterized by Variance-to-Mean Power Relationship.

PubMed

Koyama, Shinsuke

2015-07-01

We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship. Based on this, a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.

Demonstration of fundamental statistics by studying timing of electronics signals in a physics-based laboratory

NASA Astrophysics Data System (ADS)

Beach, Shaun E.; Semkow, Thomas M.; Remling, David J.; Bradt, Clayton J.

2017-07-01

We have developed accessible methods to demonstrate fundamental statistics in several phenomena, in the context of teaching electronic signal processing in a physics-based college-level curriculum. A relationship between the exponential time-interval distribution and Poisson counting distribution for a Markov process with constant rate is derived in a novel way and demonstrated using nuclear counting. Negative binomial statistics is demonstrated as a model for overdispersion and justified by the effect of electronic noise in nuclear counting. The statistics of digital packets on a computer network are shown to be compatible with the fractal-point stochastic process leading to a power-law as well as generalized inverse Gaussian density distributions of time intervals between packets.

Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning.

PubMed

Kuroda, S; Yamamoto, K; Miyamoto, H; Doya, K; Kawat, M

2001-03-01

Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals.

Modeling health survey data with excessive zero and K responses.

PubMed

Lin, Ting Hsiang; Tsai, Min-Hsiao

2013-04-30

Zero-inflated Poisson regression is a popular tool used to analyze data with excessive zeros. Although much work has already been performed to fit zero-inflated data, most models heavily depend on special features of the individual data. To be specific, this means that there is a sizable group of respondents who endorse the same answers making the data have peaks. In this paper, we propose a new model with the flexibility to model excessive counts other than zero, and the model is a mixture of multinomial logistic and Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts, including zeros, K (where K is a positive integer) and all other values. The Poisson regression component models the counts that are assumed to follow a Poisson distribution. Two examples are provided to illustrate our models when the data have counts containing many ones and sixes. As a result, the zero-inflated and K-inflated models exhibit a better fit than the zero-inflated Poisson and standard Poisson regressions. Copyright © 2012 John Wiley & Sons, Ltd.

Determining X-ray source intensity and confidence bounds in crowded fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Primini, F. A.; Kashyap, V. L., E-mail: fap@head.cfa.harvard.edu

We present a rigorous description of the general problem of aperture photometry in high-energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability density function for the expected source intensity for various cases of interest, including the important cases in which both source and background apertures contain contributions from the source, and when multiple source apertures partially overlap. A Bayesian approach offers the advantages of allowing one to (1) include explicit prior information on source intensities, (2) propagate posterior distributions as priors for future observations, and (3) use Poisson likelihoods,more » making the treatment valid in the low-counts regime. Elements of this approach have been implemented in the Chandra Source Catalog.« less

Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

PubMed

Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

2011-01-01

Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

Radio pulsar glitches as a state-dependent Poisson process

NASA Astrophysics Data System (ADS)

Fulgenzi, W.; Melatos, A.; Hughes, B. D.

2017-10-01

Gross-Pitaevskii simulations of vortex avalanches in a neutron star superfluid are limited computationally to ≲102 vortices and ≲102 avalanches, making it hard to study the long-term statistics of radio pulsar glitches in realistically sized systems. Here, an idealized, mean-field model of the observed Gross-Pitaevskii dynamics is presented, in which vortex unpinning is approximated as a state-dependent, compound Poisson process in a single random variable, the spatially averaged crust-superfluid lag. Both the lag-dependent Poisson rate and the conditional distribution of avalanche-driven lag decrements are inputs into the model, which is solved numerically (via Monte Carlo simulations) and analytically (via a master equation). The output statistics are controlled by two dimensionless free parameters: α, the glitch rate at a reference lag, multiplied by the critical lag for unpinning, divided by the spin-down rate; and β, the minimum fraction of the lag that can be restored by a glitch. The system evolves naturally to a self-regulated stationary state, whose properties are determined by α/αc(β), where αc(β) ≈ β-1/2 is a transition value. In the regime α ≳ αc(β), one recovers qualitatively the power-law size and exponential waiting-time distributions observed in many radio pulsars and Gross-Pitaevskii simulations. For α ≪ αc(β), the size and waiting-time distributions are both power-law-like, and a correlation emerges between size and waiting time until the next glitch, contrary to what is observed in most pulsars. Comparisons with astrophysical data are restricted by the small sample sizes available at present, with ≤35 events observed per pulsar.

Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation

NASA Astrophysics Data System (ADS)

Theodorsen, A.; E Garcia, O.; Rypdal, M.

2017-05-01

Filtered Poisson processes are often used as reference models for intermittent fluctuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model parameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the model parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.

Evaluating for a geospatial relationship between radon levels and thyroid cancer in Pennsylvania.

PubMed

Goyal, Neerav; Camacho, Fabian; Mangano, Joseph; Goldenberg, David

2015-01-01

To determine whether there is an association between radon levels and the rise in incidence of thyroid cancer in Pennsylvania. Epidemiological study of the state of Pennsylvania. We used information from the Pennsylvania Cancer Registry and the Pennsylvania Department of Energy. From the registry, information regarding thyroid incidence by county and zip code was recorded. Information regarding radon levels per county was recorded from the state. Poisson regression models were fit predicting county-level thyroid incidence and change as a function of radon/lagged radon levels. To account for measurement error in the radon levels, a Bayesian Model extending the Poisson models was fit. Geospatial clustering analysis was also performed. No association was noted between cumulative radon levels and thyroid incidence. In the Poisson modeling, no significant association was noted between county radon level and thyroid cancer incidence (P = .23). Looking for a lag between the radon level and its effect, no significant effect was seen with a lag of 0 to 6 years between exposure and effect (P = .063 to P = .59). The Bayesian models also failed to show a statistically significant association. A cluster of high thyroid cancer incidence was found in western Pennsylvania. Through a variety of models, no association was elicited between annual radon levels recorded in Pennsylvania and the rising incidence of thyroid cancer. However, a cluster of thyroid cancer incidence was found in western Pennsylvania. Further studies may be helpful in looking for other exposures or associations. © 2014 The American Laryngological, Rhinological and Otological Society, Inc.

Relation Between Firing Statistics of Spiking Neuron with Delayed Fast Inhibitory Feedback and Without Feedback

NASA Astrophysics Data System (ADS)

Vidybida, Alexander; Shchur, Olha

We consider a class of spiking neuronal models, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed with a Poisson process. Each output impulse is applied to the neuron itself after a finite delay Δ. This impulse acts as being delivered through a fast Cl-type inhibitory synapse. We derive a general relation which allows calculating exactly the probability density function (pdf) p(t) of output interspike intervals of a neuron with feedback based on known pdf p0(t) for the same neuron without feedback and on the properties of the feedback line (the Δ value). Similar relations between corresponding moments are derived. Furthermore, we prove that the initial segment of pdf p0(t) for a neuron with a fixed threshold level is the same for any neuron satisfying the imposed conditions and is completely determined by the input stream. For the Poisson input stream, we calculate that initial segment exactly and, based on it, obtain exactly the initial segment of pdf p(t) for a neuron with feedback. That is the initial segment of p(t) is model-independent as well. The obtained expressions are checked by means of Monte Carlo simulation. The course of p(t) has a pronounced peculiarity, which makes it impossible to approximate p(t) by Poisson or another simple stochastic process.

A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep

PubMed Central

Naya, Hugo; Urioste, Jorge I; Chang, Yu-Mei; Rodrigues-Motta, Mariana; Kremer, Roberto; Gianola, Daniel

2008-01-01

Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP) models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep. PMID:18558072

Geographically weighted poisson regression semiparametric on modeling of the number of tuberculosis cases (Case study: Bandung city)

NASA Astrophysics Data System (ADS)

Octavianty, Toharudin, Toni; Jaya, I. G. N. Mindra

2017-03-01

Tuberculosis (TB) is a disease caused by a bacterium, called Mycobacterium tuberculosis, which typically attacks the lungs but can also affect the kidney, spine, and brain (Centers for Disease Control and Prevention). Indonesia had the largest number of TB cases after India (Global Tuberculosis Report 2015 by WHO). The distribution of Mycobacterium tuberculosis genotypes in Indonesia showed the high genetic diversity and tended to vary by geographic regions. For instance, in Bandung city, the prevalence rate of TB morbidity is quite high. A number of TB patients belong to the counted data. To determine the factors that significantly influence the number of tuberculosis patients in each location of the observations can be used statistical analysis tool that is Geographically Weighted Poisson Regression Semiparametric (GWPRS). GWPRS is an extension of the Poisson regression and GWPR that is influenced by geographical factors, and there is also variables that influence globally and locally. Using the TB Data in Bandung city (in 2015), the results show that the global and local variables that influence the number of tuberculosis patients in every sub-district.

The origin of bursts and heavy tails in human dynamics.

PubMed

Barabási, Albert-László

2005-05-12

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behaviour into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Statistical procedures for analyzing mental health services data.

PubMed

Elhai, Jon D; Calhoun, Patrick S; Ford, Julian D

2008-08-15

In mental health services research, analyzing service utilization data often poses serious problems, given the presence of substantially skewed data distributions. This article presents a non-technical introduction to statistical methods specifically designed to handle the complexly distributed datasets that represent mental health service use, including Poisson, negative binomial, zero-inflated, and zero-truncated regression models. A flowchart is provided to assist the investigator in selecting the most appropriate method. Finally, a dataset of mental health service use reported by medical patients is described, and a comparison of results across several different statistical methods is presented. Implications of matching data analytic techniques appropriately with the often complexly distributed datasets of mental health services utilization variables are discussed.

A novel statistical method for quantitative comparison of multiple ChIP-seq datasets.

PubMed

Chen, Li; Wang, Chi; Qin, Zhaohui S; Wu, Hao

2015-06-15

ChIP-seq is a powerful technology to measure the protein binding or histone modification strength in the whole genome scale. Although there are a number of methods available for single ChIP-seq data analysis (e.g. 'peak detection'), rigorous statistical method for quantitative comparison of multiple ChIP-seq datasets with the considerations of data from control experiment, signal to noise ratios, biological variations and multiple-factor experimental designs is under-developed. In this work, we develop a statistical method to perform quantitative comparison of multiple ChIP-seq datasets and detect genomic regions showing differential protein binding or histone modification. We first detect peaks from all datasets and then union them to form a single set of candidate regions. The read counts from IP experiment at the candidate regions are assumed to follow Poisson distribution. The underlying Poisson rates are modeled as an experiment-specific function of artifacts and biological signals. We then obtain the estimated biological signals and compare them through the hypothesis testing procedure in a linear model framework. Simulations and real data analyses demonstrate that the proposed method provides more accurate and robust results compared with existing ones. An R software package ChIPComp is freely available at http://web1.sph.emory.edu/users/hwu30/software/ChIPComp.html. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data.

PubMed

Sim, Shin Zhu; Gupta, Ramesh C; Ong, Seng Huat

2018-01-09

In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.

Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.

PubMed

Zhang, Jiachao; Hirakawa, Keigo

2017-04-01

This paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs. A quantile analysis in pixel, wavelet transform, and variance stabilization domains reveal that the tails of Poisson, signal-dependent Gaussian, and Poisson-Gaussian models are too short to capture real sensor noise behavior. A new Poisson mixture noise model is proposed to correct the mismatch of tail behavior. Based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data, we propose a mixture of Poisson denoising method to remove the denoising artifacts without affecting image details, such as edge and textures. Experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique.

Spatial distribution of psychotic disorders in an urban area of France: an ecological study.

PubMed

Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei

2016-05-18

Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation.

Modeling bursts and heavy tails in human dynamics

NASA Astrophysics Data System (ADS)

Vázquez, Alexei; Oliveira, João Gama; Dezsö, Zoltán; Goh, Kwang-Il; Kondor, Imre; Barabási, Albert-László

2006-03-01

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution P(τw)˜τw-α with α=3/2 . The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by α=1 . We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display α=1 , the surface mail based communication belongs to the α=3/2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.

Modeling bursts and heavy tails in human dynamics.

PubMed

Vázquez, Alexei; Oliveira, João Gama; Dezsö, Zoltán; Goh, Kwang-Il; Kondor, Imre; Barabási, Albert-László

2006-03-01

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can handle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution P(tau(w)) approximately tau(w)(-alpha) with alpha=3/2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by alpha=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display alpha=1, the surface mail based communication belongs to the alpha=3/2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.

RAD-ADAPT: Software for modelling clonogenic assay data in radiation biology.

PubMed

Zhang, Yaping; Hu, Kaiqiang; Beumer, Jan H; Bakkenist, Christopher J; D'Argenio, David Z

2017-04-01

We present a comprehensive software program, RAD-ADAPT, for the quantitative analysis of clonogenic assays in radiation biology. Two commonly used models for clonogenic assay analysis, the linear-quadratic model and single-hit multi-target model, are included in the software. RAD-ADAPT uses maximum likelihood estimation method to obtain parameter estimates with the assumption that cell colony count data follow a Poisson distribution. The program has an intuitive interface, generates model prediction plots, tabulates model parameter estimates, and allows automatic statistical comparison of parameters between different groups. The RAD-ADAPT interface is written using the statistical software R and the underlying computations are accomplished by the ADAPT software system for pharmacokinetic/pharmacodynamic systems analysis. The use of RAD-ADAPT is demonstrated using an example that examines the impact of pharmacologic ATM and ATR kinase inhibition on human lung cancer cell line A549 after ionizing radiation. Copyright © 2017 Elsevier B.V. All rights reserved.

Fragment size distribution statistics in dynamic fragmentation of laser shock-loaded tin

NASA Astrophysics Data System (ADS)

He, Weihua; Xin, Jianting; Zhao, Yongqiang; Chu, Genbai; Xi, Tao; Shui, Min; Lu, Feng; Gu, Yuqiu

2017-06-01

This work investigates the geometric statistics method to characterize the size distribution of tin fragments produced in the laser shock-loaded dynamic fragmentation process. In the shock experiments, the ejection of the tin sample with etched V-shape groove in the free surface are collected by the soft recovery technique. Subsequently, the produced fragments are automatically detected with the fine post-shot analysis techniques including the X-ray micro-tomography and the improved watershed method. To characterize the size distributions of the fragments, a theoretical random geometric statistics model based on Poisson mixtures is derived for dynamic heterogeneous fragmentation problem, which reveals linear combinational exponential distribution. The experimental data related to fragment size distributions of the laser shock-loaded tin sample are examined with the proposed theoretical model, and its fitting performance is compared with that of other state-of-the-art fragment size distribution models. The comparison results prove that our proposed model can provide far more reasonable fitting result for the laser shock-loaded tin.

Bayesian analysis of volcanic eruptions

NASA Astrophysics Data System (ADS)

Ho, Chih-Hsiang

1990-10-01

The simple Poisson model generally gives a good fit to many volcanoes for volcanic eruption forecasting. Nonetheless, empirical evidence suggests that volcanic activity in successive equal time-periods tends to be more variable than a simple Poisson with constant eruptive rate. An alternative model is therefore examined in which eruptive rate(λ) for a given volcano or cluster(s) of volcanoes is described by a gamma distribution (prior) rather than treated as a constant value as in the assumptions of a simple Poisson model. Bayesian analysis is performed to link two distributions together to give the aggregate behavior of the volcanic activity. When the Poisson process is expanded to accomodate a gamma mixing distribution on λ, a consequence of this mixed (or compound) Poisson model is that the frequency distribution of eruptions in any given time-period of equal length follows the negative binomial distribution (NBD). Applications of the proposed model and comparisons between the generalized model and simple Poisson model are discussed based on the historical eruptive count data of volcanoes Mauna Loa (Hawaii) and Etna (Italy). Several relevant facts lead to the conclusion that the generalized model is preferable for practical use both in space and time.

Universal self-similarity of propagating populations

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-07-01

This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d -dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common—yet arbitrary—motion pattern; each particle has its own random propagation parameters—emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles’ displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles’ underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.

Universal self-similarity of propagating populations.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-07-01

This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d-dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common--yet arbitrary--motion pattern; each particle has its own random propagation parameters--emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles' displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles' underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.

Atomic clocks and the continuous-time random-walk

NASA Astrophysics Data System (ADS)

Formichella, Valerio; Camparo, James; Tavella, Patrizia

2017-11-01

Atomic clocks play a fundamental role in many fields, most notably they generate Universal Coordinated Time and are at the heart of all global navigation satellite systems. Notwithstanding their excellent timekeeping performance, their output frequency does vary: it can display deterministic frequency drift; diverse continuous noise processes result in nonstationary clock noise (e.g., random-walk frequency noise, modelled as a Wiener process), and the clock frequency may display sudden changes (i.e., "jumps"). Typically, the clock's frequency instability is evaluated by the Allan or Hadamard variances, whose functional forms can identify the different operative noise processes. Here, we show that the Allan and Hadamard variances of a particular continuous-time random-walk, the compound Poisson process, have the same functional form as for a Wiener process with drift. The compound Poisson process, introduced as a model for observed frequency jumps, is an alternative to the Wiener process for modelling random walk frequency noise. This alternate model fits well the behavior of the rubidium clocks flying on GPS Block-IIR satellites. Further, starting from jump statistics, the model can be improved by considering a more general form of continuous-time random-walk, and this could bring new insights into the physics of atomic clocks.

Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels.

PubMed

Park, H M; Lee, J S; Kim, T W

2007-11-15

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.

Applications of spatial statistical network models to stream data

USGS Publications Warehouse

Isaak, Daniel J.; Peterson, Erin E.; Ver Hoef, Jay M.; Wenger, Seth J.; Falke, Jeffrey A.; Torgersen, Christian E.; Sowder, Colin; Steel, E. Ashley; Fortin, Marie-Josée; Jordan, Chris E.; Ruesch, Aaron S.; Som, Nicholas; Monestiez, Pascal

2014-01-01

Streams and rivers host a significant portion of Earth's biodiversity and provide important ecosystem services for human populations. Accurate information regarding the status and trends of stream resources is vital for their effective conservation and management. Most statistical techniques applied to data measured on stream networks were developed for terrestrial applications and are not optimized for streams. A new class of spatial statistical model, based on valid covariance structures for stream networks, can be used with many common types of stream data (e.g., water quality attributes, habitat conditions, biological surveys) through application of appropriate distributions (e.g., Gaussian, binomial, Poisson). The spatial statistical network models account for spatial autocorrelation (i.e., nonindependence) among measurements, which allows their application to databases with clustered measurement locations. Large amounts of stream data exist in many areas where spatial statistical analyses could be used to develop novel insights, improve predictions at unsampled sites, and aid in the design of efficient monitoring strategies at relatively low cost. We review the topic of spatial autocorrelation and its effects on statistical inference, demonstrate the use of spatial statistics with stream datasets relevant to common research and management questions, and discuss additional applications and development potential for spatial statistics on stream networks. Free software for implementing the spatial statistical network models has been developed that enables custom applications with many stream databases.

Bayesian hierarchical modeling for detecting safety signals in clinical trials.

PubMed

Xia, H Amy; Ma, Haijun; Carlin, Bradley P

2011-09-01

Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.

Trends in Mortality After Primary Cytoreductive Surgery for Ovarian Cancer: A Systematic Review and Metaregression of Randomized Clinical Trials and Observational Studies.

PubMed

Di Donato, Violante; Kontopantelis, Evangelos; Aletti, Giovanni; Casorelli, Assunta; Piacenti, Ilaria; Bogani, Giorgio; Lecce, Francesca; Benedetti Panici, Pierluigi

2017-06-01

Primary cytoreductive surgery (PDS) followed by platinum-based chemotherapy is the cornerstone of treatment and the absence of residual tumor after PDS is universally considered the most important prognostic factor. The aim of the present analysis was to evaluate trend and predictors of 30-day mortality in patients undergoing primary cytoreduction for ovarian cancer. Literature was searched for records reporting 30-day mortality after PDS. All cohorts were rated for quality. Simple and multiple Poisson regression models were used to quantify the association between 30-day mortality and the following: overall or severe complications, proportion of patients with stage IV disease, median age, year of publication, and weighted surgical complexity index. Using the multiple regression model, we calculated the risk of perioperative mortality at different levels for statistically significant covariates of interest. Simple regression identified median age and proportion of patients with stage IV disease as statistically significant predictors of 30-day mortality. When included in the multiple Poisson regression model, both remained statistically significant, with an incidence rate ratio of 1.087 for median age and 1.017 for stage IV disease. Disease stage was a strong predictor, with the risk estimated to increase from 2.8% (95% confidence interval 2.02-3.66) for stage III to 16.1% (95% confidence interval 6.18-25.93) for stage IV, for a cohort with a median age of 65 years. Metaregression demonstrated that increased age and advanced clinical stage were independently associated with an increased risk of mortality, and the combined effects of both factors greatly increased the risk.

A statistical model investigating the prevalence of tuberculosis in New York City using counting processes with two change-points

PubMed Central

ACHCAR, J. A.; MARTINEZ, E. Z.; RUFFINO-NETTO, A.; PAULINO, C. D.; SOARES, P.

2008-01-01

SUMMARY We considered a Bayesian analysis for the prevalence of tuberculosis cases in New York City from 1970 to 2000. This counting dataset presented two change-points during this period. We modelled this counting dataset considering non-homogeneous Poisson processes in the presence of the two-change points. A Bayesian analysis for the data is considered using Markov chain Monte Carlo methods. Simulated Gibbs samples for the parameters of interest were obtained using WinBugs software. PMID:18346287

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach.

PubMed

Mohammadi, Tayeb; Kheiri, Soleiman; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach

PubMed Central

Mohammadi, Tayeb; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models. PMID:27703493

Modelling infant mortality rate in Central Java, Indonesia use generalized poisson regression method

NASA Astrophysics Data System (ADS)

Prahutama, Alan; Sudarno

2018-05-01

The infant mortality rate is the number of deaths under one year of age occurring among the live births in a given geographical area during a given year, per 1,000 live births occurring among the population of the given geographical area during the same year. This problem needs to be addressed because it is an important element of a country’s economic development. High infant mortality rate will disrupt the stability of a country as it relates to the sustainability of the population in the country. One of regression model that can be used to analyze the relationship between dependent variable Y in the form of discrete data and independent variable X is Poisson regression model. Recently The regression modeling used for data with dependent variable is discrete, among others, poisson regression, negative binomial regression and generalized poisson regression. In this research, generalized poisson regression modeling gives better AIC value than poisson regression. The most significant variable is the Number of health facilities (X1), while the variable that gives the most influence to infant mortality rate is the average breastfeeding (X9).

Modified Regression Correlation Coefficient for Poisson Regression Model

NASA Astrophysics Data System (ADS)

Kaengthong, Nattacha; Domthong, Uthumporn

2017-09-01

This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).

Semi-Poisson statistics in quantum chaos.

PubMed

García-García, Antonio M; Wang, Jiao

2006-03-01

We investigate the quantum properties of a nonrandom Hamiltonian with a steplike singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by semi-Poisson statistics (SP) typical of pseudointegrable systems. It is also shown that our results are universal, namely, they depend exclusively on the presence of the steplike singularity and are not modified by smooth perturbations of the potential or the addition of a magnetic flux. Although the quantum properties of our system are similar to those of a disordered conductor at the Anderson transition, we report important quantitative differences in both the level statistics and the multifractal dimensions controlling the transition. Finally, the study of quantum transport properties suggests that the classical singularity induces quantum anomalous diffusion. We discuss how these findings may be experimentally corroborated by using ultracold atoms techniques.

Comparison of robustness to outliers between robust poisson models and log-binomial models when estimating relative risks for common binary outcomes: a simulation study.

PubMed

Chen, Wansu; Shi, Jiaxiao; Qian, Lei; Azen, Stanley P

2014-06-26

To estimate relative risks or risk ratios for common binary outcomes, the most popular model-based methods are the robust (also known as modified) Poisson and the log-binomial regression. Of the two methods, it is believed that the log-binomial regression yields more efficient estimators because it is maximum likelihood based, while the robust Poisson model may be less affected by outliers. Evidence to support the robustness of robust Poisson models in comparison with log-binomial models is very limited. In this study a simulation was conducted to evaluate the performance of the two methods in several scenarios where outliers existed. The findings indicate that for data coming from a population where the relationship between the outcome and the covariate was in a simple form (e.g. log-linear), the two models yielded comparable biases and mean square errors. However, if the true relationship contained a higher order term, the robust Poisson models consistently outperformed the log-binomial models even when the level of contamination is low. The robust Poisson models are more robust (or less sensitive) to outliers compared to the log-binomial models when estimating relative risks or risk ratios for common binary outcomes. Users should be aware of the limitations when choosing appropriate models to estimate relative risks or risk ratios.

Possible Statistics of Two Coupled Random Fields: Application to Passive Scalar

NASA Technical Reports Server (NTRS)

Dubrulle, B.; He, Guo-Wei; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random elds at different scales. We nd the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian velocity field; and ii) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.

Nambu-Poisson gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-06-01

We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model.

Bayesian dynamic modeling of time series of dengue disease case counts

PubMed Central

López-Quílez, Antonio; Torres-Prieto, Alexander

2017-01-01

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health. PMID:28671941

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

PubMed

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

The Validity of Poisson Assumptions in a Combined Loglinear/MDS Mapping Model.

ERIC Educational Resources Information Center

Everett, James E.

1993-01-01

Addresses objections to the validity of assuming a Poisson loglinear model as the generating process for citations from one journal into another. Fluctuations in citation rate, serial dependence on citations, impossibility of distinguishing between rate changes and serial dependence, evidence for changes in Poisson rate, and transitivity…

Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

PubMed

Faul, Franz; Erdfelder, Edgar; Buchner, Axel; Lang, Albert-Georg

2009-11-01

G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

A new computer code for discrete fracture network modelling

NASA Astrophysics Data System (ADS)

Xu, Chaoshui; Dowd, Peter

2010-03-01

The authors describe a comprehensive software package for two- and three-dimensional stochastic rock fracture simulation using marked point processes. Fracture locations can be modelled by a Poisson, a non-homogeneous, a cluster or a Cox point process; fracture geometries and properties are modelled by their respective probability distributions. Virtual sampling tools such as plane, window and scanline sampling are included in the software together with a comprehensive set of statistical tools including histogram analysis, probability plots, rose diagrams and hemispherical projections. The paper describes in detail the theoretical basis of the implementation and provides a case study in rock fracture modelling to demonstrate the application of the software.

Bayesian multivariate Poisson abundance models for T-cell receptor data.

PubMed

Greene, Joshua; Birtwistle, Marc R; Ignatowicz, Leszek; Rempala, Grzegorz A

2013-06-07

A major feature of an adaptive immune system is its ability to generate B- and T-cell clones capable of recognizing and neutralizing specific antigens. These clones recognize antigens with the help of the surface molecules, called antigen receptors, acquired individually during the clonal development process. In order to ensure a response to a broad range of antigens, the number of different receptor molecules is extremely large, resulting in a huge clonal diversity of both B- and T-cell receptor populations and making their experimental comparisons statistically challenging. To facilitate such comparisons, we propose a flexible parametric model of multivariate count data and illustrate its use in a simultaneous analysis of multiple antigen receptor populations derived from mammalian T-cells. The model relies on a representation of the observed receptor counts as a multivariate Poisson abundance mixture (m PAM). A Bayesian parameter fitting procedure is proposed, based on the complete posterior likelihood, rather than the conditional one used typically in similar settings. The new procedure is shown to be considerably more efficient than its conditional counterpart (as measured by the Fisher information) in the regions of m PAM parameter space relevant to model T-cell data. Copyright © 2013 Elsevier Ltd. All rights reserved.

Stationary and non-stationary occurrences of miniature end plate potentials are well described as stationary and non-stationary Poisson processes in the mollusc Navanax inermis.

PubMed

Cappell, M S; Spray, D C; Bennett, M V

1988-06-28

Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.

Zero-inflated Poisson model based likelihood ratio test for drug safety signal detection.

PubMed

Huang, Lan; Zheng, Dan; Zalkikar, Jyoti; Tiwari, Ram

2017-02-01

In recent decades, numerous methods have been developed for data mining of large drug safety databases, such as Food and Drug Administration's (FDA's) Adverse Event Reporting System, where data matrices are formed by drugs such as columns and adverse events as rows. Often, a large number of cells in these data matrices have zero cell counts and some of them are "true zeros" indicating that the drug-adverse event pairs cannot occur, and these zero counts are distinguished from the other zero counts that are modeled zero counts and simply indicate that the drug-adverse event pairs have not occurred yet or have not been reported yet. In this paper, a zero-inflated Poisson model based likelihood ratio test method is proposed to identify drug-adverse event pairs that have disproportionately high reporting rates, which are also called signals. The maximum likelihood estimates of the model parameters of zero-inflated Poisson model based likelihood ratio test are obtained using the expectation and maximization algorithm. The zero-inflated Poisson model based likelihood ratio test is also modified to handle the stratified analyses for binary and categorical covariates (e.g. gender and age) in the data. The proposed zero-inflated Poisson model based likelihood ratio test method is shown to asymptotically control the type I error and false discovery rate, and its finite sample performance for signal detection is evaluated through a simulation study. The simulation results show that the zero-inflated Poisson model based likelihood ratio test method performs similar to Poisson model based likelihood ratio test method when the estimated percentage of true zeros in the database is small. Both the zero-inflated Poisson model based likelihood ratio test and likelihood ratio test methods are applied to six selected drugs, from the 2006 to 2011 Adverse Event Reporting System database, with varying percentages of observed zero-count cells.

Counting statistics for genetic switches based on effective interaction approximation

NASA Astrophysics Data System (ADS)

Ohkubo, Jun

2012-09-01

Applicability of counting statistics for a system with an infinite number of states is investigated. The counting statistics has been studied a lot for a system with a finite number of states. While it is possible to use the scheme in order to count specific transitions in a system with an infinite number of states in principle, we have non-closed equations in general. A simple genetic switch can be described by a master equation with an infinite number of states, and we use the counting statistics in order to count the number of transitions from inactive to active states in the gene. To avoid having the non-closed equations, an effective interaction approximation is employed. As a result, it is shown that the switching problem can be treated as a simple two-state model approximately, which immediately indicates that the switching obeys non-Poisson statistics.

Bayesian Poisson hierarchical models for crash data analysis: Investigating the impact of model choice on site-specific predictions.

PubMed

Khazraee, S Hadi; Johnson, Valen; Lord, Dominique

2018-08-01

The Poisson-gamma (PG) and Poisson-lognormal (PLN) regression models are among the most popular means for motor vehicle crash data analysis. Both models belong to the Poisson-hierarchical family of models. While numerous studies have compared the overall performance of alternative Bayesian Poisson-hierarchical models, little research has addressed the impact of model choice on the expected crash frequency prediction at individual sites. This paper sought to examine whether there are any trends among candidate models predictions e.g., that an alternative model's prediction for sites with certain conditions tends to be higher (or lower) than that from another model. In addition to the PG and PLN models, this research formulated a new member of the Poisson-hierarchical family of models: the Poisson-inverse gamma (PIGam). Three field datasets (from Texas, Michigan and Indiana) covering a wide range of over-dispersion characteristics were selected for analysis. This study demonstrated that the model choice can be critical when the calibrated models are used for prediction at new sites, especially when the data are highly over-dispersed. For all three datasets, the PIGam model would predict higher expected crash frequencies than would the PLN and PG models, in order, indicating a clear link between the models predictions and the shape of their mixing distributions (i.e., gamma, lognormal, and inverse gamma, respectively). The thicker tail of the PIGam and PLN models (in order) may provide an advantage when the data are highly over-dispersed. The analysis results also illustrated a major deficiency of the Deviance Information Criterion (DIC) in comparing the goodness-of-fit of hierarchical models; models with drastically different set of coefficients (and thus predictions for new sites) may yield similar DIC values, because the DIC only accounts for the parameters in the lowest (observation) level of the hierarchy and ignores the higher levels (regression coefficients). Copyright © 2018. Published by Elsevier Ltd.

Repairable-conditionally repairable damage model based on dual Poisson processes.

PubMed

Lind, B K; Persson, L M; Edgren, M R; Hedlöf, I; Brahme, A

2003-09-01

The advent of intensity-modulated radiation therapy makes it increasingly important to model the response accurately when large volumes of normal tissues are irradiated by controlled graded dose distributions aimed at maximizing tumor cure and minimizing normal tissue toxicity. The cell survival model proposed here is very useful and flexible for accurate description of the response of healthy tissues as well as tumors in classical and truly radiobiologically optimized radiation therapy. The repairable-conditionally repairable (RCR) model distinguishes between two different types of damage, namely the potentially repairable, which may also be lethal, i.e. if unrepaired or misrepaired, and the conditionally repairable, which may be repaired or may lead to apoptosis if it has not been repaired correctly. When potentially repairable damage is being repaired, for example by nonhomologous end joining, conditionally repairable damage may require in addition a high-fidelity correction by homologous repair. The induction of both types of damage is assumed to be described by Poisson statistics. The resultant cell survival expression has the unique ability to fit most experimental data well at low doses (the initial hypersensitive range), intermediate doses (on the shoulder of the survival curve), and high doses (on the quasi-exponential region of the survival curve). The complete Poisson expression can be approximated well by a simple bi-exponential cell survival expression, S(D) = e(-aD) + bDe(-cD), where the first term describes the survival of undamaged cells and the last term represents survival after complete repair of sublethal damage. The bi-exponential expression makes it easy to derive D(0), D(q), n and alpha, beta values to facilitate comparison with classical cell survival models.

Multiscale hidden Markov models for photon-limited imaging

NASA Astrophysics Data System (ADS)

Nowak, Robert D.

1999-06-01

Photon-limited image analysis is often hindered by low signal-to-noise ratios. A novel Bayesian multiscale modeling and analysis method is developed in this paper to assist in these challenging situations. In addition to providing a very natural and useful framework for modeling an d processing images, Bayesian multiscale analysis is often much less computationally demanding compared to classical Markov random field models. This paper focuses on a probabilistic graph model called the multiscale hidden Markov model (MHMM), which captures the key inter-scale dependencies present in natural image intensities. The MHMM framework presented here is specifically designed for photon-limited imagin applications involving Poisson statistics, and applications to image intensity analysis are examined.

Evaluation of Shiryaev-Roberts procedure for on-line environmental radiation monitoring.

PubMed

Watson, Mara M; Seliman, Ayman F; Bliznyuk, Valery N; DeVol, Timothy A

2018-04-30

Water can become contaminated as a result of a leak from a nuclear facility, such as a waste facility, or from clandestine nuclear activity. Low-level on-line radiation monitoring is needed to detect these events in real time. A Bayesian control chart method, Shiryaev-Roberts (SR) procedure, was compared with classical methods, 3-σ and cumulative sum (CUSUM), for quantifying an accumulating signal from an extractive scintillating resin flow-cell detection system. Solutions containing 0.10-5.0 Bq/L of 99 Tc, as T99cO 4 - were pumped through a flow cell packed with extractive scintillating resin used in conjunction with a Beta-RAM Model 5 HPLC detector. While T99cO 4 - accumulated on the resin, time series data were collected. Control chart methods were applied to the data using statistical algorithms developed in MATLAB. SR charts were constructed using Poisson (Poisson SR) and Gaussian (Gaussian SR) probability distributions of count data to estimate the likelihood ratio. Poisson and Gaussian SR charts required less volume of radioactive solution at a fixed concentration to exceed the control limit in most cases than 3-σ and CUSUM control charts, particularly solutions with lower activity. SR is thus the ideal control chart for low-level on-line radiation monitoring. Once the control limit was exceeded, activity concentrations were estimated from the SR control chart using the control chart slope on a semi-logarithmic plot. A linear regression fit was applied to averaged slope data for five activity concentration groupings for Poisson and Gaussian SR control charts. A correlation coefficient (R 2 ) of 0.77 for Poisson SR and 0.90 for Gaussian SR suggest this method will adequately estimate activity concentration for an unknown solution. Copyright © 2018 Elsevier Ltd. All rights reserved.

[Application of negative binomial regression and modified Poisson regression in the research of risk factors for injury frequency].

PubMed

Cao, Qingqing; Wu, Zhenqiang; Sun, Ying; Wang, Tiezhu; Han, Tengwei; Gu, Chaomei; Sun, Yehuan

2011-11-01

To Eexplore the application of negative binomial regression and modified Poisson regression analysis in analyzing the influential factors for injury frequency and the risk factors leading to the increase of injury frequency. 2917 primary and secondary school students were selected from Hefei by cluster random sampling method and surveyed by questionnaire. The data on the count event-based injuries used to fitted modified Poisson regression and negative binomial regression model. The risk factors incurring the increase of unintentional injury frequency for juvenile students was explored, so as to probe the efficiency of these two models in studying the influential factors for injury frequency. The Poisson model existed over-dispersion (P < 0.0001) based on testing by the Lagrangemultiplier. Therefore, the over-dispersion dispersed data using a modified Poisson regression and negative binomial regression model, was fitted better. respectively. Both showed that male gender, younger age, father working outside of the hometown, the level of the guardian being above junior high school and smoking might be the results of higher injury frequencies. On a tendency of clustered frequency data on injury event, both the modified Poisson regression analysis and negative binomial regression analysis can be used. However, based on our data, the modified Poisson regression fitted better and this model could give a more accurate interpretation of relevant factors affecting the frequency of injury.

Classifying next-generation sequencing data using a zero-inflated Poisson model.

PubMed

Zhou, Yan; Wan, Xiang; Zhang, Baoxue; Tong, Tiejun

2018-04-15

With the development of high-throughput techniques, RNA-sequencing (RNA-seq) is becoming increasingly popular as an alternative for gene expression analysis, such as RNAs profiling and classification. Identifying which type of diseases a new patient belongs to with RNA-seq data has been recognized as a vital problem in medical research. As RNA-seq data are discrete, statistical methods developed for classifying microarray data cannot be readily applied for RNA-seq data classification. Witten proposed a Poisson linear discriminant analysis (PLDA) to classify the RNA-seq data in 2011. Note, however, that the count datasets are frequently characterized by excess zeros in real RNA-seq or microRNA sequence data (i.e. when the sequence depth is not enough or small RNAs with the length of 18-30 nucleotides). Therefore, it is desired to develop a new model to analyze RNA-seq data with an excess of zeros. In this paper, we propose a Zero-Inflated Poisson Logistic Discriminant Analysis (ZIPLDA) for RNA-seq data with an excess of zeros. The new method assumes that the data are from a mixture of two distributions: one is a point mass at zero, and the other follows a Poisson distribution. We then consider a logistic relation between the probability of observing zeros and the mean of the genes and the sequencing depth in the model. Simulation studies show that the proposed method performs better than, or at least as well as, the existing methods in a wide range of settings. Two real datasets including a breast cancer RNA-seq dataset and a microRNA-seq dataset are also analyzed, and they coincide with the simulation results that our proposed method outperforms the existing competitors. The software is available at http://www.math.hkbu.edu.hk/∼tongt. xwan@comp.hkbu.edu.hk or tongt@hkbu.edu.hk. Supplementary data are available at Bioinformatics online.

Handling nonnormality and variance heterogeneity for quantitative sublethal toxicity tests.

PubMed

Ritz, Christian; Van der Vliet, Leana

2009-09-01

The advantages of using regression-based techniques to derive endpoints from environmental toxicity data are clear, and slowly, this superior analytical technique is gaining acceptance. As use of regression-based analysis becomes more widespread, some of the associated nuances and potential problems come into sharper focus. Looking at data sets that cover a broad spectrum of standard test species, we noticed that some model fits to data failed to meet two key assumptions-variance homogeneity and normality-that are necessary for correct statistical analysis via regression-based techniques. Failure to meet these assumptions often is caused by reduced variance at the concentrations showing severe adverse effects. Although commonly used with linear regression analysis, transformation of the response variable only is not appropriate when fitting data using nonlinear regression techniques. Through analysis of sample data sets, including Lemna minor, Eisenia andrei (terrestrial earthworm), and algae, we show that both the so-called Box-Cox transformation and use of the Poisson distribution can help to correct variance heterogeneity and nonnormality and so allow nonlinear regression analysis to be implemented. Both the Box-Cox transformation and the Poisson distribution can be readily implemented into existing protocols for statistical analysis. By correcting for nonnormality and variance heterogeneity, these two statistical tools can be used to encourage the transition to regression-based analysis and the depreciation of less-desirable and less-flexible analytical techniques, such as linear interpolation.

Dynamic properties of small-scale solar wind plasma fluctuations.

PubMed

Riazantseva, M O; Budaev, V P; Zelenyi, L M; Zastenker, G N; Pavlos, G P; Safrankova, J; Nemecek, Z; Prech, L; Nemec, F

2015-05-13

The paper presents the latest results of the studies of small-scale fluctuations in a turbulent flow of solar wind (SW) using measurements with extremely high temporal resolution (up to 0.03 s) of the bright monitor of SW (BMSW) plasma spectrometer operating on astrophysical SPECTR-R spacecraft at distances up to 350,000 km from the Earth. The spectra of SW ion flux fluctuations in the range of scales between 0.03 and 100 s are systematically analysed. The difference of slopes in low- and high-frequency parts of spectra and the frequency of the break point between these two characteristic slopes was analysed for different conditions in the SW. The statistical properties of the SW ion flux fluctuations were thoroughly analysed on scales less than 10 s. A high level of intermittency is demonstrated. The extended self-similarity of SW ion flux turbulent flow is constantly observed. The approximation of non-Gaussian probability distribution function of ion flux fluctuations by the Tsallis statistics shows the non-extensive character of SW fluctuations. Statistical characteristics of ion flux fluctuations are compared with the predictions of a log-Poisson model. The log-Poisson parametrization of the structure function scaling has shown that well-defined filament-like plasma structures are, as a rule, observed in the turbulent SW flows. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Local box-counting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statistics

NASA Astrophysics Data System (ADS)

Sakhr, Jamal; Nieminen, John M.

2018-03-01

Two decades ago, Wang and Ong, [Phys. Rev. A 55, 1522 (1997)], 10.1103/PhysRevA.55.1522 hypothesized that the local box-counting dimension of a discrete quantum spectrum should depend exclusively on the nearest-neighbor spacing distribution (NNSD) of the spectrum. In this Rapid Communication, we validate their hypothesis by deriving an explicit formula for the local box-counting dimension of a countably-infinite discrete quantum spectrum. This formula expresses the local box-counting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closed-form approximations to the local box-counting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local box-counting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numerically computed local box-counting dimension.

Including long-range dependence in integrate-and-fire models of the high interspike-interval variability of cortical neurons.

PubMed

Jackson, B Scott

2004-10-01

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (nonPoissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have long-range dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

An order statistics approach to the halo model for galaxies

NASA Astrophysics Data System (ADS)

Paul, Niladri; Paranjape, Aseem; Sheth, Ravi K.

2017-04-01

We use the halo model to explore the implications of assuming that galaxy luminosities in groups are randomly drawn from an underlying luminosity function. We show that even the simplest of such order statistics models - one in which this luminosity function p(L) is universal - naturally produces a number of features associated with previous analyses based on the 'central plus Poisson satellites' hypothesis. These include the monotonic relation of mean central luminosity with halo mass, the lognormal distribution around this mean and the tight relation between the central and satellite mass scales. In stark contrast to observations of galaxy clustering; however, this model predicts no luminosity dependence of large-scale clustering. We then show that an extended version of this model, based on the order statistics of a halo mass dependent luminosity function p(L|m), is in much better agreement with the clustering data as well as satellite luminosities, but systematically underpredicts central luminosities. This brings into focus the idea that central galaxies constitute a distinct population that is affected by different physical processes than are the satellites. We model this physical difference as a statistical brightening of the central luminosities, over and above the order statistics prediction. The magnitude gap between the brightest and second brightest group galaxy is predicted as a by-product, and is also in good agreement with observations. We propose that this order statistics framework provides a useful language in which to compare the halo model for galaxies with more physically motivated galaxy formation models.

Statistical model for speckle pattern optimization.

PubMed

Su, Yong; Zhang, Qingchuan; Gao, Zeren

2017-11-27

Image registration is the key technique of optical metrologies such as digital image correlation (DIC), particle image velocimetry (PIV), and speckle metrology. Its performance depends critically on the quality of image pattern, and thus pattern optimization attracts extensive attention. In this article, a statistical model is built to optimize speckle patterns that are composed of randomly positioned speckles. It is found that the process of speckle pattern generation is essentially a filtered Poisson process. The dependence of measurement errors (including systematic errors, random errors, and overall errors) upon speckle pattern generation parameters is characterized analytically. By minimizing the errors, formulas of the optimal speckle radius are presented. Although the primary motivation is from the field of DIC, we believed that scholars in other optical measurement communities, such as PIV and speckle metrology, will benefit from these discussions.

Statistical Parameter Study of the Time Interval Distribution for Nonparalyzable, Paralyzable, and Hybrid Dead Time Models

NASA Astrophysics Data System (ADS)

Syam, Nur Syamsi; Maeng, Seongjin; Kim, Myo Gwang; Lim, Soo Yeon; Lee, Sang Hoon

2018-05-01

A large dead time of a Geiger Mueller (GM) detector may cause a large count loss in radiation measurements and consequently may cause distortion of the Poisson statistic of radiation events into a new distribution. The new distribution will have different statistical parameters compared to the original distribution. Therefore, the variance, skewness, and excess kurtosis in association with the observed count rate of the time interval distribution for well-known nonparalyzable, paralyzable, and nonparalyzable-paralyzable hybrid dead time models of a Geiger Mueller detector were studied using Monte Carlo simulation (GMSIM). These parameters were then compared with the statistical parameters of a perfect detector to observe the change in the distribution. The results show that the behaviors of the statistical parameters for the three dead time models were different. The values of the skewness and the excess kurtosis of the nonparalyzable model are equal or very close to those of the perfect detector, which are ≅2 for skewness, and ≅6 for excess kurtosis, while the statistical parameters in the paralyzable and hybrid model obtain minimum values that occur around the maximum observed count rates. The different trends of the three models resulting from the GMSIM simulation can be used to distinguish the dead time behavior of a GM counter; i.e. whether the GM counter can be described best by using the nonparalyzable, paralyzable, or hybrid model. In a future study, these statistical parameters need to be analyzed further to determine the possibility of using them to determine a dead time for each model, particularly for paralyzable and hybrid models.

An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces.

PubMed

Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying

2013-03-08

Poisson disk sampling plays an important role in a variety of visual computing, due to its useful statistical property in distribution and the absence of aliasing artifacts. While many effective techniques have been proposed to generate Poisson disk distribution in Euclidean space, relatively few work has been reported to the surface counterpart. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. We propose a new technique for parallelizing the dart throwing. Rather than the conventional approaches that explicitly partition the spatial domain to generate the samples in parallel, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. It is worth noting that our algorithm is accurate as the generated Poisson disks are uniformly and randomly distributed without bias. Our method is intrinsic in that all the computations are based on the intrinsic metric and are independent of the embedding space. This intrinsic feature allows us to generate Poisson disk distributions on arbitrary surfaces. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

Renewal models and coseismic stress transfer in the Corinth Gulf, Greece, fault system

NASA Astrophysics Data System (ADS)

Console, Rodolfo; Falcone, Giuseppe; Karakostas, Vassilis; Murru, Maura; Papadimitriou, Eleftheria; Rhoades, David

2013-07-01

model interevent times and Coulomb static stress transfer on the rupture segments along the Corinth Gulf extension zone, a region with a wealth of observations on strong-earthquake recurrence behavior. From the available information on past seismic activity, we have identified eight segments without significant overlapping that are aligned along the southern boundary of the Corinth rift. We aim to test if strong earthquakes on these segments are characterized by some kind of time-predictable behavior, rather than by complete randomness. The rationale for time-predictable behavior is based on the characteristic earthquake hypothesis, the necessary ingredients of which are a known faulting geometry and slip rate. The tectonic loading rate is characterized by slip of 6 mm/yr on the westernmost fault segment, diminishing to 4 mm/yr on the easternmost segment, based on the most reliable geodetic data. In this study, we employ statistical and physical modeling to account for stress transfer among these fault segments. The statistical modeling is based on the definition of a probability density distribution of the interevent times for each segment. Both the Brownian Passage-Time (BPT) and Weibull distributions are tested. The time-dependent hazard rate thus obtained is then modified by the inclusion of a permanent physical effect due to the Coulomb static stress change caused by failure of neighboring faults since the latest characteristic earthquake on the fault of interest. The validity of the renewal model is assessed retrospectively, using the data of the last 300 years, by comparison with a plain time-independent Poisson model, by means of statistical tools including the Relative Operating Characteristic diagram, the R-score, the probability gain and the log-likelihood ratio. We treat the uncertainties in the parameters of each examined fault source, such as linear dimensions, depth of the fault center, focal mechanism, recurrence time, coseismic slip, and aperiodicity of the statistical distribution, by a Monte Carlo technique. The Monte Carlo samples for all these parameters are drawn from a uniform distribution within their uncertainty limits. We find that the BPT and the Weibull renewal models yield comparable results, and both of them perform significantly better than the Poisson hypothesis. No clear performance enhancement is achieved by the introduction of the Coulomb static stress change into the renewal model.

Using statistical anomaly detection models to find clinical decision support malfunctions.

PubMed

Ray, Soumi; McEvoy, Dustin S; Aaron, Skye; Hickman, Thu-Trang; Wright, Adam

2018-05-11

Malfunctions in Clinical Decision Support (CDS) systems occur due to a multitude of reasons, and often go unnoticed, leading to potentially poor outcomes. Our goal was to identify malfunctions within CDS systems. We evaluated 6 anomaly detection models: (1) Poisson Changepoint Model, (2) Autoregressive Integrated Moving Average (ARIMA) Model, (3) Hierarchical Divisive Changepoint (HDC) Model, (4) Bayesian Changepoint Model, (5) Seasonal Hybrid Extreme Studentized Deviate (SHESD) Model, and (6) E-Divisive with Median (EDM) Model and characterized their ability to find known anomalies. We analyzed 4 CDS alerts with known malfunctions from the Longitudinal Medical Record (LMR) and Epic® (Epic Systems Corporation, Madison, WI, USA) at Brigham and Women's Hospital, Boston, MA. The 4 rules recommend lead testing in children, aspirin therapy in patients with coronary artery disease, pneumococcal vaccination in immunocompromised adults and thyroid testing in patients taking amiodarone. Poisson changepoint, ARIMA, HDC, Bayesian changepoint and the SHESD model were able to detect anomalies in an alert for lead screening in children and in an alert for pneumococcal conjugate vaccine in immunocompromised adults. EDM was able to detect anomalies in an alert for monitoring thyroid function in patients on amiodarone. Malfunctions/anomalies occur frequently in CDS alert systems. It is important to be able to detect such anomalies promptly. Anomaly detection models are useful tools to aid such detections.

Vesicle Motion during Sustained Exocytosis in Chromaffin Cells: Numerical Model Based on Amperometric Measurements.

PubMed

Jarukanont, Daungruthai; Bonifas Arredondo, Imelda; Femat, Ricardo; Garcia, Martin E

2015-01-01

Chromaffin cells release catecholamines by exocytosis, a process that includes vesicle docking, priming and fusion. Although all these steps have been intensively studied, some aspects of their mechanisms, particularly those regarding vesicle transport to the active sites situated at the membrane, are still unclear. In this work, we show that it is possible to extract information on vesicle motion in Chromaffin cells from the combination of Langevin simulations and amperometric measurements. We developed a numerical model based on Langevin simulations of vesicle motion towards the cell membrane and on the statistical analysis of vesicle arrival times. We also performed amperometric experiments in bovine-adrenal Chromaffin cells under Ba2+ stimulation to capture neurotransmitter releases during sustained exocytosis. In the sustained phase, each amperometric peak can be related to a single release from a new vesicle arriving at the active site. The amperometric signal can then be mapped into a spike-series of release events. We normalized the spike-series resulting from the current peaks using a time-rescaling transformation, thus making signals coming from different cells comparable. We discuss why the obtained spike-series may contain information about the motion of all vesicles leading to release of catecholamines. We show that the release statistics in our experiments considerably deviate from Poisson processes. Moreover, the interspike-time probability is reasonably well described by two-parameter gamma distributions. In order to interpret this result we computed the vesicles' arrival statistics from our Langevin simulations. As expected, assuming purely diffusive vesicle motion we obtain Poisson statistics. However, if we assume that all vesicles are guided toward the membrane by an attractive harmonic potential, simulations also lead to gamma distributions of the interspike-time probability, in remarkably good agreement with experiment. We also show that including the fusion-time statistics in our model does not produce any significant changes on the results. These findings indicate that the motion of the whole ensemble of vesicles towards the membrane is directed and reflected in the amperometric signals. Our results confirm the conclusions of previous imaging studies performed on single vesicles that vesicles' motion underneath plasma membranes is not purely random, but biased towards the membrane.

Vesicle Motion during Sustained Exocytosis in Chromaffin Cells: Numerical Model Based on Amperometric Measurements

PubMed Central

Jarukanont, Daungruthai; Bonifas Arredondo, Imelda; Femat, Ricardo; Garcia, Martin E.

2015-01-01

Chromaffin cells release catecholamines by exocytosis, a process that includes vesicle docking, priming and fusion. Although all these steps have been intensively studied, some aspects of their mechanisms, particularly those regarding vesicle transport to the active sites situated at the membrane, are still unclear. In this work, we show that it is possible to extract information on vesicle motion in Chromaffin cells from the combination of Langevin simulations and amperometric measurements. We developed a numerical model based on Langevin simulations of vesicle motion towards the cell membrane and on the statistical analysis of vesicle arrival times. We also performed amperometric experiments in bovine-adrenal Chromaffin cells under Ba2+ stimulation to capture neurotransmitter releases during sustained exocytosis. In the sustained phase, each amperometric peak can be related to a single release from a new vesicle arriving at the active site. The amperometric signal can then be mapped into a spike-series of release events. We normalized the spike-series resulting from the current peaks using a time-rescaling transformation, thus making signals coming from different cells comparable. We discuss why the obtained spike-series may contain information about the motion of all vesicles leading to release of catecholamines. We show that the release statistics in our experiments considerably deviate from Poisson processes. Moreover, the interspike-time probability is reasonably well described by two-parameter gamma distributions. In order to interpret this result we computed the vesicles’ arrival statistics from our Langevin simulations. As expected, assuming purely diffusive vesicle motion we obtain Poisson statistics. However, if we assume that all vesicles are guided toward the membrane by an attractive harmonic potential, simulations also lead to gamma distributions of the interspike-time probability, in remarkably good agreement with experiment. We also show that including the fusion-time statistics in our model does not produce any significant changes on the results. These findings indicate that the motion of the whole ensemble of vesicles towards the membrane is directed and reflected in the amperometric signals. Our results confirm the conclusions of previous imaging studies performed on single vesicles that vesicles’ motion underneath plasma membranes is not purely random, but biased towards the membrane. PMID:26675312

Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading

DOE PAGES

Sanborn, Brett; Song, Bo

2018-06-03

Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratiomore » of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.« less

Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanborn, Brett; Song, Bo

Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratiomore » of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.« less

Selecting a distributional assumption for modelling relative densities of benthic macroinvertebrates

USGS Publications Warehouse

Gray, B.R.

2005-01-01

The selection of a distributional assumption suitable for modelling macroinvertebrate density data is typically challenging. Macroinvertebrate data often exhibit substantially larger variances than expected under a standard count assumption, that of the Poisson distribution. Such overdispersion may derive from multiple sources, including heterogeneity of habitat (historically and spatially), differing life histories for organisms collected within a single collection in space and time, and autocorrelation. Taken to extreme, heterogeneity of habitat may be argued to explain the frequent large proportions of zero observations in macroinvertebrate data. Sampling locations may consist of habitats defined qualitatively as either suitable or unsuitable. The former category may yield random or stochastic zeroes and the latter structural zeroes. Heterogeneity among counts may be accommodated by treating the count mean itself as a random variable, while extra zeroes may be accommodated using zero-modified count assumptions, including zero-inflated and two-stage (or hurdle) approaches. These and linear assumptions (following log- and square root-transformations) were evaluated using 9 years of mayfly density data from a 52 km, ninth-order reach of the Upper Mississippi River (n = 959). The data exhibited substantial overdispersion relative to that expected under a Poisson assumption (i.e. variance:mean ratio = 23 ??? 1), and 43% of the sampling locations yielded zero mayflies. Based on the Akaike Information Criterion (AIC), count models were improved most by treating the count mean as a random variable (via a Poisson-gamma distributional assumption) and secondarily by zero modification (i.e. improvements in AIC values = 9184 units and 47-48 units, respectively). Zeroes were underestimated by the Poisson, log-transform and square root-transform models, slightly by the standard negative binomial model but not by the zero-modified models (61%, 24%, 32%, 7%, and 0%, respectively). However, the zero-modified Poisson models underestimated small counts (1 ??? y ??? 4) and overestimated intermediate counts (7 ??? y ??? 23). Counts greater than zero were estimated well by zero-modified negative binomial models, while counts greater than one were also estimated well by the standard negative binomial model. Based on AIC and percent zero estimation criteria, the two-stage and zero-inflated models performed similarly. The above inferences were largely confirmed when the models were used to predict values from a separate, evaluation data set (n = 110). An exception was that, using the evaluation data set, the standard negative binomial model appeared superior to its zero-modified counterparts using the AIC (but not percent zero criteria). This and other evidence suggest that a negative binomial distributional assumption should be routinely considered when modelling benthic macroinvertebrate data from low flow environments. Whether negative binomial models should themselves be routinely examined for extra zeroes requires, from a statistical perspective, more investigation. However, this question may best be answered by ecological arguments that may be specific to the sampled species and locations. ?? 2004 Elsevier B.V. All rights reserved.

Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks.

PubMed

Conesa, D; Martínez-Beneito, M A; Amorós, R; López-Quílez, A

2015-04-01

Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epidemic phase. To do so, we propose a hidden Markov model in which the transition between both phases is modelled as a function of the epidemic state of the previous week. Different options for modelling the rates are described, including the option of modelling the mean at each phase as autoregressive processes of order 0, 1 or 2. Bayesian inference is carried out to provide the probability of being in an epidemic state at any given moment. The methodology is applied to various influenza data sets. The results indicate that our methods outperform previous approaches in terms of sensitivity, specificity and timeliness. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation

PubMed Central

Cobb, Loren; Krishnamurthy, Ashok; Mandel, Jan; Beezley, Jonathan D.

2014-01-01

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely. PMID:25113590

PET image reconstruction: a robust state space approach.

PubMed

Liu, Huafeng; Tian, Yi; Shi, Pengcheng

2005-01-01

Statistical iterative reconstruction algorithms have shown improved image quality over conventional nonstatistical methods in PET by using accurate system response models and measurement noise models. Strictly speaking, however, PET measurements, pre-corrected for accidental coincidences, are neither Poisson nor Gaussian distributed and thus do not meet basic assumptions of these algorithms. In addition, the difficulty in determining the proper system response model also greatly affects the quality of the reconstructed images. In this paper, we explore the usage of state space principles for the estimation of activity map in tomographic PET imaging. The proposed strategy formulates the organ activity distribution through tracer kinetics models, and the photon-counting measurements through observation equations, thus makes it possible to unify the dynamic reconstruction problem and static reconstruction problem into a general framework. Further, it coherently treats the uncertainties of the statistical model of the imaging system and the noisy nature of measurement data. Since H(infinity) filter seeks minimummaximum-error estimates without any assumptions on the system and data noise statistics, it is particular suited for PET image reconstruction where the statistical properties of measurement data and the system model are very complicated. The performance of the proposed framework is evaluated using Shepp-Logan simulated phantom data and real phantom data with favorable results.

Optimisation of GaN LEDs and the reduction of efficiency droop using active machine learning

DOE PAGES

Rouet-Leduc, Bertrand; Barros, Kipton Marcos; Lookman, Turab; ...

2016-04-26

A fundamental challenge in the design of LEDs is to maximise electro-luminescence efficiency at high current densities. We simulate GaN-based LED structures that delay the onset of efficiency droop by spreading carrier concentrations evenly across the active region. Statistical analysis and machine learning effectively guide the selection of the next LED structure to be examined based upon its expected efficiency as well as model uncertainty. This active learning strategy rapidly constructs a model that predicts Poisson-Schrödinger simulations of devices, and that simultaneously produces structures with higher simulated efficiencies.

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Generalized Linear Models of Home Activity for Automatic Detection of Mild Cognitive Impairment in Older Adults*

PubMed Central

Akl, Ahmad; Snoek, Jasper; Mihailidis, Alex

2015-01-01

With a globally aging population, the burden of care of cognitively impaired older adults is becoming increasingly concerning. Instances of Alzheimer’s disease and other forms of dementia are becoming ever more frequent. Earlier detection of cognitive impairment offers significant benefits, but remains difficult to do in practice. In this paper, we develop statistical models of the behavior of older adults within their homes using sensor data in order to detect the early onset of cognitive decline. Specifically, we use inhomogenous Poisson processes to model the presence of subjects within different rooms throughout the day in the home using unobtrusive sensing technologies. We compare the distributions learned from cognitively intact and impaired subjects using information theoretic tools and observe statistical differences between the two populations which we believe can be used to help detect the onset of cognitive decline. PMID:25570050

Generalized Linear Models of home activity for automatic detection of mild cognitive impairment in older adults.

PubMed

Akl, Ahmad; Snoek, Jasper; Mihailidis, Alex

2014-01-01

With a globally aging population, the burden of care of cognitively impaired older adults is becoming increasingly concerning. Instances of Alzheimer's disease and other forms of dementia are becoming ever more frequent. Earlier detection of cognitive impairment offers significant benefits, but remains difficult to do in practice. In this paper, we develop statistical models of the behavior of older adults within their homes using sensor data in order to detect the early onset of cognitive decline. Specifically, we use inhomogenous Poisson processes to model the presence of subjects within different rooms throughout the day in the home using unobtrusive sensing technologies. We compare the distributions learned from cognitively intact and impaired subjects using information theoretic tools and observe statistical differences between the two populations which we believe can be used to help detect the onset of cognitive decline.

A Classroom Note on the Binomial and Poisson Distributions: Biomedical Examples for Use in Teaching Introductory Statistics

ERIC Educational Resources Information Center

Holland, Bart K.

2006-01-01

A generally-educated individual should have some insight into how decisions are made in the very wide range of fields that employ statistical and probabilistic reasoning. Also, students of introductory probability and statistics are often best motivated by specific applications rather than by theory and mathematical development, because most…

Estimating safety effects of pavement management factors utilizing Bayesian random effect models.

PubMed

Jiang, Ximiao; Huang, Baoshan; Zaretzki, Russell L; Richards, Stephen; Yan, Xuedong

2013-01-01

Previous studies of pavement management factors that relate to the occurrence of traffic-related crashes are rare. Traditional research has mostly employed summary statistics of bidirectional pavement quality measurements in extended longitudinal road segments over a long time period, which may cause a loss of important information and result in biased parameter estimates. The research presented in this article focuses on crash risk of roadways with overall fair to good pavement quality. Real-time and location-specific data were employed to estimate the effects of pavement management factors on the occurrence of crashes. This research is based on the crash data and corresponding pavement quality data for the Tennessee state route highways from 2004 to 2009. The potential temporal and spatial correlations among observations caused by unobserved factors were considered. Overall 6 models were built accounting for no correlation, temporal correlation only, and both the temporal and spatial correlations. These models included Poisson, negative binomial (NB), one random effect Poisson and negative binomial (OREP, ORENB), and two random effect Poisson and negative binomial (TREP, TRENB) models. The Bayesian method was employed to construct these models. The inference is based on the posterior distribution from the Markov chain Monte Carlo (MCMC) simulation. These models were compared using the deviance information criterion. Analysis of the posterior distribution of parameter coefficients indicates that the pavement management factors indexed by Present Serviceability Index (PSI) and Pavement Distress Index (PDI) had significant impacts on the occurrence of crashes, whereas the variable rutting depth was not significant. Among other factors, lane width, median width, type of terrain, and posted speed limit were significant in affecting crash frequency. The findings of this study indicate that a reduction in pavement roughness would reduce the likelihood of traffic-related crashes. Hence, maintaining a low level of pavement roughness is strongly suggested. In addition, the results suggested that the temporal correlation among observations was significant and that the ORENB model outperformed all other models.

A Poisson Log-Normal Model for Constructing Gene Covariation Network Using RNA-seq Data.

PubMed

Choi, Yoonha; Coram, Marc; Peng, Jie; Tang, Hua

2017-07-01

Constructing expression networks using transcriptomic data is an effective approach for studying gene regulation. A popular approach for constructing such a network is based on the Gaussian graphical model (GGM), in which an edge between a pair of genes indicates that the expression levels of these two genes are conditionally dependent, given the expression levels of all other genes. However, GGMs are not appropriate for non-Gaussian data, such as those generated in RNA-seq experiments. We propose a novel statistical framework that maximizes a penalized likelihood, in which the observed count data follow a Poisson log-normal distribution. To overcome the computational challenges, we use Laplace's method to approximate the likelihood and its gradients, and apply the alternating directions method of multipliers to find the penalized maximum likelihood estimates. The proposed method is evaluated and compared with GGMs using both simulated and real RNA-seq data. The proposed method shows improved performance in detecting edges that represent covarying pairs of genes, particularly for edges connecting low-abundant genes and edges around regulatory hubs.

Approximations to camera sensor noise

NASA Astrophysics Data System (ADS)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

What are hierarchical models and how do we analyze them?

USGS Publications Warehouse

Royle, Andy

2016-01-01

In this chapter we provide a basic definition of hierarchical models and introduce the two canonical hierarchical models in this book: site occupancy and N-mixture models. The former is a hierarchical extension of logistic regression and the latter is a hierarchical extension of Poisson regression. We introduce basic concepts of probability modeling and statistical inference including likelihood and Bayesian perspectives. We go through the mechanics of maximizing the likelihood and characterizing the posterior distribution by Markov chain Monte Carlo (MCMC) methods. We give a general perspective on topics such as model selection and assessment of model fit, although we demonstrate these topics in practice in later chapters (especially Chapters 5, 6, 7, and 10 Chapter 5 Chapter 6 Chapter 7 Chapter 10)

Statistical Analyses of Raw Material Data for MTM45-1/CF7442A-36% RW: CMH Cure Cycle

NASA Technical Reports Server (NTRS)

Coroneos, Rula; Pai, Shantaram, S.; Murthy, Pappu

2013-01-01

This report describes statistical characterization of physical properties of the composite material system MTM45-1/CF7442A, which has been tested and is currently being considered for use on spacecraft structures. This composite system is made of 6K plain weave graphite fibers in a highly toughened resin system. This report summarizes the distribution types and statistical details of the tests and the conditions for the experimental data generated. These distributions will be used in multivariate regression analyses to help determine material and design allowables for similar material systems and to establish a procedure for other material systems. Additionally, these distributions will be used in future probabilistic analyses of spacecraft structures. The specific properties that are characterized are the ultimate strength, modulus, and Poisson??s ratio by using a commercially available statistical package. Results are displayed using graphical and semigraphical methods and are included in the accompanying appendixes.

Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

NASA Astrophysics Data System (ADS)

Wang, Fengwen

2018-05-01

This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson's ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson's ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson's ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson's ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson's ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson's ratios, material architectures for any Poisson's ratio in the interval of ν ∈ [ - 0.78 , 0.00 ] are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson's ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson's ratio are achievable.

Statistical Interior Tomography

PubMed Central

Xu, Qiong; Wang, Ge; Sieren, Jered; Hoffman, Eric A.

2011-01-01

This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data. PMID:21233044

SGR-like behaviour of the repeating FRB 121102

NASA Astrophysics Data System (ADS)

Wang, F. Y.; Yu, H.

2017-03-01

Fast radio bursts (FRBs) are millisecond-duration radio signals occurring at cosmological distances. However the physical model of FRBs is mystery, many models have been proposed. Here we study the frequency distributions of peak flux, fluence, duration and waiting time for the repeating FRB 121102. The cumulative distributions of peak flux, fluence and duration show power-law forms. The waiting time distribution also shows power-law distribution, and is consistent with a non-stationary Poisson process. These distributions are similar as those of soft gamma repeaters (SGRs). We also use the statistical results to test the proposed models for FRBs. These distributions are consistent with the predictions from avalanche models of slowly driven nonlinear dissipative systems.

A space-time scan statistic for detecting emerging outbreaks.

PubMed

Tango, Toshiro; Takahashi, Kunihiko; Kohriyama, Kazuaki

2011-03-01

As a major analytical method for outbreak detection, Kulldorff's space-time scan statistic (2001, Journal of the Royal Statistical Society, Series A 164, 61-72) has been implemented in many syndromic surveillance systems. Since, however, it is based on circular windows in space, it has difficulty correctly detecting actual noncircular clusters. Takahashi et al. (2008, International Journal of Health Geographics 7, 14) proposed a flexible space-time scan statistic with the capability of detecting noncircular areas. It seems to us, however, that the detection of the most likely cluster defined in these space-time scan statistics is not the same as the detection of localized emerging disease outbreaks because the former compares the observed number of cases with the conditional expected number of cases. In this article, we propose a new space-time scan statistic which compares the observed number of cases with the unconditional expected number of cases, takes a time-to-time variation of Poisson mean into account, and implements an outbreak model to capture localized emerging disease outbreaks more timely and correctly. The proposed models are illustrated with data from weekly surveillance of the number of absentees in primary schools in Kitakyushu-shi, Japan, 2006. © 2010, The International Biometric Society.

DETECTING UNSPECIFIED STRUCTURE IN LOW-COUNT IMAGES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stein, Nathan M.; Dyk, David A. van; Kashyap, Vinay L.

Unexpected structure in images of astronomical sources often presents itself upon visual inspection of the image, but such apparent structure may either correspond to true features in the source or be due to noise in the data. This paper presents a method for testing whether inferred structure in an image with Poisson noise represents a significant departure from a baseline (null) model of the image. To infer image structure, we conduct a Bayesian analysis of a full model that uses a multiscale component to allow flexible departures from the posited null model. As a test statistic, we use a tailmore » probability of the posterior distribution under the full model. This choice of test statistic allows us to estimate a computationally efficient upper bound on a p-value that enables us to draw strong conclusions even when there are limited computational resources that can be devoted to simulations under the null model. We demonstrate the statistical performance of our method on simulated images. Applying our method to an X-ray image of the quasar 0730+257, we find significant evidence against the null model of a single point source and uniform background, lending support to the claim of an X-ray jet.« less

WAITING TIME DISTRIBUTION OF SOLAR ENERGETIC PARTICLE EVENTS MODELED WITH A NON-STATIONARY POISSON PROCESS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, C.; Su, W.; Fang, C.

2014-09-10

We present a study of the waiting time distributions (WTDs) of solar energetic particle (SEP) events observed with the spacecraft WIND and GOES. The WTDs of both solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail of ∼Δt {sup –γ}. The SEEs display a broken power-law WTD. The power-law index is γ{sub 1} = 0.99 for the short waiting times (<70 hr) and γ{sub 2} = 1.92 for large waiting times (>100 hr). The break of the WTD of SEEs is probably due to the modulation of the corotating interaction regions. The power-law index, γ ∼more » 1.82, is derived for the WTD of the SPEs which is consistent with the WTD of type II radio bursts, indicating a close relationship between the shock wave and the production of energetic protons. The WTDs of SEP events can be modeled with a non-stationary Poisson process, which was proposed to understand the waiting time statistics of solar flares. We generalize the method and find that, if the SEP event rate λ = 1/Δt varies as the time distribution of event rate f(λ) = Aλ{sup –α}exp (– βλ), the time-dependent Poisson distribution can produce a power-law tail WTD of ∼Δt {sup α} {sup –3}, where 0 ≤ α < 2.« less

Transition from Poissonian to Gaussian-orthogonal-ensemble level statistics in a modified Artin's billiard

NASA Astrophysics Data System (ADS)

Csordás, A.; Graham, R.; Szépfalusy, P.; Vattay, G.

1994-01-01

One wall of an Artin's billiard on the Poincaré half-plane is replaced by a one-parameter (cp) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuous and gradual transition from the Poisson-like to Gaussian-orthogonal-ensemble (GOE) level statistics due to the small perturbations breaking the symmetry responsible for the ``arithmetic chaos'' at cp=1 is studied. Another GOE-->Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in both cases. The study supports the existence of a scaling region around cp=1. A finite-size scaling relation for the Brody parameter as a function of 1-cp and the number of levels considered can be established.

Conditional modeling of antibody titers using a zero-inflated poisson random effects model: application to Fabrazyme.

PubMed

Bonate, Peter L; Sung, Crystal; Welch, Karen; Richards, Susan

2009-10-01

Patients that are exposed to biotechnology-derived therapeutics often develop antibodies to the therapeutic, the magnitude of which is assessed by measuring antibody titers. A statistical approach for analyzing antibody titer data conditional on seroconversion is presented. The proposed method is to first transform the antibody titer data based on a geometric series using a common ratio of 2 and a scale factor of 50 and then analyze the exponent using a zero-inflated or hurdle model assuming a Poisson or negative binomial distribution with random effects to account for patient heterogeneity. Patient specific covariates can be used to model the probability of developing an antibody response, i.e., seroconversion, as well as the magnitude of the antibody titer itself. The method was illustrated using antibody titer data from 87 male seroconverted Fabry patients receiving Fabrazyme. Titers from five clinical trials were collected over 276 weeks of therapy with anti-Fabrazyme IgG titers ranging from 100 to 409,600 after exclusion of seronegative patients. The best model to explain seroconversion was a zero-inflated Poisson (ZIP) model where cumulative dose (under a constant dose regimen of dosing every 2 weeks) influenced the probability of seroconversion. There was an 80% chance of seroconversion when the cumulative dose reached 210 mg (90% confidence interval: 194-226 mg). No difference in antibody titers was noted between Japanese or Western patients. Once seroconverted, antibody titers did not remain constant but decreased in an exponential manner from an initial magnitude to a new lower steady-state value. The expected titer after the new steady-state titer had been achieved was 870 (90% CI: 630-1109). The half-life to the new steady-state value after seroconversion was 44 weeks (90% CI: 17-70 weeks). Time to seroconversion did not appear to be correlated with titer at the time of seroconversion. The method can be adequately used to model antibody titer data.

Modification of Poisson Distribution in Radioactive Particle Counting.

ERIC Educational Resources Information Center

Drotter, Michael T.

This paper focuses on radioactive practicle counting statistics in laboratory and field applications, intended to aid the Health Physics technician's understanding of the effect of indeterminant errors on radioactive particle counting. It indicates that although the statistical analysis of radioactive disintegration is best described by a Poisson…

Double asymptotics for the chi-square statistic.

PubMed

Rempała, Grzegorz A; Wesołowski, Jacek

2016-12-01

Consider distributional limit of the Pearson chi-square statistic when the number of classes m n increases with the sample size n and [Formula: see text]. Under mild moment conditions, the limit is Gaussian for λ = ∞, Poisson for finite λ > 0, and degenerate for λ = 0.

Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer.

PubMed

Lim, Jongil; Whitcomb, John; Boyd, James; Varghese, Julian

2007-01-01

A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.

Applying the Anderson-Darling test to suicide clusters: evidence of contagion at U. S. universities?

PubMed

MacKenzie, Donald W

2013-01-01

Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Suicide dates were collected for MIT and Cornell for 1990-2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

A systematic review of models to predict recruitment to multicentre clinical trials.

PubMed

Barnard, Katharine D; Dent, Louise; Cook, Andrew

2010-07-06

Less than one third of publicly funded trials managed to recruit according to their original plan often resulting in request for additional funding and/or time extensions. The aim was to identify models which might be useful to a major public funder of randomised controlled trials when estimating likely time requirements for recruiting trial participants. The requirements of a useful model were identified as usability, based on experience, able to reflect time trends, accounting for centre recruitment and contribution to a commissioning decision. A systematic review of English language articles using MEDLINE and EMBASE. Search terms included: randomised controlled trial, patient, accrual, predict, enroll, models, statistical; Bayes Theorem; Decision Theory; Monte Carlo Method and Poisson. Only studies discussing prediction of recruitment to trials using a modelling approach were included. Information was extracted from articles by one author, and checked by a second, using a pre-defined form. Out of 326 identified abstracts, only 8 met all the inclusion criteria. Of these 8 studies examined, there are five major classes of model discussed: the unconditional model, the conditional model, the Poisson model, Bayesian models and Monte Carlo simulation of Markov models. None of these meet all the pre-identified needs of the funder. To meet the needs of a number of research programmes, a new model is required as a matter of importance. Any model chosen should be validated against both retrospective and prospective data, to ensure the predictions it gives are superior to those currently used.

Relaxed Poisson cure rate models.

PubMed

Rodrigues, Josemar; Cordeiro, Gauss M; Cancho, Vicente G; Balakrishnan, N

2016-03-01

The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Free Fermions and the Classical Compact Groups

NASA Astrophysics Data System (ADS)

Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil

2018-06-01

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

Full Bayes Poisson gamma, Poisson lognormal, and zero inflated random effects models: Comparing the precision of crash frequency estimates.

PubMed

Aguero-Valverde, Jonathan

2013-01-01

In recent years, complex statistical modeling approaches have being proposed to handle the unobserved heterogeneity and the excess of zeros frequently found in crash data, including random effects and zero inflated models. This research compares random effects, zero inflated, and zero inflated random effects models using a full Bayes hierarchical approach. The models are compared not just in terms of goodness-of-fit measures but also in terms of precision of posterior crash frequency estimates since the precision of these estimates is vital for ranking of sites for engineering improvement. Fixed-over-time random effects models are also compared to independent-over-time random effects models. For the crash dataset being analyzed, it was found that once the random effects are included in the zero inflated models, the probability of being in the zero state is drastically reduced, and the zero inflated models degenerate to their non zero inflated counterparts. Also by fixing the random effects over time the fit of the models and the precision of the crash frequency estimates are significantly increased. It was found that the rankings of the fixed-over-time random effects models are very consistent among them. In addition, the results show that by fixing the random effects over time, the standard errors of the crash frequency estimates are significantly reduced for the majority of the segments on the top of the ranking. Copyright © 2012 Elsevier Ltd. All rights reserved.

Evaluating the double Poisson generalized linear model.

PubMed

Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique

2013-10-01

The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. Copyright © 2013 Elsevier Ltd. All rights reserved.

Poisson's spot and Gouy phase

NASA Astrophysics Data System (ADS)

da Paz, I. G.; Soldati, Rodolfo; Cabral, L. A.; de Oliveira, J. G. G.; Sampaio, Marcos

2016-12-01

Recently there have been experimental results on Poisson spot matter-wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for Poisson's spot with matter waves based on the Babinet principle, in which we use the results for free propagation and single-slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter-wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium (D2) molecules.

Models for patients' recruitment in clinical trials and sensitivity analysis.

PubMed

Mijoule, Guillaume; Savy, Stéphanie; Savy, Nicolas

2012-07-20

Taking a decision on the feasibility and estimating the duration of patients' recruitment in a clinical trial are very important but very hard questions to answer, mainly because of the huge variability of the system. The more elaborated works on this topic are those of Anisimov and co-authors, where they investigate modelling of the enrolment period by using Gamma-Poisson processes, which allows to develop statistical tools that can help the manager of the clinical trial to answer these questions and thus help him to plan the trial. The main idea is to consider an ongoing study at an intermediate time, denoted t(1). Data collected on [0,t(1)] allow to calibrate the parameters of the model, which are then used to make predictions on what will happen after t(1). This method allows us to estimate the probability of ending the trial on time and give possible corrective actions to the trial manager especially regarding how many centres have to be open to finish on time. In this paper, we investigate a Pareto-Poisson model, which we compare with the Gamma-Poisson one. We will discuss the accuracy of the estimation of the parameters and compare the models on a set of real case data. We make the comparison on various criteria : the expected recruitment duration, the quality of fitting to the data and its sensitivity to parameter errors. We discuss the influence of the centres opening dates on the estimation of the duration. This is a very important question to deal with in the setting of our data set. In fact, these dates are not known. For this discussion, we consider a uniformly distributed approach. Finally, we study the sensitivity of the expected duration of the trial with respect to the parameters of the model : we calculate to what extent an error on the estimation of the parameters generates an error in the prediction of the duration.

Simple and Hierarchical Models for Stochastic Test Misgrading.

ERIC Educational Resources Information Center

Wang, Jianjun

1993-01-01

Test misgrading is treated as a stochastic process. The expected number of misgradings, inter-occurrence time of misgradings, and waiting time for the "n"th misgrading are discussed based on a simple Poisson model and a hierarchical Beta-Poisson model. Examples of model construction are given. (SLD)

Occurrence analysis of daily rainfalls through non-homogeneous Poissonian processes

NASA Astrophysics Data System (ADS)

Sirangelo, B.; Ferrari, E.; de Luca, D. L.

2011-06-01

A stochastic model based on a non-homogeneous Poisson process, characterised by a time-dependent intensity of rainfall occurrence, is employed to explain seasonal effects of daily rainfalls exceeding prefixed threshold values. The data modelling has been performed with a partition of observed daily rainfall data into a calibration period for parameter estimation and a validation period for checking on occurrence process changes. The model has been applied to a set of rain gauges located in different geographical areas of Southern Italy. The results show a good fit for time-varying intensity of rainfall occurrence process by 2-harmonic Fourier law and no statistically significant evidence of changes in the validation period for different threshold values.

A stochastic automata network for earthquake simulation and hazard estimation

NASA Astrophysics Data System (ADS)

Belubekian, Maya Ernest

1998-11-01

This research develops a model for simulation of earthquakes on seismic faults with available earthquake catalog data. The model allows estimation of the seismic hazard at a site of interest and assessment of the potential damage and loss in a region. There are two approaches for studying the earthquakes: mechanistic and stochastic. In the mechanistic approach, seismic processes, such as changes in stress or slip on faults, are studied in detail. In the stochastic approach, earthquake occurrences are simulated as realizations of a certain stochastic process. In this dissertation, a stochastic earthquake occurrence model is developed that uses the results from dislocation theory for the estimation of slip released in earthquakes. The slip accumulation and release laws and the event scheduling mechanism adopted in the model result in a memoryless Poisson process for the small and moderate events and in a time- and space-dependent process for large events. The minimum and maximum of the hazard are estimated by the model when the initial conditions along the faults correspond to a situation right after a largest event and after a long seismic gap, respectively. These estimates are compared with the ones obtained from a Poisson model. The Poisson model overestimates the hazard after the maximum event and underestimates it in the period of a long seismic quiescence. The earthquake occurrence model is formulated as a stochastic automata network. Each fault is divided into cells, or automata, that interact by means of information exchange. The model uses a statistical method called bootstrap for the evaluation of the confidence bounds on its results. The parameters of the model are adjusted to the target magnitude patterns obtained from the catalog. A case study is presented for the city of Palo Alto, where the hazard is controlled by the San Andreas, Hayward and Calaveras faults. The results of the model are used to evaluate the damage and loss distribution in Palo Alto. The sensitivity analysis of the model results to the variation in basic parameters shows that the maximum magnitude has the most significant impact on the hazard, especially for long forecast periods.

Identification d’une Classe de Processus de Poisson Filtres (Identification of a Class of Filtered Poisson Processes).

DTIC Science & Technology

1983-05-20

Poisson processes is introduced: the amplitude has a law which is spherically invariant and the filter is real, linear and causal. It is shown how such a model can be identified from experimental data. (Author)

A brief history of numbers and statistics with cytometric applications.

PubMed

Watson, J V

2001-02-15

A brief history of numbers and statistics traces the development of numbers from prehistory to completion of our current system of numeration with the introduction of the decimal fraction by Viete, Stevin, Burgi, and Galileo at the turn of the 16th century. This was followed by the development of what we now know as probability theory by Pascal, Fermat, and Huygens in the mid-17th century which arose in connection with questions in gambling with dice and can be regarded as the origin of statistics. The three main probability distributions on which statistics depend were introduced and/or formalized between the mid-17th and early 19th centuries: the binomial distribution by Pascal; the normal distribution by de Moivre, Gauss, and Laplace, and the Poisson distribution by Poisson. The formal discipline of statistics commenced with the works of Pearson, Yule, and Gosset at the turn of the 19th century when the first statistical tests were introduced. Elementary descriptions of the statistical tests most likely to be used in conjunction with cytometric data are given and it is shown how these can be applied to the analysis of difficult immunofluorescence distributions when there is overlap between the labeled and unlabeled cell populations. Copyright 2001 Wiley-Liss, Inc.

Occurrence analysis of daily rainfalls by using non-homogeneous Poissonian processes

NASA Astrophysics Data System (ADS)

Sirangelo, B.; Ferrari, E.; de Luca, D. L.

2009-09-01

In recent years several temporally homogeneous stochastic models have been applied to describe the rainfall process. In particular stochastic analysis of daily rainfall time series may contribute to explain the statistic features of the temporal variability related to the phenomenon. Due to the evident periodicity of the physical process, these models have to be used only to short temporal intervals in which occurrences and intensities of rainfalls can be considered reliably homogeneous. To this aim, occurrences of daily rainfalls can be considered as a stationary stochastic process in monthly periods. In this context point process models are widely used for at-site analysis of daily rainfall occurrence; they are continuous time series models, and are able to explain intermittent feature of rainfalls and simulate interstorm periods. With a different approach, periodic features of daily rainfalls can be interpreted by using a temporally non-homogeneous stochastic model characterized by parameters expressed as continuous functions in the time. In this case, great attention has to be paid to the parsimony of the models, as regards the number of parameters and the bias introduced into the generation of synthetic series, and to the influence of threshold values in extracting peak storm database from recorded daily rainfall heights. In this work, a stochastic model based on a non-homogeneous Poisson process, characterized by a time-dependent intensity of rainfall occurrence, is employed to explain seasonal effects of daily rainfalls exceeding prefixed threshold values. In particular, variation of rainfall occurrence intensity ? (t) is modelled by using Fourier series analysis, in which the non-homogeneous process is transformed into a homogeneous and unit one through a proper transformation of time domain, and the choice of the minimum number of harmonics is evaluated applying available statistical tests. The procedure is applied to a dataset of rain gauges located in different geographical zones of Mediterranean area. Time series have been selected on the basis of the availability of at least 50 years in the time period 1921-1985, chosen as calibration period, and of all the years of observation in the subsequent validation period 1986-2005, whose daily rainfall occurrence process variability is under hypothesis. Firstly, for each time series and for each fixed threshold value, parameters estimation of the non-homogeneous Poisson model is carried out, referred to calibration period. As second step, in order to test the hypothesis that daily rainfall occurrence process preserves the same behaviour in more recent time periods, the intensity distribution evaluated for calibration period is also adopted for the validation period. Starting from this and using a Monte Carlo approach, 1000 synthetic generations of daily rainfall occurrences, of length equal to validation period, have been carried out, and for each simulation sample ?(t) has been evaluated. This procedure is adopted because of the complexity of determining analytical statistical confidence limits referred to the sample intensity ?(t). Finally, sample intensity, theoretical function of the calibration period and 95% statistical band, evaluated by Monte Carlo approach, are matching, together with considering, for each threshold value, the mean square error (MSE) between the theoretical ?(t) and the sample one of recorded data, and his correspondent 95% one tail statistical band, estimated from the MSE values between the sample ?(t) of each synthetic series and the theoretical one. The results obtained may be very useful in the context of the identification and calibration of stochastic rainfall models based on historical precipitation data. Further applications of the non-homogeneous Poisson model will concern the joint analyses of the storm occurrence process with the rainfall height marks, interpreted by using a temporally homogeneous model in proper sub-year intervals.

Effect of Poisson's loss factor of rubbery material on underwater sound absorption of anechoic coatings

NASA Astrophysics Data System (ADS)

Zhong, Jie; Zhao, Honggang; Yang, Haibin; Yin, Jianfei; Wen, Jihong

2018-06-01

Rubbery coatings embedded with air cavities are commonly used on underwater structures to reduce reflection of incoming sound waves. In this paper, the relationships between Poisson's and modulus loss factors of rubbery materials are theoretically derived, the different effects of the tiny Poisson's loss factor on characterizing the loss factors of shear and longitudinal moduli are revealed. Given complex Young's modulus and dynamic Poisson's ratio, it is found that the shear loss factor has almost invisible variation with the Poisson's loss factor and is very close to the loss factor of Young's modulus, while the longitudinal loss factor almost linearly decreases with the increase of Poisson's loss factor. Then, a finite element (FE) model is used to investigate the effect of the tiny Poisson's loss factor, which is generally neglected in some FE models, on the underwater sound absorption of rubbery coatings. Results show that the tiny Poisson's loss factor has a significant effect on the sound absorption of homogeneous coatings within the concerned frequency range, while it has both frequency- and structure-dependent influence on the sound absorption of inhomogeneous coatings with embedded air cavities. Given the material parameters and cavity dimensions, more obvious effect can be observed for the rubbery coating with a larger lattice constant and/or a thicker cover layer.

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

M≥7 Earthquake rupture forecast and time-dependent probability for the Sea of Marmara region, Turkey

USGS Publications Warehouse

Murru, Maura; Akinci, Aybige; Falcone, Guiseppe; Pucci, Stefano; Console, Rodolfo; Parsons, Thomas E.

2016-01-01

We forecast time-independent and time-dependent earthquake ruptures in the Marmara region of Turkey for the next 30 years using a new fault-segmentation model. We also augment time-dependent Brownian Passage Time (BPT) probability with static Coulomb stress changes (ΔCFF) from interacting faults. We calculate Mw > 6.5 probability from 26 individual fault sources in the Marmara region. We also consider a multisegment rupture model that allows higher-magnitude ruptures over some segments of the Northern branch of the North Anatolian Fault Zone (NNAF) beneath the Marmara Sea. A total of 10 different Mw=7.0 to Mw=8.0 multisegment ruptures are combined with the other regional faults at rates that balance the overall moment accumulation. We use Gaussian random distributions to treat parameter uncertainties (e.g., aperiodicity, maximum expected magnitude, slip rate, and consequently mean recurrence time) of the statistical distributions associated with each fault source. We then estimate uncertainties of the 30-year probability values for the next characteristic event obtained from three different models (Poisson, BPT, and BPT+ΔCFF) using a Monte Carlo procedure. The Gerede fault segment located at the eastern end of the Marmara region shows the highest 30-yr probability, with a Poisson value of 29%, and a time-dependent interaction probability of 48%. We find an aggregated 30-yr Poisson probability of M >7.3 earthquakes at Istanbul of 35%, which increases to 47% if time dependence and stress transfer are considered. We calculate a 2-fold probability gain (ratio time-dependent to time-independent) on the southern strands of the North Anatolian Fault Zone.

77 FR 13691 - Qualification of Drivers; Exemption Applications; Vision

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-07

..., ocular hypertension, retinal detachment, cataracts and corneal scaring. In most cases, their eye... Application of Multiple Regression Analysis of a Poisson Process,'' Journal of American Statistical...

Validation of the Poisson Stochastic Radiative Transfer Model

NASA Technical Reports Server (NTRS)

Zhuravleva, Tatiana; Marshak, Alexander

2004-01-01

A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.

Probabilistic structural analysis methods for improving Space Shuttle engine reliability

NASA Technical Reports Server (NTRS)

Boyce, L.

1989-01-01

Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.

Framework for adaptive multiscale analysis of nonhomogeneous point processes.

PubMed

Helgason, Hannes; Bartroff, Jay; Abry, Patrice

2011-01-01

We develop the methodology for hypothesis testing and model selection in nonhomogeneous Poisson processes, with an eye toward the application of modeling and variability detection in heart beat data. Modeling the process' non-constant rate function using templates of simple basis functions, we develop the generalized likelihood ratio statistic for a given template and a multiple testing scheme to model-select from a family of templates. A dynamic programming algorithm inspired by network flows is used to compute the maximum likelihood template in a multiscale manner. In a numerical example, the proposed procedure is nearly as powerful as the super-optimal procedures that know the true template size and true partition, respectively. Extensions to general history-dependent point processes is discussed.

Analytic drain current model for III-V cylindrical nanowire transistors

NASA Astrophysics Data System (ADS)

Marin, E. G.; Ruiz, F. G.; Schmidt, V.; Godoy, A.; Riel, H.; Gámiz, F.

2015-07-01

An analytical model is proposed to determine the drain current of III-V cylindrical nanowires (NWs). The model uses the gradual channel approximation and takes into account the complete analytical solution of the Poisson and Schrödinger equations for the Γ-valley and for an arbitrary number of subbands. Fermi-Dirac statistics are considered to describe the 1D electron gas in the NWs, being the resulting recursive Fermi-Dirac integral of order -1/2 successfully integrated under reasonable assumptions. The model has been validated against numerical simulations showing excellent agreement for different semiconductor materials, diameters up to 40 nm, gate overdrive biases up to 0.7 V, and densities of interface states up to 1013eV-1cm-2 .

SGR-like behaviour of the repeating FRB 121102

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, F.Y.; Yu, H., E-mail: fayinwang@nju.edu.cn, E-mail: yuhai@smail.nju.edu.cn

2017-03-01

Fast radio bursts (FRBs) are millisecond-duration radio signals occurring at cosmological distances. However the physical model of FRBs is mystery, many models have been proposed. Here we study the frequency distributions of peak flux, fluence, duration and waiting time for the repeating FRB 121102. The cumulative distributions of peak flux, fluence and duration show power-law forms. The waiting time distribution also shows power-law distribution, and is consistent with a non-stationary Poisson process. These distributions are similar as those of soft gamma repeaters (SGRs). We also use the statistical results to test the proposed models for FRBs. These distributions are consistentmore » with the predictions from avalanche models of slowly driven nonlinear dissipative systems.« less

Diversity of Poissonian populations.

PubMed

Eliazar, Iddo I; Sokolov, Igor M

2010-01-01

Populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering. The statistical modeling of such populations leads naturally to Poissonian populations-Poisson processes on the real line with a distinguished maximal point. Poissonian populations are infinite objects underlying key issues in statistical physics, probability theory, and random fractals. Due to their infiniteness, measuring the diversity of Poissonian populations depends on the lower-bound cut-off applied. This research characterizes the classes of Poissonian populations whose diversities are invariant with respect to the cut-off level applied and establishes an elemental connection between these classes and extreme-value theory. The measures of diversity considered are variance and dispersion, Simpson's index and inverse participation ratio, Shannon's entropy and Rényi's entropy, and Gini's index.

Statistical short-term earthquake prediction.

PubMed

Kagan, Y Y; Knopoff, L

1987-06-19

A statistical procedure, derived from a theoretical model of fracture growth, is used to identify a foreshock sequence while it is in progress. As a predictor, the procedure reduces the average uncertainty in the rate of occurrence for a future strong earthquake by a factor of more than 1000 when compared with the Poisson rate of occurrence. About one-third of all main shocks with local magnitude greater than or equal to 4.0 in central California can be predicted in this way, starting from a 7-year database that has a lower magnitude cut off of 1.5. The time scale of such predictions is of the order of a few hours to a few days for foreshocks in the magnitude range from 2.0 to 5.0.

Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment

PubMed Central

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso

2016-01-01

ABSTRACT Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. IMPORTANCE We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation. PMID:27940547

Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2017-02-15

Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation. Copyright © 2017 Koyama et al.

The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability

PubMed Central

Reich, Steven

2014-01-01

Neuronal variability plays a central role in neural coding and impacts the dynamics of neuronal networks. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in response to presynaptic action potentials and are recovered stochastically in time. The dynamics of this process of vesicle release and recovery interacts with variability in the arrival times of presynaptic spikes to shape the variability of the postsynaptic response. We use continuous time Markov chain methods to analyze a model of short term synaptic depression with stochastic vesicle dynamics coupled with three different models of presynaptic spiking: one model in which the timing of presynaptic action potentials are modeled as a Poisson process, one in which action potentials occur more regularly than a Poisson process (sub-Poisson) and one in which action potentials occur more irregularly (super-Poisson). We use this analysis to investigate how variability in a presynaptic spike train is transformed by short term depression and stochastic vesicle dynamics to determine the variability of the postsynaptic response. We find that sub-Poisson presynaptic spiking increases the average rate at which vesicles are released, that the number of vesicles released over a time window is more variable for smaller time windows than larger time windows and that fast presynaptic spiking gives rise to Poisson-like variability of the postsynaptic response even when presynaptic spike times are non-Poisson. Our results complement and extend previously reported theoretical results and provide possible explanations for some trends observed in recorded data. PMID:23354693

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Assessment of Poisson, probit and linear models for genetic analysis of presence and number of black spots in Corriedale sheep.

PubMed

Peñagaricano, F; Urioste, J I; Naya, H; de los Campos, G; Gianola, D

2011-04-01

Black skin spots are associated with pigmented fibres in wool, an important quality fault. Our objective was to assess alternative models for genetic analysis of presence (BINBS) and number (NUMBS) of black spots in Corriedale sheep. During 2002-08, 5624 records from 2839 animals in two flocks, aged 1 through 6 years, were taken at shearing. Four models were considered: linear and probit for BINBS and linear and Poisson for NUMBS. All models included flock-year and age as fixed effects and animal and permanent environmental as random effects. Models were fitted to the whole data set and were also compared based on their predictive ability in cross-validation. Estimates of heritability ranged from 0.154 to 0.230 for BINBS and 0.269 to 0.474 for NUMBS. For BINBS, the probit model fitted slightly better to the data than the linear model. Predictions of random effects from these models were highly correlated, and both models exhibited similar predictive ability. For NUMBS, the Poisson model, with a residual term to account for overdispersion, performed better than the linear model in goodness of fit and predictive ability. Predictions of random effects from the Poisson model were more strongly correlated with those from BINBS models than those from the linear model. Overall, the use of probit or linear models for BINBS and of a Poisson model with a residual for NUMBS seems a reasonable choice for genetic selection purposes in Corriedale sheep. © 2010 Blackwell Verlag GmbH.

Method selection and adaptation for distributed monitoring of infectious diseases for syndromic surveillance.

PubMed

Xing, Jian; Burkom, Howard; Tokars, Jerome

2011-12-01

Automated surveillance systems require statistical methods to recognize increases in visit counts that might indicate an outbreak. In prior work we presented methods to enhance the sensitivity of C2, a commonly used time series method. In this study, we compared the enhanced C2 method with five regression models. We used emergency department chief complaint data from US CDC BioSense surveillance system, aggregated by city (total of 206 hospitals, 16 cities) during 5/2008-4/2009. Data for six syndromes (asthma, gastrointestinal, nausea and vomiting, rash, respiratory, and influenza-like illness) was used and was stratified by mean count (1-19, 20-49, ≥50 per day) into 14 syndrome-count categories. We compared the sensitivity for detecting single-day artificially-added increases in syndrome counts. Four modifications of the C2 time series method, and five regression models (two linear and three Poisson), were tested. A constant alert rate of 1% was used for all methods. Among the regression models tested, we found that a Poisson model controlling for the logarithm of total visits (i.e., visits both meeting and not meeting a syndrome definition), day of week, and 14-day time period was best. Among 14 syndrome-count categories, time series and regression methods produced approximately the same sensitivity (<5% difference) in 6; in six categories, the regression method had higher sensitivity (range 6-14% improvement), and in two categories the time series method had higher sensitivity. When automated data are aggregated to the city level, a Poisson regression model that controls for total visits produces the best overall sensitivity for detecting artificially added visit counts. This improvement was achieved without increasing the alert rate, which was held constant at 1% for all methods. These findings will improve our ability to detect outbreaks in automated surveillance system data. Published by Elsevier Inc.

The Dependent Poisson Race Model and Modeling Dependence in Conjoint Choice Experiments

ERIC Educational Resources Information Center

Ruan, Shiling; MacEachern, Steven N.; Otter, Thomas; Dean, Angela M.

2008-01-01

Conjoint choice experiments are used widely in marketing to study consumer preferences amongst alternative products. We develop a class of choice models, belonging to the class of Poisson race models, that describe a "random utility" which lends itself to a process-based description of choice. The models incorporate a dependence structure which…

An Evaluation of the Euroncap Crash Test Safety Ratings in the Real World

PubMed Central

Segui-Gomez, Maria; Lopez-Valdes, Francisco J.; Frampton, Richard

2007-01-01

We investigated whether the rating obtained in the EuroNCAP test procedures correlates with injury protection to vehicle occupants in real crashes using data in the UK Cooperative Crash Injury Study (CCIS) database from 1996 to 2005. Multivariate Poisson regression models were developed, using the Abbreviated Injury Scale (AIS) score by body region as the dependent variable and the EuroNCAP score for that particular body region, seat belt use, mass ratio and Equivalent Test Speed (ETS) as independent variables. Our models identified statistically significant relationships between injury severity and safety belt use, mass ratio and ETS. We could not identify any statistically significant relationships between the EuroNCAP body region scores and real injury outcome except for the protection to pelvis-femur-knee in frontal impacts where scoring “green” is significantly better than scoring “yellow” or “red”.

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models.

PubMed

Evangelista, Luiz Roberto; Lenzi, Ervin Kaminski; Barbero, Giovanni

2013-11-20

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

On temporal stochastic modeling of precipitation, nesting models across scales

NASA Astrophysics Data System (ADS)

Paschalis, Athanasios; Molnar, Peter; Fatichi, Simone; Burlando, Paolo

2014-01-01

We analyze the performance of composite stochastic models of temporal precipitation which can satisfactorily reproduce precipitation properties across a wide range of temporal scales. The rationale is that a combination of stochastic precipitation models which are most appropriate for specific limited temporal scales leads to better overall performance across a wider range of scales than single models alone. We investigate different model combinations. For the coarse (daily) scale these are models based on Alternating renewal processes, Markov chains, and Poisson cluster models, which are then combined with a microcanonical Multiplicative Random Cascade model to disaggregate precipitation to finer (minute) scales. The composite models were tested on data at four sites in different climates. The results show that model combinations improve the performance in key statistics such as probability distributions of precipitation depth, autocorrelation structure, intermittency, reproduction of extremes, compared to single models. At the same time they remain reasonably parsimonious. No model combination was found to outperform the others at all sites and for all statistics, however we provide insight on the capabilities of specific model combinations. The results for the four different climates are similar, which suggests a degree of generality and wider applicability of the approach.

A flexible count data model to fit the wide diversity of expression profiles arising from extensively replicated RNA-seq experiments

PubMed Central

2013-01-01

Background High-throughput RNA sequencing (RNA-seq) offers unprecedented power to capture the real dynamics of gene expression. Experimental designs with extensive biological replication present a unique opportunity to exploit this feature and distinguish expression profiles with higher resolution. RNA-seq data analysis methods so far have been mostly applied to data sets with few replicates and their default settings try to provide the best performance under this constraint. These methods are based on two well-known count data distributions: the Poisson and the negative binomial. The way to properly calibrate them with large RNA-seq data sets is not trivial for the non-expert bioinformatics user. Results Here we show that expression profiles produced by extensively-replicated RNA-seq experiments lead to a rich diversity of count data distributions beyond the Poisson and the negative binomial, such as Poisson-Inverse Gaussian or Pólya-Aeppli, which can be captured by a more general family of count data distributions called the Poisson-Tweedie. The flexibility of the Poisson-Tweedie family enables a direct fitting of emerging features of large expression profiles, such as heavy-tails or zero-inflation, without the need to alter a single configuration parameter. We provide a software package for R called tweeDEseq implementing a new test for differential expression based on the Poisson-Tweedie family. Using simulations on synthetic and real RNA-seq data we show that tweeDEseq yields P-values that are equally or more accurate than competing methods under different configuration parameters. By surveying the tiny fraction of sex-specific gene expression changes in human lymphoblastoid cell lines, we also show that tweeDEseq accurately detects differentially expressed genes in a real large RNA-seq data set with improved performance and reproducibility over the previously compared methodologies. Finally, we compared the results with those obtained from microarrays in order to check for reproducibility. Conclusions RNA-seq data with many replicates leads to a handful of count data distributions which can be accurately estimated with the statistical model illustrated in this paper. This method provides a better fit to the underlying biological variability; this may be critical when comparing groups of RNA-seq samples with markedly different count data distributions. The tweeDEseq package forms part of the Bioconductor project and it is available for download at http://www.bioconductor.org. PMID:23965047

A systematic review of models to predict recruitment to multicentre clinical trials

PubMed Central

2010-01-01

Background Less than one third of publicly funded trials managed to recruit according to their original plan often resulting in request for additional funding and/or time extensions. The aim was to identify models which might be useful to a major public funder of randomised controlled trials when estimating likely time requirements for recruiting trial participants. The requirements of a useful model were identified as usability, based on experience, able to reflect time trends, accounting for centre recruitment and contribution to a commissioning decision. Methods A systematic review of English language articles using MEDLINE and EMBASE. Search terms included: randomised controlled trial, patient, accrual, predict, enrol, models, statistical; Bayes Theorem; Decision Theory; Monte Carlo Method and Poisson. Only studies discussing prediction of recruitment to trials using a modelling approach were included. Information was extracted from articles by one author, and checked by a second, using a pre-defined form. Results Out of 326 identified abstracts, only 8 met all the inclusion criteria. Of these 8 studies examined, there are five major classes of model discussed: the unconditional model, the conditional model, the Poisson model, Bayesian models and Monte Carlo simulation of Markov models. None of these meet all the pre-identified needs of the funder. Conclusions To meet the needs of a number of research programmes, a new model is required as a matter of importance. Any model chosen should be validated against both retrospective and prospective data, to ensure the predictions it gives are superior to those currently used. PMID:20604946

Questionable Validity of Poisson Assumptions in a Combined Loglinear/MDS Mapping Model.

ERIC Educational Resources Information Center

Gleason, John M.

1993-01-01

This response to an earlier article on a combined log-linear/MDS model for mapping journals by citation analysis discusses the underlying assumptions of the Poisson model with respect to characteristics of the citation process. The importance of empirical data analysis is also addressed. (nine references) (LRW)

On supermatrix models, Poisson geometry, and noncommutative supersymmetric gauge theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klimčík, Ctirad

2015-12-15

We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the UOSp(2|1) supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.

Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

NASA Astrophysics Data System (ADS)

Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

2016-07-01

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

Climatology of Station Storm Rainfall in the Continental United States: Parameters of the Bartlett-Lewis and Poisson Rectangular Pulses Models

NASA Technical Reports Server (NTRS)

Hawk, Kelly Lynn; Eagleson, Peter S.

1992-01-01

The parameters of two stochastic models of point rainfall, the Bartlett-Lewis model and the Poisson rectangular pulses model, are estimated for each month of the year from the historical records of hourly precipitation at more than seventy first-order stations in the continental United States. The parameters are presented both in tabular form and as isopleths on maps. The Poisson rectangular pulses parameters are useful in implementing models of the land surface water balance. The Bartlett-Lewis parameters are useful in disaggregating precipitation to a time period shorter than that of existing observations. Information is also included on a floppy disk.

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle.

PubMed

Osche, G R

2000-08-20

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

Deformation mechanisms in negative Poisson's ratio materials - Structural aspects

NASA Technical Reports Server (NTRS)

Lakes, R.

1991-01-01

Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with non-central force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.

Evaluation of the statistical evidence for Characteristic Earthquakes in the frequency-magnitude distributions of Sumatra and other subduction zone regions

NASA Astrophysics Data System (ADS)

Naylor, M.; Main, I. G.; Greenhough, J.; Bell, A. F.; McCloskey, J.

2009-04-01

The Sumatran Boxing Day earthquake and subsequent large events provide an opportunity to re-evaluate the statistical evidence for characteristic earthquake events in frequency-magnitude distributions. Our aims are to (i) improve intuition regarding the properties of samples drawn from power laws, (ii) illustrate using random samples how appropriate Poisson confidence intervals can both aid the eye and provide an appropriate statistical evaluation of data drawn from power-law distributions, and (iii) apply these confidence intervals to test for evidence of characteristic earthquakes in subduction-zone frequency-magnitude distributions. We find no need for a characteristic model to describe frequency magnitude distributions in any of the investigated subduction zones, including Sumatra, due to an emergent skew in residuals of power law count data at high magnitudes combined with a sample bias for examining large earthquakes as candidate characteristic events.

An application of queueing theory to the design of channel requirements for special purpose communications satellites. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Hein, G. F.

1974-01-01

Special purpose satellites are very cost sensitive to the number of broadcast channels, usually will have Poisson arrivals, fairly low utilization (less than 35%), and a very high availability requirement. To solve the problem of determining the effects of limiting C the number of channels, the Poisson arrival, infinite server queueing model will be modified to describe the many server case. The model is predicated on the reproductive property of the Poisson distribution.

Aksz Construction of Topological Open p-BRANE Action and Nambu Brackets

NASA Astrophysics Data System (ADS)

Bouwknegt, Peter; Jurčo, Branislav

2013-04-01

We review the AKSZ construction as applied to the topological open membranes and Poisson sigma models. We describe a generalization to open topological p-branes. Also, we propose a related (not necessarily BV) Nambu-Poisson sigma model.

Technical and biological variance structure in mRNA-Seq data: life in the real world

PubMed Central

2012-01-01

Background mRNA expression data from next generation sequencing platforms is obtained in the form of counts per gene or exon. Counts have classically been assumed to follow a Poisson distribution in which the variance is equal to the mean. The Negative Binomial distribution which allows for over-dispersion, i.e., for the variance to be greater than the mean, is commonly used to model count data as well. Results In mRNA-Seq data from 25 subjects, we found technical variation to generally follow a Poisson distribution as has been reported previously and biological variability was over-dispersed relative to the Poisson model. The mean-variance relationship across all genes was quadratic, in keeping with a Negative Binomial (NB) distribution. Over-dispersed Poisson and NB distributional assumptions demonstrated marked improvements in goodness-of-fit (GOF) over the standard Poisson model assumptions, but with evidence of over-fitting in some genes. Modeling of experimental effects improved GOF for high variance genes but increased the over-fitting problem. Conclusions These conclusions will guide development of analytical strategies for accurate modeling of variance structure in these data and sample size determination which in turn will aid in the identification of true biological signals that inform our understanding of biological systems. PMID:22769017

Application of Poisson random effect models for highway network screening.

PubMed

Jiang, Ximiao; Abdel-Aty, Mohamed; Alamili, Samer

2014-02-01

In recent years, Bayesian random effect models that account for the temporal and spatial correlations of crash data became popular in traffic safety research. This study employs random effect Poisson Log-Normal models for crash risk hotspot identification. Both the temporal and spatial correlations of crash data were considered. Potential for Safety Improvement (PSI) were adopted as a measure of the crash risk. Using the fatal and injury crashes that occurred on urban 4-lane divided arterials from 2006 to 2009 in the Central Florida area, the random effect approaches were compared to the traditional Empirical Bayesian (EB) method and the conventional Bayesian Poisson Log-Normal model. A series of method examination tests were conducted to evaluate the performance of different approaches. These tests include the previously developed site consistence test, method consistence test, total rank difference test, and the modified total score test, as well as the newly proposed total safety performance measure difference test. Results show that the Bayesian Poisson model accounting for both temporal and spatial random effects (PTSRE) outperforms the model that with only temporal random effect, and both are superior to the conventional Poisson Log-Normal model (PLN) and the EB model in the fitting of crash data. Additionally, the method evaluation tests indicate that the PTSRE model is significantly superior to the PLN model and the EB model in consistently identifying hotspots during successive time periods. The results suggest that the PTSRE model is a superior alternative for road site crash risk hotspot identification. Copyright © 2013 Elsevier Ltd. All rights reserved.

On Subset Selection Procedures for Poisson Processes and Some Applications to the Binomial and Multinomial Problems

DTIC Science & Technology

1976-07-01

PURDUE UNIVERSITY DEPARTMENT OF STATISTICS DIVISION OF MATHEMATICAL SCIENCES ON SUBSET SELECTION PROCEDURES FOR POISSON PROCESSES AND SOME...Mathematical Sciences Mimeograph Series #457, July 1976 This research was supported by the Office of Naval Research under Contract NOOO14-75-C-0455 at Purdue...11 CON PC-111 riFIC-F ,A.F ANO ADDPFS Office of INaval ResearchJu#07 Washington, DC07 36AE 14~~~ rjCr; NF A ’ , A FAA D F 6 - I S it 9 i 1, - ,1 I

Integer lattice gas with Monte Carlo collision operator recovers the lattice Boltzmann method with Poisson-distributed fluctuations

NASA Astrophysics Data System (ADS)

Blommel, Thomas; Wagner, Alexander J.

2018-02-01

We examine a new kind of lattice gas that closely resembles modern lattice Boltzmann methods. This new kind of lattice gas, which we call a Monte Carlo lattice gas, has interesting properties that shed light on the origin of the multirelaxation time collision operator, and it derives the equilibrium distribution for an entropic lattice Boltzmann. Furthermore these lattice gas methods have Galilean invariant fluctuations given by a Poisson statistics, giving further insight into the properties that we should expect for fluctuating lattice Boltzmann methods.

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

Minimum risk wavelet shrinkage operator for Poisson image denoising.

PubMed

Cheng, Wu; Hirakawa, Keigo

2015-05-01

The pixel values of images taken by an image sensor are said to be corrupted by Poisson noise. To date, multiscale Poisson image denoising techniques have processed Haar frame and wavelet coefficients--the modeling of coefficients is enabled by the Skellam distribution analysis. We extend these results by solving for shrinkage operators for Skellam that minimizes the risk functional in the multiscale Poisson image denoising setting. The minimum risk shrinkage operator of this kind effectively produces denoised wavelet coefficients with minimum attainable L2 error.

Equivalence of MAXENT and Poisson point process models for species distribution modeling in ecology.

PubMed

Renner, Ian W; Warton, David I

2013-03-01

Modeling the spatial distribution of a species is a fundamental problem in ecology. A number of modeling methods have been developed, an extremely popular one being MAXENT, a maximum entropy modeling approach. In this article, we show that MAXENT is equivalent to a Poisson regression model and hence is related to a Poisson point process model, differing only in the intercept term, which is scale-dependent in MAXENT. We illustrate a number of improvements to MAXENT that follow from these relations. In particular, a point process model approach facilitates methods for choosing the appropriate spatial resolution, assessing model adequacy, and choosing the LASSO penalty parameter, all currently unavailable to MAXENT. The equivalence result represents a significant step in the unification of the species distribution modeling literature. Copyright © 2013, The International Biometric Society.

QMRA for Drinking Water: 2. The Effect of Pathogen Clustering in Single-Hit Dose-Response Models.

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson-distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional "single-hit" dose-response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose-response models in terms of probability generating functions. It is shown formally that the theoretical single-hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single-hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single-hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose-response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose-response assessment as well as practical risk characterization are discussed. © 2016 Society for Risk Analysis.

Maximizing Statistical Power When Verifying Probabilistic Forecasts of Hydrometeorological Events

NASA Astrophysics Data System (ADS)

DeChant, C. M.; Moradkhani, H.

2014-12-01

Hydrometeorological events (i.e. floods, droughts, precipitation) are increasingly being forecasted probabilistically, owing to the uncertainties in the underlying causes of the phenomenon. In these forecasts, the probability of the event, over some lead time, is estimated based on some model simulations or predictive indicators. By issuing probabilistic forecasts, agencies may communicate the uncertainty in the event occurring. Assuming that the assigned probability of the event is correct, which is referred to as a reliable forecast, the end user may perform some risk management based on the potential damages resulting from the event. Alternatively, an unreliable forecast may give false impressions of the actual risk, leading to improper decision making when protecting resources from extreme events. Due to this requisite for reliable forecasts to perform effective risk management, this study takes a renewed look at reliability assessment in event forecasts. Illustrative experiments will be presented, showing deficiencies in the commonly available approaches (Brier Score, Reliability Diagram). Overall, it is shown that the conventional reliability assessment techniques do not maximize the ability to distinguish between a reliable and unreliable forecast. In this regard, a theoretical formulation of the probabilistic event forecast verification framework will be presented. From this analysis, hypothesis testing with the Poisson-Binomial distribution is the most exact model available for the verification framework, and therefore maximizes one's ability to distinguish between a reliable and unreliable forecast. Application of this verification system was also examined within a real forecasting case study, highlighting the additional statistical power provided with the use of the Poisson-Binomial distribution.

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

PubMed

Schuss, Z; Nadler, B; Eisenberg, R S

2001-09-01

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

PubMed

Wan, Wai-Yin; Chan, Jennifer S K

2009-08-01

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

Poisson-event-based analysis of cell proliferation.

PubMed

Summers, Huw D; Wills, John W; Brown, M Rowan; Rees, Paul

2015-05-01

A protocol for the assessment of cell proliferation dynamics is presented. This is based on the measurement of cell division events and their subsequent analysis using Poisson probability statistics. Detailed analysis of proliferation dynamics in heterogeneous populations requires single cell resolution within a time series analysis and so is technically demanding to implement. Here, we show that by focusing on the events during which cells undergo division rather than directly on the cells themselves a simplified image acquisition and analysis protocol can be followed, which maintains single cell resolution and reports on the key metrics of cell proliferation. The technique is demonstrated using a microscope with 1.3 μm spatial resolution to track mitotic events within A549 and BEAS-2B cell lines, over a period of up to 48 h. Automated image processing of the bright field images using standard algorithms within the ImageJ software toolkit yielded 87% accurate recording of the manually identified, temporal, and spatial positions of the mitotic event series. Analysis of the statistics of the interevent times (i.e., times between observed mitoses in a field of view) showed that cell division conformed to a nonhomogeneous Poisson process in which the rate of occurrence of mitotic events, λ exponentially increased over time and provided values of the mean inter mitotic time of 21.1 ± 1.2 hours for the A549 cells and 25.0 ± 1.1 h for the BEAS-2B cells. Comparison of the mitotic event series for the BEAS-2B cell line to that predicted by random Poisson statistics indicated that temporal synchronisation of the cell division process was occurring within 70% of the population and that this could be increased to 85% through serum starvation of the cell culture. © 2015 International Society for Advancement of Cytometry.

Estimating time since infection in early homogeneous HIV-1 samples using a poisson model

PubMed Central

2010-01-01

Background The occurrence of a genetic bottleneck in HIV sexual or mother-to-infant transmission has been well documented. This results in a majority of new infections being homogeneous, i.e., initiated by a single genetic strain. Early after infection, prior to the onset of the host immune response, the viral population grows exponentially. In this simple setting, an approach for estimating evolutionary and demographic parameters based on comparison of diversity measures is a feasible alternative to the existing Bayesian methods (e.g., BEAST), which are instead based on the simulation of genealogies. Results We have devised a web tool that analyzes genetic diversity in acutely infected HIV-1 patients by comparing it to a model of neutral growth. More specifically, we consider a homogeneous infection (i.e., initiated by a unique genetic strain) prior to the onset of host-induced selection, where we can assume a random accumulation of mutations. Previously, we have shown that such a model successfully describes about 80% of sexual HIV-1 transmissions provided the samples are drawn early enough in the infection. Violation of the model is an indicator of either heterogeneous infections or the initiation of selection. Conclusions When the underlying assumptions of our model (homogeneous infection prior to selection and fast exponential growth) are met, we are under a very particular scenario for which we can use a forward approach (instead of backwards in time as provided by coalescent methods). This allows for more computationally efficient methods to derive the time since the most recent common ancestor. Furthermore, the tool performs statistical tests on the Hamming distance frequency distribution, and outputs summary statistics (mean of the best fitting Poisson distribution, goodness of fit p-value, etc). The tool runs within minutes and can readily accommodate the tens of thousands of sequences generated through new ultradeep pyrosequencing technologies. The tool is available on the LANL website. PMID:20973976

Identifiability in N-mixture models: a large-scale screening test with bird data.

PubMed

Kéry, Marc

2018-02-01

Binomial N-mixture models have proven very useful in ecology, conservation, and monitoring: they allow estimation and modeling of abundance separately from detection probability using simple counts. Recently, doubts about parameter identifiability have been voiced. I conducted a large-scale screening test with 137 bird data sets from 2,037 sites. I found virtually no identifiability problems for Poisson and zero-inflated Poisson (ZIP) binomial N-mixture models, but negative-binomial (NB) models had problems in 25% of all data sets. The corresponding multinomial N-mixture models had no problems. Parameter estimates under Poisson and ZIP binomial and multinomial N-mixture models were extremely similar. Identifiability problems became a little more frequent with smaller sample sizes (267 and 50 sites), but were unaffected by whether the models did or did not include covariates. Hence, binomial N-mixture model parameters with Poisson and ZIP mixtures typically appeared identifiable. In contrast, NB mixtures were often unidentifiable, which is worrying since these were often selected by Akaike's information criterion. Identifiability of binomial N-mixture models should always be checked. If problems are found, simpler models, integrated models that combine different observation models or the use of external information via informative priors or penalized likelihoods, may help. © 2017 by the Ecological Society of America.

Effect of noise on defect chaos in a reaction-diffusion model.

PubMed

Wang, Hongli; Ouyang, Qi

2005-06-01

The influence of noise on defect chaos due to breakup of spiral waves through Doppler and Eckhaus instabilities is investigated numerically with a modified Fitzhugh-Nagumo model. By numerical simulations we show that the noise can drastically enhance the creation and annihilation rates of topological defects. The noise-free probability distribution function for defects in this model is found not to fit with the previously reported squared-Poisson distribution. Under the influence of noise, the distributions are flattened, and can fit with the squared-Poisson or the modified-Poisson distribution. The defect lifetime and diffusive property of defects under the influence of noise are also checked in this model.

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2013-09-01

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

Educational Aspirations: Markov and Poisson Models. Rural Industrial Development Project Working Paper Number 14, August 1971.

ERIC Educational Resources Information Center

Kayser, Brian D.

The fit of educational aspirations of Illinois rural high school youths to 3 related one-parameter mathematical models was investigated. The models used were the continuous-time Markov chain model, the discrete-time Markov chain, and the Poisson distribution. The sample of 635 students responded to questionnaires from 1966 to 1969 as part of an…

Time to burn: Modeling wildland arson as an autoregressive crime function

Treesearch

Jeffrey P. Prestemon; David T. Butry

2005-01-01

Six Poisson autoregressive models of order p [PAR(p)] of daily wildland arson ignition counts are estimated for five locations in Florida (1994-2001). In addition, a fixed effects time-series Poisson model of annual arson counts is estimated for all Florida counties (1995-2001). PAR(p) model estimates reveal highly significant arson ignition autocorrelation, lasting up...

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

Comparing statistical methods for analyzing skewed longitudinal count data with many zeros: an example of smoking cessation.

PubMed

Xie, Haiyi; Tao, Jill; McHugo, Gregory J; Drake, Robert E

2013-07-01

Count data with skewness and many zeros are common in substance abuse and addiction research. Zero-adjusting models, especially zero-inflated models, have become increasingly popular in analyzing this type of data. This paper reviews and compares five mixed-effects Poisson family models commonly used to analyze count data with a high proportion of zeros by analyzing a longitudinal outcome: number of smoking quit attempts from the New Hampshire Dual Disorders Study. The findings of our study indicated that count data with many zeros do not necessarily require zero-inflated or other zero-adjusting models. For rare event counts or count data with small means, a simpler model such as the negative binomial model may provide a better fit. Copyright © 2013 Elsevier Inc. All rights reserved.

Improving removal-based estimates of abundance by sampling a population of spatially distinct subpopulations

USGS Publications Warehouse

Dorazio, R.M.; Jelks, H.L.; Jordan, F.

2005-01-01

 A statistical modeling framework is described for estimating the abundances of spatially distinct subpopulations of animals surveyed using removal sampling. To illustrate this framework, hierarchical models are developed using the Poisson and negative-binomial distributions to model variation in abundance among subpopulations and using the beta distribution to model variation in capture probabilities. These models are fitted to the removal counts observed in a survey of a federally endangered fish species. The resulting estimates of abundance have similar or better precision than those computed using the conventional approach of analyzing the removal counts of each subpopulation separately. Extension of the hierarchical models to include spatial covariates of abundance is straightforward and may be used to identify important features of an animal's habitat or to predict the abundance of animals at unsampled locations.

A multi-level approach for investigating socio-economic and agricultural risk factors associated with rates of reported cases of Escherichia coli O157 in humans in Alberta, Canada.

PubMed

Pearl, D L; Louie, M; Chui, L; Doré, K; Grimsrud, K M; Martin, S W; Michel, P; Svenson, L W; McEwen, S A

2009-10-01

Using negative binomial and multi-level Poisson models, the authors determined the statistical significance of agricultural and socio-economic risk factors for rates of reported disease associated with Escherichia coli O157 in census subdivisions (CSDs) in Alberta, Canada, 2000-2002. Variables relating to population stability, aboriginal composition of the CSDs, and the economic relationship between CSDs and urban centres were significant risk factors. The percentage of individuals living in low-income households was not a statistically significant risk factor for rates of disease. The statistical significance of cattle density, recorded at a higher geographical level, depended on the method used to correct for overdispersion, the number of levels included in the multi-level models, and the choice of using all reported cases or only sporadic cases. Our results highlight the importance of local socio-economic risk factors in determining rates of disease associated with E. coli O157, but their relationship with individual risk factors requires further evaluation.

Statistical Models for the Analysis of Zero-Inflated Pain Intensity Numeric Rating Scale Data.

PubMed

Goulet, Joseph L; Buta, Eugenia; Bathulapalli, Harini; Gueorguieva, Ralitza; Brandt, Cynthia A

2017-03-01

Pain intensity is often measured in clinical and research settings using the 0 to 10 numeric rating scale (NRS). NRS scores are recorded as discrete values, and in some samples they may display a high proportion of zeroes and a right-skewed distribution. Despite this, statistical methods for normally distributed data are frequently used in the analysis of NRS data. We present results from an observational cross-sectional study examining the association of NRS scores with patient characteristics using data collected from a large cohort of 18,935 veterans in Department of Veterans Affairs care diagnosed with a potentially painful musculoskeletal disorder. The mean (variance) NRS pain was 3.0 (7.5), and 34% of patients reported no pain (NRS = 0). We compared the following statistical models for analyzing NRS scores: linear regression, generalized linear models (Poisson and negative binomial), zero-inflated and hurdle models for data with an excess of zeroes, and a cumulative logit model for ordinal data. We examined model fit, interpretability of results, and whether conclusions about the predictor effects changed across models. In this study, models that accommodate zero inflation provided a better fit than the other models. These models should be considered for the analysis of NRS data with a large proportion of zeroes. We examined and analyzed pain data from a large cohort of veterans with musculoskeletal disorders. We found that many reported no current pain on the NRS on the diagnosis date. We present several alternative statistical methods for the analysis of pain intensity data with a large proportion of zeroes. Published by Elsevier Inc.

Scaling laws and fluctuations in the statistics of word frequencies

NASA Astrophysics Data System (ADS)

Gerlach, Martin; Altmann, Eduardo G.

2014-11-01

In this paper, we combine statistical analysis of written texts and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. The average vocabulary of an ensemble of fixed-length texts is known to scale sublinearly with the total number of words (Heaps’ law). Analyzing the fluctuations around this average in three large databases (Google-ngram, English Wikipedia, and a collection of scientific articles), we find that the standard deviation scales linearly with the average (Taylor's law), in contrast to the prediction of decaying fluctuations obtained using simple sampling arguments. We explain both scaling laws (Heaps’ and Taylor) by modeling the usage of words using a Poisson process with a fat-tailed distribution of word frequencies (Zipf's law) and topic-dependent frequencies of individual words (as in topic models). Considering topical variations lead to quenched averages, turn the vocabulary size a non-self-averaging quantity, and explain the empirical observations. For the numerous practical applications relying on estimations of vocabulary size, our results show that uncertainties remain large even for long texts. We show how to account for these uncertainties in measurements of lexical richness of texts with different lengths.

Modeling species-abundance relationships in multi-species collections

USGS Publications Warehouse

Peng, S.; Yin, Z.; Ren, H.; Guo, Q.

2003-01-01

Species-abundance relationship is one of the most fundamental aspects of community ecology. Since Motomura first developed the geometric series model to describe the feature of community structure, ecologists have developed many other models to fit the species-abundance data in communities. These models can be classified into empirical and theoretical ones, including (1) statistical models, i.e., negative binomial distribution (and its extension), log-series distribution (and its extension), geometric distribution, lognormal distribution, Poisson-lognormal distribution, (2) niche models, i.e., geometric series, broken stick, overlapping niche, particulate niche, random assortment, dominance pre-emption, dominance decay, random fraction, weighted random fraction, composite niche, Zipf or Zipf-Mandelbrot model, and (3) dynamic models describing community dynamics and restrictive function of environment on community. These models have different characteristics and fit species-abundance data in various communities or collections. Among them, log-series distribution, lognormal distribution, geometric series, and broken stick model have been most widely used.

Beta-Poisson model for single-cell RNA-seq data analyses.

PubMed

Vu, Trung Nghia; Wills, Quin F; Kalari, Krishna R; Niu, Nifang; Wang, Liewei; Rantalainen, Mattias; Pawitan, Yudi

2016-07-15

Single-cell RNA-sequencing technology allows detection of gene expression at the single-cell level. One typical feature of the data is a bimodality in the cellular distribution even for highly expressed genes, primarily caused by a proportion of non-expressing cells. The standard and the over-dispersed gamma-Poisson models that are commonly used in bulk-cell RNA-sequencing are not able to capture this property. We introduce a beta-Poisson mixture model that can capture the bimodality of the single-cell gene expression distribution. We further integrate the model into the generalized linear model framework in order to perform differential expression analyses. The whole analytical procedure is called BPSC. The results from several real single-cell RNA-seq datasets indicate that ∼90% of the transcripts are well characterized by the beta-Poisson model; the model-fit from BPSC is better than the fit of the standard gamma-Poisson model in > 80% of the transcripts. Moreover, in differential expression analyses of simulated and real datasets, BPSC performs well against edgeR, a conventional method widely used in bulk-cell RNA-sequencing data, and against scde and MAST, two recent methods specifically designed for single-cell RNA-seq data. An R package BPSC for model fitting and differential expression analyses of single-cell RNA-seq data is available under GPL-3 license at https://github.com/nghiavtr/BPSC CONTACT: yudi.pawitan@ki.se or mattias.rantalainen@ki.se Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

The statistical overlap theory of chromatography using power law (fractal) statistics.

PubMed

Schure, Mark R; Davis, Joe M

2011-12-30

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics. Copyright © 2011 Elsevier B.V. All rights reserved.

Prediction of forest fires occurrences with area-level Poisson mixed models.

PubMed

Boubeta, Miguel; Lombardía, María José; Marey-Pérez, Manuel Francisco; Morales, Domingo

2015-05-01

The number of fires in forest areas of Galicia (north-west of Spain) during the summer period is quite high. Local authorities are interested in analyzing the factors that explain this phenomenon. Poisson regression models are good tools for describing and predicting the number of fires per forest areas. This work employs area-level Poisson mixed models for treating real data about fires in forest areas. A parametric bootstrap method is applied for estimating the mean squared errors of fires predictors. The developed methodology and software are applied to a real data set of fires in forest areas of Galicia. Copyright © 2015 Elsevier Ltd. All rights reserved.

Poisson point process modeling for polyphonic music transcription.

PubMed

Peeling, Paul; Li, Chung-fai; Godsill, Simon

2007-04-01

Peaks detected in the frequency domain spectrum of a musical chord are modeled as realizations of a nonhomogeneous Poisson point process. When several notes are superimposed to make a chord, the processes for individual notes combine to give another Poisson process, whose likelihood is easily computable. This avoids a data association step linking individual harmonics explicitly with detected peaks in the spectrum. The likelihood function is ideal for Bayesian inference about the unknown note frequencies in a chord. Here, maximum likelihood estimation of fundamental frequencies shows very promising performance on real polyphonic piano music recordings.

The distribution of catchment coverage by stationary rainstorms

NASA Technical Reports Server (NTRS)

Eagleson, P. S.

1984-01-01

The occurrence of wetted rainstorm area within a catchment is modeled as a Poisson arrival process in which each storm is composed of stationary, nonoverlapping, independent random cell clusters whose centers are Poisson-distributed in space and whose areas are fractals. The two Poisson parameters and hence the first two moments of the wetted fraction are derived in terms of catchment average characteristics of the (observable) station precipitation. The model is used to estimate spatial properties of tropical air mass thunderstorms on six tropical catchments in the Sudan.

Zero-inflated Poisson regression models for QTL mapping applied to tick-resistance in a Gyr × Holstein F2 population

PubMed Central

Silva, Fabyano Fonseca; Tunin, Karen P.; Rosa, Guilherme J.M.; da Silva, Marcos V.B.; Azevedo, Ana Luisa Souza; da Silva Verneque, Rui; Machado, Marco Antonio; Packer, Irineu Umberto

2011-01-01

Now a days, an important and interesting alternative in the control of tick-infestation in cattle is to select resistant animals, and identify the respective quantitative trait loci (QTLs) and DNA markers, for posterior use in breeding programs. The number of ticks/animal is characterized as a discrete-counting trait, which could potentially follow Poisson distribution. However, in the case of an excess of zeros, due to the occurrence of several noninfected animals, zero-inflated Poisson and generalized zero-inflated distribution (GZIP) may provide a better description of the data. Thus, the objective here was to compare through simulation, Poisson and ZIP models (simple and generalized) with classical approaches, for QTL mapping with counting phenotypes under different scenarios, and to apply these approaches to a QTL study of tick resistance in an F2 cattle (Gyr × Holstein) population. It was concluded that, when working with zero-inflated data, it is recommendable to use the generalized and simple ZIP model for analysis. On the other hand, when working with data with zeros, but not zero-inflated, the Poisson model or a data-transformation-approach, such as square-root or Box-Cox transformation, are applicable. PMID:22215960

The Poisson model limits in NBA basketball: Complexity in team sports

NASA Astrophysics Data System (ADS)

Martín-González, Juan Manuel; de Saá Guerra, Yves; García-Manso, Juan Manuel; Arriaza, Enrique; Valverde-Estévez, Teresa

2016-12-01

Team sports are frequently studied by researchers. There is presumption that scoring in basketball is a random process and that can be described using the Poisson Model. Basketball is a collaboration-opposition sport, where the non-linear local interactions among players are reflected in the evolution of the score that ultimately determines the winner. In the NBA, the outcomes of close games are often decided in the last minute, where fouls play a main role. We examined 6130 NBA games in order to analyze the time intervals between baskets and scoring dynamics. Most numbers of baskets (n) over a time interval (ΔT) follow a Poisson distribution, but some (e.g., ΔT = 10 s, n > 3) behave as a Power Law. The Poisson distribution includes most baskets in any game, in most game situations, but in close games in the last minute, the numbers of events are distributed following a Power Law. The number of events can be adjusted by a mixture of two distributions. In close games, both teams try to maintain their advantage solely in order to reach the last minute: a completely different game. For this reason, we propose to use the Poisson model as a reference. The complex dynamics will emerge from the limits of this model.

A poisson process model for hip fracture risk.

PubMed

Schechner, Zvi; Luo, Gangming; Kaufman, Jonathan J; Siffert, Robert S

2010-08-01

The primary method for assessing fracture risk in osteoporosis relies primarily on measurement of bone mass. Estimation of fracture risk is most often evaluated using logistic or proportional hazards models. Notwithstanding the success of these models, there is still much uncertainty as to who will or will not suffer a fracture. This has led to a search for other components besides mass that affect bone strength. The purpose of this paper is to introduce a new mechanistic stochastic model that characterizes the risk of hip fracture in an individual. A Poisson process is used to model the occurrence of falls, which are assumed to occur at a rate, lambda. The load induced by a fall is assumed to be a random variable that has a Weibull probability distribution. The combination of falls together with loads leads to a compound Poisson process. By retaining only those occurrences of the compound Poisson process that result in a hip fracture, a thinned Poisson process is defined that itself is a Poisson process. The fall rate is modeled as an affine function of age, and hip strength is modeled as a power law function of bone mineral density (BMD). The risk of hip fracture can then be computed as a function of age and BMD. By extending the analysis to a Bayesian framework, the conditional densities of BMD given a prior fracture and no prior fracture can be computed and shown to be consistent with clinical observations. In addition, the conditional probabilities of fracture given a prior fracture and no prior fracture can also be computed, and also demonstrate results similar to clinical data. The model elucidates the fact that the hip fracture process is inherently random and improvements in hip strength estimation over and above that provided by BMD operate in a highly "noisy" environment and may therefore have little ability to impact clinical practice.

An unbiased risk estimator for image denoising in the presence of mixed poisson-gaussian noise.

PubMed

Le Montagner, Yoann; Angelini, Elsa D; Olivo-Marin, Jean-Christophe

2014-03-01

The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.

The Use of Crow-AMSAA Plots to Assess Mishap Trends

NASA Technical Reports Server (NTRS)

Dawson, Jeffrey W.

2011-01-01

Crow-AMSAA (CA) plots are used to model reliability growth. Use of CA plots has expanded into other areas, such as tracking events of interest to management, maintenance problems, and safety mishaps. Safety mishaps can often be successfully modeled using a Poisson probability distribution. CA plots show a Poisson process in log-log space. If the safety mishaps are a stable homogenous Poisson process, a linear fit to the points in a CA plot will have a slope of one. Slopes of greater than one indicate a nonhomogenous Poisson process, with increasing occurrence. Slopes of less than one indicate a nonhomogenous Poisson process, with decreasing occurrence. Changes in slope, known as "cusps," indicate a change in process, which could be an improvement or a degradation. After presenting the CA conceptual framework, examples are given of trending slips, trips and falls, and ergonomic incidents at NASA (from Agency-level data). Crow-AMSAA plotting is a robust tool for trending safety mishaps that can provide insight into safety performance over time.

Modelling recurrent events: comparison of statistical models with continuous and discontinuous risk intervals on recurrent malaria episodes data

PubMed Central

2014-01-01

Background Recurrent events data analysis is common in biomedicine. Literature review indicates that most statistical models used for such data are often based on time to the first event or consider events within a subject as independent. Even when taking into account the non-independence of recurrent events within subjects, data analyses are mostly done with continuous risk interval models, which may not be appropriate for treatments with sustained effects (e.g., drug treatments of malaria patients). Furthermore, results can be biased in cases of a confounding factor implying different risk exposure, e.g. in malaria transmission: if subjects are located at zones showing different environmental factors implying different risk exposures. Methods This work aimed to compare four different approaches by analysing recurrent malaria episodes from a clinical trial assessing the effectiveness of three malaria treatments [artesunate + amodiaquine (AS + AQ), artesunate + sulphadoxine-pyrimethamine (AS + SP) or artemether-lumefantrine (AL)], with continuous and discontinuous risk intervals: Andersen-Gill counting process (AG-CP), Prentice-Williams-Peterson counting process (PWP-CP), a shared gamma frailty model, and Generalized Estimating Equations model (GEE) using Poisson distribution. Simulations were also made to analyse the impact of the addition of a confounding factor on malaria recurrent episodes. Results Using the discontinuous interval analysis, AG-CP and Shared gamma frailty models provided similar estimations of treatment effect on malaria recurrent episodes when adjusted on age category. The patients had significant decreased risk of recurrent malaria episodes when treated with AS + AQ or AS + SP arms compared to AL arm; Relative Risks were: 0.75 (95% CI (Confidence Interval): 0.62-0.89), 0.74 (95% CI: 0.62-0.88) respectively for AG-CP model and 0.76 (95% CI: 0.64-0.89), 0.74 (95% CI: 0.62-0.87) for the Shared gamma frailty model. With both discontinuous and continuous risk intervals analysis, GEE Poisson distribution models failed to detect the effect of AS + AQ arm compared to AL arm when adjusted for age category. The discontinuous risk interval analysis was found to be the more appropriate approach. Conclusion Repeated event in infectious diseases such as malaria can be analysed with appropriate existing models that account for the correlation between multiple events within subjects with common statistical software packages, after properly setting up the data structures. PMID:25073652

Progress on Discrete Fracture Network models with implications on the predictions of permeability and flow channeling structure

NASA Astrophysics Data System (ADS)

Darcel, C.; Davy, P.; Le Goc, R.; Maillot, J.; Selroos, J. O.

2017-12-01

We present progress on Discrete Fracture Network (DFN) flow modeling, including realistic advanced DFN spatial structures and local fracture transmissivity properties, through an application to the Forsmark site in Sweden. DFN models are a framework to combine fracture datasets from different sources and scales and to interpolate them in combining statistical distributions and stereological relations. The resulting DFN upscaling function - size density distribution - is a model component key to extrapolating fracture size densities between data gaps, from borehole core up to site scale. Another important feature of DFN models lays in the spatial correlations between fractures, with still unevaluated consequences on flow predictions. Indeed, although common Poisson (i.e. spatially random) models are widely used, they do not reflect these geological evidences for more complex structures. To model them, we define a DFN growth process from kinematic rules for nucleation, growth and stopping conditions. It mimics in a simplified way the geological fracturing processes and produces DFN characteristics -both upscaling function and spatial correlations- fully consistent with field observations. DFN structures are first compared for constant transmissivities. Flow simulations for the kinematic and equivalent Poisson DFN models show striking differences: with the kinematic DFN, connectivity and permeability are significantly smaller, down to a difference of one order of magnitude, and flow is much more channelized. Further flow analyses are performed with more realistic transmissivity distribution conditions (sealed parts, relations to fracture sizes, orientations and in-situ stress field). The relative importance of the overall DFN structure in the final flow predictions is discussed.

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2017-07-01

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<β and β>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve. © 2016 Society for Risk Analysis.

Using the Gamma-Poisson Model to Predict Library Circulations.

ERIC Educational Resources Information Center

Burrell, Quentin L.

1990-01-01

Argues that the gamma mixture of Poisson processes, for all its perceived defects, can be used to make predictions regarding future library book circulations of a quality adequate for general management requirements. The use of the model is extensively illustrated with data from two academic libraries. (Nine references) (CLB)

Extensions of Rasch's Multiplicative Poisson Model.

ERIC Educational Resources Information Center

Jansen, Margo G. H.; van Duijn, Marijtje A. J.

1992-01-01

A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)

Poisson-Based Inference for Perturbation Models in Adaptive Spelling Training

ERIC Educational Resources Information Center

Baschera, Gian-Marco; Gross, Markus

2010-01-01

We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

NASA Astrophysics Data System (ADS)

Konno, Hidetoshi; Tamura, Yoshiyasu

2018-01-01

In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).

An efficient parallel sampling technique for Multivariate Poisson-Lognormal model: Analysis with two crash count datasets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhan, Xianyuan; Aziz, H. M. Abdul; Ukkusuri, Satish V.

Our study investigates the Multivariate Poisson-lognormal (MVPLN) model that jointly models crash frequency and severity accounting for correlations. The ordinary univariate count models analyze crashes of different severity level separately ignoring the correlations among severity levels. The MVPLN model is capable to incorporate the general correlation structure and takes account of the over dispersion in the data that leads to a superior data fitting. But, the traditional estimation approach for MVPLN model is computationally expensive, which often limits the use of MVPLN model in practice. In this work, a parallel sampling scheme is introduced to improve the original Markov Chainmore » Monte Carlo (MCMC) estimation approach of the MVPLN model, which significantly reduces the model estimation time. Two MVPLN models are developed using the pedestrian vehicle crash data collected in New York City from 2002 to 2006, and the highway-injury data from Washington State (5-year data from 1990 to 1994) The Deviance Information Criteria (DIC) is used to evaluate the model fitting. The estimation results show that the MVPLN models provide a superior fit over univariate Poisson-lognormal (PLN), univariate Poisson, and Negative Binomial models. Moreover, the correlations among the latent effects of different severity levels are found significant in both datasets that justifies the importance of jointly modeling crash frequency and severity accounting for correlations.« less

An efficient parallel sampling technique for Multivariate Poisson-Lognormal model: Analysis with two crash count datasets

DOE PAGES

Zhan, Xianyuan; Aziz, H. M. Abdul; Ukkusuri, Satish V.

2015-11-19

Our study investigates the Multivariate Poisson-lognormal (MVPLN) model that jointly models crash frequency and severity accounting for correlations. The ordinary univariate count models analyze crashes of different severity level separately ignoring the correlations among severity levels. The MVPLN model is capable to incorporate the general correlation structure and takes account of the over dispersion in the data that leads to a superior data fitting. But, the traditional estimation approach for MVPLN model is computationally expensive, which often limits the use of MVPLN model in practice. In this work, a parallel sampling scheme is introduced to improve the original Markov Chainmore » Monte Carlo (MCMC) estimation approach of the MVPLN model, which significantly reduces the model estimation time. Two MVPLN models are developed using the pedestrian vehicle crash data collected in New York City from 2002 to 2006, and the highway-injury data from Washington State (5-year data from 1990 to 1994) The Deviance Information Criteria (DIC) is used to evaluate the model fitting. The estimation results show that the MVPLN models provide a superior fit over univariate Poisson-lognormal (PLN), univariate Poisson, and Negative Binomial models. Moreover, the correlations among the latent effects of different severity levels are found significant in both datasets that justifies the importance of jointly modeling crash frequency and severity accounting for correlations.« less

Dynamics of a prey-predator system under Poisson white noise excitation

NASA Astrophysics Data System (ADS)

Pan, Shan-Shan; Zhu, Wei-Qiu

2014-10-01

The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

Bayesian semi-parametric analysis of Poisson change-point regression models: application to policy making in Cali, Colombia.

PubMed

Park, Taeyoung; Krafty, Robert T; Sánchez, Alvaro I

2012-07-27

A Poisson regression model with an offset assumes a constant baseline rate after accounting for measured covariates, which may lead to biased estimates of coefficients in an inhomogeneous Poisson process. To correctly estimate the effect of time-dependent covariates, we propose a Poisson change-point regression model with an offset that allows a time-varying baseline rate. When the nonconstant pattern of a log baseline rate is modeled with a nonparametric step function, the resulting semi-parametric model involves a model component of varying dimension and thus requires a sophisticated varying-dimensional inference to obtain correct estimates of model parameters of fixed dimension. To fit the proposed varying-dimensional model, we devise a state-of-the-art MCMC-type algorithm based on partial collapse. The proposed model and methods are used to investigate an association between daily homicide rates in Cali, Colombia and policies that restrict the hours during which the legal sale of alcoholic beverages is permitted. While simultaneously identifying the latent changes in the baseline homicide rate which correspond to the incidence of sociopolitical events, we explore the effect of policies governing the sale of alcohol on homicide rates and seek a policy that balances the economic and cultural dependencies on alcohol sales to the health of the public.

Negative Binomial Process Count and Mixture Modeling.

PubMed

Zhou, Mingyuan; Carin, Lawrence

2015-02-01

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

Multivariate poisson lognormal modeling of crashes by type and severity on rural two lane highways.

PubMed

Wang, Kai; Ivan, John N; Ravishanker, Nalini; Jackson, Eric

2017-02-01

In an effort to improve traffic safety, there has been considerable interest in estimating crash prediction models and identifying factors contributing to crashes. To account for crash frequency variations among crash types and severities, crash prediction models have been estimated by type and severity. The univariate crash count models have been used by researchers to estimate crashes by crash type or severity, in which the crash counts by type or severity are assumed to be independent of one another and modelled separately. When considering crash types and severities simultaneously, this may neglect the potential correlations between crash counts due to the presence of shared unobserved factors across crash types or severities for a specific roadway intersection or segment, and might lead to biased parameter estimation and reduce model accuracy. The focus on this study is to estimate crashes by both crash type and crash severity using the Integrated Nested Laplace Approximation (INLA) Multivariate Poisson Lognormal (MVPLN) model, and identify the different effects of contributing factors on different crash type and severity counts on rural two-lane highways. The INLA MVPLN model can simultaneously model crash counts by crash type and crash severity by accounting for the potential correlations among them and significantly decreases the computational time compared with a fully Bayesian fitting of the MVPLN model using Markov Chain Monte Carlo (MCMC) method. This paper describes estimation of MVPLN models for three-way stop controlled (3ST) intersections, four-way stop controlled (4ST) intersections, four-way signalized (4SG) intersections, and roadway segments on rural two-lane highways. Annual Average Daily traffic (AADT) and variables describing roadway conditions (including presence of lighting, presence of left-turn/right-turn lane, lane width and shoulder width) were used as predictors. A Univariate Poisson Lognormal (UPLN) was estimated by crash type and severity for each highway facility, and their prediction results are compared with the MVPLN model based on the Average Predicted Mean Absolute Error (APMAE) statistic. A UPLN model for total crashes was also estimated to compare the coefficients of contributing factors with the models that estimate crashes by crash type and severity. The model coefficient estimates show that the signs of coefficients for presence of left-turn lane, presence of right-turn lane, land width and speed limit are different across crash type or severity counts, which suggest that estimating crashes by crash type or severity might be more helpful in identifying crash contributing factors. The standard errors of covariates in the MVPLN model are slightly lower than the UPLN model when the covariates are statistically significant, and the crash counts by crash type and severity are significantly correlated. The model prediction comparisons illustrate that the MVPLN model outperforms the UPLN model in prediction accuracy. Therefore, when predicting crash counts by crash type and crash severity for rural two-lane highways, the MVPLN model should be considered to avoid estimation error and to account for the potential correlations among crash type counts and crash severity counts. Copyright © 2016 Elsevier Ltd. All rights reserved.

A comparative study of count models: application to pedestrian-vehicle crashes along Malaysia federal roads.

PubMed

Hosseinpour, Mehdi; Pour, Mehdi Hossein; Prasetijo, Joewono; Yahaya, Ahmad Shukri; Ghadiri, Seyed Mohammad Reza

2013-01-01

The objective of this study was to examine the effects of various roadway characteristics on the incidence of pedestrian-vehicle crashes by developing a set of crash prediction models on 543 km of Malaysia federal roads over a 4-year time span between 2007 and 2010. Four count models including the Poisson, negative binomial (NB), hurdle Poisson (HP), and hurdle negative binomial (HNB) models were developed and compared to model the number of pedestrian crashes. The results indicated the presence of overdispersion in the pedestrian crashes (PCs) and showed that it is due to excess zero rather than variability in the crash data. To handle the issue, the hurdle Poisson model was found to be the best model among the considered models in terms of comparative measures. Moreover, the variables average daily traffic, heavy vehicle traffic, speed limit, land use, and area type were significantly associated with PCs.

Entanglement complexity in quantum many-body dynamics, thermalization, and localization

NASA Astrophysics Data System (ADS)

Yang, Zhi-Cheng; Hamma, Alioscia; Giampaolo, Salvatore M.; Mucciolo, Eduardo R.; Chamon, Claudio

2017-07-01

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.

Statistical analysis of excitation energies in actinide and rare-earth nuclei

NASA Astrophysics Data System (ADS)

Levon, A. I.; Magner, A. G.; Radionov, S. V.

2018-04-01

Statistical analysis of distributions of the collective states in actinide and rare-earth nuclei is performed in terms of the nearest-neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of rare-earth and actinide nuclei. The spectra are closer to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter result is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings, and our linear approach improves the comparison with experimental data at all desired spacings.

On the statistical properties of viral misinformation in online social media

NASA Astrophysics Data System (ADS)

Bessi, Alessandro

2017-03-01

The massive diffusion of online social media allows for the rapid and uncontrolled spreading of conspiracy theories, hoaxes, unsubstantiated claims, and false news. Such an impressive amount of misinformation can influence policy preferences and encourage behaviors strongly divergent from recommended practices. In this paper, we study the statistical properties of viral misinformation in online social media. By means of methods belonging to Extreme Value Theory, we show that the number of extremely viral posts over time follows a homogeneous Poisson process, and that the interarrival times between such posts are independent and identically distributed, following an exponential distribution. Moreover, we characterize the uncertainty around the rate parameter of the Poisson process through Bayesian methods. Finally, we are able to derive the predictive posterior probability distribution of the number of posts exceeding a certain threshold of shares over a finite interval of time.

A Negative Binomial Regression Model for Accuracy Tests

ERIC Educational Resources Information Center

Hung, Lai-Fa

2012-01-01

Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an…

Modeling environmental noise exceedances using non-homogeneous Poisson processes.

PubMed

Guarnaccia, Claudio; Quartieri, Joseph; Barrios, Juan M; Rodrigues, Eliane R

2014-10-01

In this work a non-homogeneous Poisson model is considered to study noise exposure. The Poisson process, counting the number of times that a sound level surpasses a threshold, is used to estimate the probability that a population is exposed to high levels of noise a certain number of times in a given time interval. The rate function of the Poisson process is assumed to be of a Weibull type. The presented model is applied to community noise data from Messina, Sicily (Italy). Four sets of data are used to estimate the parameters involved in the model. After the estimation and tuning are made, a way of estimating the probability that an environmental noise threshold is exceeded a certain number of times in a given time interval is presented. This estimation can be very useful in the study of noise exposure of a population and also to predict, given the current behavior of the data, the probability of occurrence of high levels of noise in the near future. One of the most important features of the model is that it implicitly takes into account different noise sources, which need to be treated separately when using usual models.

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

PubMed Central

Yang, Sejung; Lee, Byung-Uk

2015-01-01

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138

Large-area measurements of CIB power spectra with Planck HFI maps

NASA Astrophysics Data System (ADS)

Mak, D. S. Y.; Challinor, A.; Efstathiou, G.; Lagache, G.

We present new measurements of the power spectra of the cosmic infrared background (CIB) anisotropies using the Planck 2015 full-mission HFI data at 353, 545, and 857 GHz over 20 000 square degrees. Unlike previous Planck measurements of the CIB power spectra, we do not rely on external HI data to remove Galactic dust emission from the Planck maps. Instead, we model the Galactic emission at the level of the power spectra, using templates constructed directly from the Planck data by exploiting the statistical isotropy of all extragalactic emission components. This allows us to work at the full resolution of Planck over large sky areas. We construct a likelihood based on the measured spectra (for multipoles 50 <= l <= 2500) using analytic covariance matrices that account for masking and the realistic instrumental noise properties. The results of an MCMC exploration of this likelihood are presented, based on simple parameterised models of the CIB power that arises from clustering of infrared galaxies. We explore simultaneously the parameters describing the clustered power, the Poisson power levels, and the amplitudes of the Galactic power spectrum templates across the six frequency (cross-)spectra. The best-fit model provides a good fit to all spectra. As an example, Fig. 1 compares the measured auto spectra at 353, 545, and 857 GHz over 40% of the sky to the power in the best-fit model. We find that the power in the CIB anisotropies from galaxy clustering is roughly equal to the Poisson power at multipoles l =2000 (the clustered power dominates on larger scales), and that our dust-cleaned CIB spectra are in good agreement with previous Planck and Herschel measurements. A key feature of our analysis is that it allows one to make many internal consistency tests. We show that our results are stable to data selection and choice of survey area, demonstrating both our ability to remove Galactic dust power to high accuracy and the statistical isotropy of the CIB signal.

21st Century Projections of High Streamflow Events in the UK and Germany

NASA Astrophysics Data System (ADS)

Cioffi, Francesco; Rosario Conticello, Federico; Lall, Upmanu; Merz, Bruno

2017-04-01

Radiative effects of anthropogenic changes in atmospheric composition are expected to enhance the hydrological cycle leading to more frequent and intense floods. To explore if there will be an increased risk of river flooding in the future, 21st century projections under global warming scenarios of High Streamflow Events (HSEs) for UK and German rivers are carried out, using a model that statistically relates large-scale atmospheric predictors - 850 hPa Geopotential Height (GPH850) and Integrated Water Vapor Transport (IVT) - to the occurrence of HSEs in one or simultaneously in several streamflow gauges. Here, HSE is defined as the streamflow exceeding the 99th percentile of daily flowrate time series measured at streamflow gauges. For the common period 1960-2012, historical data from 57 streamflow gauges in UK and 61 streamflow gauges in Germany, as well as, reanalysis data of GPH850 and IVT fields, bounded from 90W to 70E and from 20N to 80N are used. The link between GPH850 configurations and HSEs, and more precisely, identification of the GPH850 states potentially able to generate HSEs, is performed by a combined Kohonen Networks (Self Organized Map, SOM) and Event Syncronization approach. Complex network and modularity methods are used to cluster streamflow gauges that share common GPH850 configurations. Then a model based on a conditional Poisson distribution, in which the parameter of the Poisson distribution is assumed to be a nonlinear function of GPH850 and IVT, allows for the identification of GPH850 state and threshold of IVT beyond which there is the HSE highest probability. Using that model, projections of 21st century changes in frequency of HSEs occurrence in UK and Germany are estimated using the simulated fields of GPH850 and IVT from selected GCMs belonging to the Coupled Model Inter-comparison Project Phase 5 (CMIP5). Among the different GCMs, those are selected whose retrospective predictor fields have consistent statistics with the corresponding reanalysis data.

Dead time corrections for inbeam γ-spectroscopy measurements

NASA Astrophysics Data System (ADS)

Boromiza, M.; Borcea, C.; Negret, A.; Olacel, A.; Suliman, G.

2017-08-01

Relatively high counting rates were registered in a proton inelastic scattering experiment on 16O and 28Si using HPGe detectors which was performed at the Tandem facility of IFIN-HH, Bucharest. In consequence, dead time corrections were needed in order to determine the absolute γ-production cross sections. Considering that the real counting rate follows a Poisson distribution, the dead time correction procedure is reformulated in statistical terms. The arriving time interval between the incoming events (Δt) obeys an exponential distribution with a single parameter - the average of the associated Poisson distribution. We use this mathematical connection to calculate and implement the dead time corrections for the counting rates of the mentioned experiment. Also, exploiting an idea introduced by Pommé et al., we describe a consistent method for calculating the dead time correction which completely eludes the complicated problem of measuring the dead time of a given detection system. Several comparisons are made between the corrections implemented through this method and by using standard (phenomenological) dead time models and we show how these results were used for correcting our experimental cross sections.

Numerical solutions for patterns statistics on Markov chains.

PubMed

Nuel, Gregory

2006-01-01

We propose here a review of the methods available to compute pattern statistics on text generated by a Markov source. Theoretical, but also numerical aspects are detailed for a wide range of techniques (exact, Gaussian, large deviations, binomial and compound Poisson). The SPatt package (Statistics for Pattern, free software available at http://stat.genopole.cnrs.fr/spatt) implementing all these methods is then used to compare all these approaches in terms of computational time and reliability in the most complete pattern statistics benchmark available at the present time.

Atmospheric pollutants and hospital admissions due to pneumonia in children

PubMed Central

Negrisoli, Juliana; Nascimento, Luiz Fernando C.

2013-01-01

OBJECTIVE: To analyze the relationship between exposure to air pollutants and hospitalizations due to pneumonia in children of Sorocaba, São Paulo, Brazil. METHODS: Time series ecological study, from 2007 to 2008. Daily data were obtained from the State Environmental Agency for Pollution Control for particulate matter, nitric oxide, nitrogen dioxide, ozone, besides air temperature and relative humidity. The data concerning pneumonia admissions were collected in the public health system of Sorocaba. Correlations between the variables of interest using Pearson cofficient were calculated. Models with lags from zero to five days after exposure to pollutants were performed to analyze the association between the exposure to environmental pollutants and hospital admissions. The analysis used the generalized linear model of Poisson regression, being significant p<0.05. RESULTS: There were 1,825 admissions for pneumonia, with a daily mean of 2.5±2.1. There was a strong correlation between pollutants and hospital admissions, except for ozone. Regarding the Poisson regression analysis with the multi-pollutant model, only nitrogen dioxide was statistically significant in the same day (relative risk - RR=1.016), as well as particulate matter with a lag of four days (RR=1.009) after exposure to pollutants. CONCLUSIONS: There was an acute effect of exposure to nitrogen dioxide and a later effect of exposure to particulate matter on children hospitalizations for pneumonia in Sorocaba. PMID:24473956

Critical elements on fitting the Bayesian multivariate Poisson Lognormal model

NASA Astrophysics Data System (ADS)

Zamzuri, Zamira Hasanah binti

2015-10-01

Motivated by a problem on fitting multivariate models to traffic accident data, a detailed discussion of the Multivariate Poisson Lognormal (MPL) model is presented. This paper reveals three critical elements on fitting the MPL model: the setting of initial estimates, hyperparameters and tuning parameters. These issues have not been highlighted in the literature. Based on simulation studies conducted, we have shown that to use the Univariate Poisson Model (UPM) estimates as starting values, at least 20,000 iterations are needed to obtain reliable final estimates. We also illustrated the sensitivity of the specific hyperparameter, which if it is not given extra attention, may affect the final estimates. The last issue is regarding the tuning parameters where they depend on the acceptance rate. Finally, a heuristic algorithm to fit the MPL model is presented. This acts as a guide to ensure that the model works satisfactorily given any data set.

Analytical model for the threshold voltage of III-V nanowire transistors including quantum effects

NASA Astrophysics Data System (ADS)

Marin, E. G.; Ruiz, F. G.; Tienda-Luna, I. M.; Godoy, A.; Gámiz, F.

2014-02-01

In this work we propose an analytical model for the threshold voltage (VT) of III-V cylindrical nanowires, that takes into consideration the two dimensional quantum confinement of the carriers, the Fermi-Dirac statistics, the wave-function penetration into the gate insulator and the non-parabolicity of the conduction band structure. A simple expression for VT is obtained assuming some suitable approximations. The model results are compared to those of a 2D self consistent Schrödinger-Poisson solver, demonstrating a good fit for different III-V materials, insulator thicknesses and nanowire sizes with diameter down to 5 nm. The VT dependence on the confinement effective mass is discussed. The different contributions to VT are analyzed showing significant variations among different III-V materials.

Poisson Growth Mixture Modeling of Intensive Longitudinal Data: An Application to Smoking Cessation Behavior

ERIC Educational Resources Information Center

Shiyko, Mariya P.; Li, Yuelin; Rindskopf, David

2012-01-01

Intensive longitudinal data (ILD) have become increasingly common in the social and behavioral sciences; count variables, such as the number of daily smoked cigarettes, are frequently used outcomes in many ILD studies. We demonstrate a generalized extension of growth mixture modeling (GMM) to Poisson-distributed ILD for identifying qualitatively…

Comparing meta-analysis and ecological-longitudinal analysis in time-series studies. A case study of the effects of air pollution on mortality in three Spanish cities.

PubMed

Saez, M; Figueiras, A; Ballester, F; Pérez-Hoyos, S; Ocaña, R; Tobías, A

2001-06-01

The objective of this paper is to introduce a different approach, called the ecological-longitudinal, to carrying out pooled analysis in time series ecological studies. Because it gives a larger number of data points and, hence, increases the statistical power of the analysis, this approach, unlike conventional ones, allows the complementation of aspects such as accommodation of random effect models, of lags, of interaction between pollutants and between pollutants and meteorological variables, that are hardly implemented in conventional approaches. The approach is illustrated by providing quantitative estimates of the short-term effects of air pollution on mortality in three Spanish cities, Barcelona, Valencia and Vigo, for the period 1992-1994. Because the dependent variable was a count, a Poisson generalised linear model was first specified. Several modelling issues are worth mentioning. Firstly, because the relations between mortality and explanatory variables were non-linear, cubic splines were used for covariate control, leading to a generalised additive model, GAM. Secondly, the effects of the predictors on the response were allowed to occur with some lag. Thirdly, the residual autocorrelation, because of imperfect control, was controlled for by means of an autoregressive Poisson GAM. Finally, the longitudinal design demanded the consideration of the existence of individual heterogeneity, requiring the consideration of mixed models. The estimates of the relative risks obtained from the individual analyses varied across cities, particularly those associated with sulphur dioxide. The highest relative risks corresponded to black smoke in Valencia. These estimates were higher than those obtained from the ecological-longitudinal analysis. Relative risks estimated from this latter analysis were practically identical across cities, 1.00638 (95% confidence intervals 1.0002, 1.0011) for a black smoke increase of 10 microg/m(3) and 1.00415 (95% CI 1.0001, 1.0007) for a increase of 10 microg/m(3) of sulphur dioxide. Because the statistical power is higher than in the individual analysis more interactions were statistically significant, especially those among air pollutants and meteorological variables. Air pollutant levels were related to mortality in the three cities of the study, Barcelona, Valencia and Vigo. These results were consistent with similar studies in other cities, with other multicentric studies and coherent with both, previous individual, for each city, and multicentric studies for all three cities.

Anonymous birth law saves babies--optimization, sustainability and public awareness.

PubMed

Grylli, Chryssa; Brockington, Ian; Fiala, Christian; Huscsava, Mercedes; Waldhoer, Thomas; Klier, Claudia M

2016-04-01

The aims of this study are to assess the impact of Austria's anonymous birth law from the time relevant statistical records are available and to evaluate the use of hatches versus anonymous hospital delivery. This study is a complete census of police-reported neonaticides (1975-2012) as well as anonymous births including baby hatches in Austria during 2002-2012. The time trends of neonaticide rates, anonymous births and baby hatches were analysed by means of Poisson and logistic regression model. Predicted and observed rates were derived and compared using a Bayesian Poisson regression model. Predicted numbers of neonaticides for the period of the active awareness campaign, 2002-2004, were more than three times larger than the observed number (p = 0.0067). Of the 365 women who benefitted from this legislation, only 11.5% chose to put their babies in a baby hatch. Since the law was introduced, a significant decreasing tendency of numbers of anonymous births (p = 047) was observed, while there was significant increase of neonaticide rates (p = 0.0001). The implementation of the anonymous delivery law is associated with a decrease in the number of police-reported neonaticides. The subsequent significantly decreasing numbers of anonymous births with an accompanying increase of neonaticides represents additional evidence for the effectiveness of the measure.

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics.

PubMed

Li, Dongming; Sun, Changming; Yang, Jinhua; Liu, Huan; Peng, Jiaqi; Zhang, Lijuan

2017-04-06

An adaptive optics (AO) system provides real-time compensation for atmospheric turbulence. However, an AO image is usually of poor contrast because of the nature of the imaging process, meaning that the image contains information coming from both out-of-focus and in-focus planes of the object, which also brings about a loss in quality. In this paper, we present a robust multi-frame adaptive optics image restoration algorithm via maximum likelihood estimation. Our proposed algorithm uses a maximum likelihood method with image regularization as the basic principle, and constructs the joint log likelihood function for multi-frame AO images based on a Poisson distribution model. To begin with, a frame selection method based on image variance is applied to the observed multi-frame AO images to select images with better quality to improve the convergence of a blind deconvolution algorithm. Then, by combining the imaging conditions and the AO system properties, a point spread function estimation model is built. Finally, we develop our iterative solutions for AO image restoration addressing the joint deconvolution issue. We conduct a number of experiments to evaluate the performances of our proposed algorithm. Experimental results show that our algorithm produces accurate AO image restoration results and outperforms the current state-of-the-art blind deconvolution methods.

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics

PubMed Central

Li, Dongming; Sun, Changming; Yang, Jinhua; Liu, Huan; Peng, Jiaqi; Zhang, Lijuan

2017-01-01

An adaptive optics (AO) system provides real-time compensation for atmospheric turbulence. However, an AO image is usually of poor contrast because of the nature of the imaging process, meaning that the image contains information coming from both out-of-focus and in-focus planes of the object, which also brings about a loss in quality. In this paper, we present a robust multi-frame adaptive optics image restoration algorithm via maximum likelihood estimation. Our proposed algorithm uses a maximum likelihood method with image regularization as the basic principle, and constructs the joint log likelihood function for multi-frame AO images based on a Poisson distribution model. To begin with, a frame selection method based on image variance is applied to the observed multi-frame AO images to select images with better quality to improve the convergence of a blind deconvolution algorithm. Then, by combining the imaging conditions and the AO system properties, a point spread function estimation model is built. Finally, we develop our iterative solutions for AO image restoration addressing the joint deconvolution issue. We conduct a number of experiments to evaluate the performances of our proposed algorithm. Experimental results show that our algorithm produces accurate AO image restoration results and outperforms the current state-of-the-art blind deconvolution methods. PMID:28383503

A generalized Poisson solver for first-principles device simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch; Brück, Sascha

2016-01-28

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative methodmore » in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.« less

Independence of the effective dielectric constant of an electrolytic solution on the ionic distribution in the linear Poisson-Nernst-Planck model.

PubMed

Alexe-Ionescu, A L; Barbero, G; Lelidis, I

2014-08-28

We consider the influence of the spatial dependence of the ions distribution on the effective dielectric constant of an electrolytic solution. We show that in the linear version of the Poisson-Nernst-Planck model, the effective dielectric constant of the solution has to be considered independent of any ionic distribution induced by the external field. This result follows from the fact that, in the linear approximation of the Poisson-Nernst-Planck model, the redistribution of the ions in the solvent due to the external field gives rise to a variation of the dielectric constant that is of the first order in the effective potential, and therefore it has to be neglected in the Poisson's equation that relates the actual electric potential across the electrolytic cell to the bulk density of ions. The analysis is performed in the case where the electrodes are perfectly blocking and the adsorption at the electrodes is negligible, and in the absence of any ion dissociation-recombination effect.

Evaluation of Shiryaev-Roberts Procedure for On-line Environmental Radiation Monitoring

NASA Astrophysics Data System (ADS)

Watson, Mara Mae

An on-line radiation monitoring system that simultaneously concentrates and detects radioactivity is needed to detect an accidental leakage from a nuclear waste disposal facility or clandestine nuclear activity. Previous studies have shown that classical control chart methods can be applied to on-line radiation monitoring data to quickly detect these events as they occur; however, Bayesian control chart methods were not included in these studies. This work will evaluate the performance of a Bayesian control chart method, the Shiryaev-Roberts (SR) procedure, compared to classical control chart methods, Shewhart 3-sigma and cumulative sum (CUSUM), for use in on-line radiation monitoring of 99Tc in water using extractive scintillating resin. Measurements were collected by pumping solutions containing 0.1-5 Bq/L of 99Tc, as 99T cO4-, through a flow cell packed with extractive scintillating resin coupled to a Beta-RAM Model 5 HPLC detector. While 99T cO4- accumulated on the resin, simultaneous measurements were acquired in 10-s intervals and then re-binned to 100-s intervals. The Bayesian statistical method, Shiryaev-Roberts procedure, and classical control chart methods, Shewhart 3-sigma and cumulative sum (CUSUM), were applied to the data using statistical algorithms developed in MATLAB RTM. Two SR control charts were constructed using Poisson distributions and Gaussian distributions to estimate the likelihood ratio, and are referred to as Poisson SR and Gaussian SR to indicate the distribution used to calculate the statistic. The Poisson and Gaussian SR methods required as little as 28.9 mL less solution at 5 Bq/L and as much as 170 mL less solution at 0.5 Bq/L to exceed the control limit than the Shewhart 3-sigma method. The Poisson SR method needed as little as 6.20 mL less solution at 5 Bq/L and up to 125 mL less solution at 0.5 Bq/L to exceed the control limit than the CUSUM method. The Gaussian SR and CUSUM method required comparable solution volumes for test solutions containing at least 1.5 Bq/L of 99T c. For activity concentrations less than 1.5 Bq/L, the Gaussian SR method required as much as 40.8 mL less solution at 0.5 Bq/L to exceed the control limit than the CUSUM method. Both SR methods were able to consistently detect test solutions containing 0.1 Bq/L, unlike the Shewhart 3-sigma and CUSUM methods. Although the Poisson SR method required as much as 178 mL less solution to exceed the control limit than the Gaussian SR method, the Gaussian SR false positive of 0% was much lower than the Poisson SR false positive rate of 1.14%. A lower false positive rate made it easier to differentiate between a false positive and an increase in mean count rate caused by activity accumulating on the resin. The SR procedure is thus the ideal tool for low-level on-line radiation monitoring using extractive scintillating resin, because it needed less volume in most cases to detect an upward shift in the mean count rate than the Shewhart 3-sigma and CUSUM methods and consistently detected lower activity concentrations. The desired results for the monitoring scheme, however, need to be considered prior to choosing between the Poisson and Gaussian distribution to estimate the likelihood ratio, because each was advantageous under different circumstances. Once the control limit was exceeded, activity concentrations were estimated from the SR control chart using the slope of the control chart on a semi-logarithmic plot. Five of nine test solutions for the Poisson SR control chart produced concentration estimates within 30% of the actual value, but the worst case was 263.2% different than the actual value. The estimations for the Gaussian SR control chart were much more precise, with six of eight solutions producing estimates within 30%. Although the activity concentrations estimations were only mediocre for the Poisson SR control chart and satisfactory for the Gaussian SR control chart, these results demonstrate that a relationship exists between activity concentration and the SR control chart magnitude that can be exploited to determine the activity concentration from the SR control chart. More complex methods should be investigated to improve activity concentration estimations from the SR control charts.

Holographic study of conventional and negative Poisson's ratio metallic foams - Elasticity, yield and micro-deformation

NASA Technical Reports Server (NTRS)

Chen, C. P.; Lakes, R. S.

1991-01-01

An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modeling on the basis of cellular rib bending. The reentrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.

Zero-state Markov switching count-data models: an empirical assessment.

PubMed

Malyshkina, Nataliya V; Mannering, Fred L

2010-01-01

In this study, a two-state Markov switching count-data model is proposed as an alternative to zero-inflated models to account for the preponderance of zeros sometimes observed in transportation count data, such as the number of accidents occurring on a roadway segment over some period of time. For this accident-frequency case, zero-inflated models assume the existence of two states: one of the states is a zero-accident count state, which has accident probabilities that are so low that they cannot be statistically distinguished from zero, and the other state is a normal-count state, in which counts can be non-negative integers that are generated by some counting process, for example, a Poisson or negative binomial. While zero-inflated models have come under some criticism with regard to accident-frequency applications - one fact is undeniable - in many applications they provide a statistically superior fit to the data. The Markov switching approach we propose seeks to overcome some of the criticism associated with the zero-accident state of the zero-inflated model by allowing individual roadway segments to switch between zero and normal-count states over time. An important advantage of this Markov switching approach is that it allows for the direct statistical estimation of the specific roadway-segment state (i.e., zero-accident or normal-count state) whereas traditional zero-inflated models do not. To demonstrate the applicability of this approach, a two-state Markov switching negative binomial model (estimated with Bayesian inference) and standard zero-inflated negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. It is shown that the Markov switching model is a viable alternative and results in a superior statistical fit relative to the zero-inflated models.

Likelihood inference for COM-Poisson cure rate model with interval-censored data and Weibull lifetimes.

PubMed

Pal, Suvra; Balakrishnan, N

2017-10-01

In this paper, we consider a competing cause scenario and assume the number of competing causes to follow a Conway-Maxwell Poisson distribution which can capture both over and under dispersion that is usually encountered in discrete data. Assuming the population of interest having a component cure and the form of the data to be interval censored, as opposed to the usually considered right-censored data, the main contribution is in developing the steps of the expectation maximization algorithm for the determination of the maximum likelihood estimates of the model parameters of the flexible Conway-Maxwell Poisson cure rate model with Weibull lifetimes. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination within the Conway-Maxwell Poisson distribution is addressed using the likelihood ratio test and information-based criteria to select a suitable competing cause distribution that provides the best fit to the data. A simulation study is also carried out to demonstrate the loss in efficiency when selecting an improper competing cause distribution which justifies the use of a flexible family of distributions for the number of competing causes. Finally, the proposed methodology and the flexibility of the Conway-Maxwell Poisson distribution are illustrated with two known data sets from the literature: smoking cessation data and breast cosmesis data.

Introduction to the use of regression models in epidemiology.

PubMed

Bender, Ralf

2009-01-01

Regression modeling is one of the most important statistical techniques used in analytical epidemiology. By means of regression models the effect of one or several explanatory variables (e.g., exposures, subject characteristics, risk factors) on a response variable such as mortality or cancer can be investigated. From multiple regression models, adjusted effect estimates can be obtained that take the effect of potential confounders into account. Regression methods can be applied in all epidemiologic study designs so that they represent a universal tool for data analysis in epidemiology. Different kinds of regression models have been developed in dependence on the measurement scale of the response variable and the study design. The most important methods are linear regression for continuous outcomes, logistic regression for binary outcomes, Cox regression for time-to-event data, and Poisson regression for frequencies and rates. This chapter provides a nontechnical introduction to these regression models with illustrating examples from cancer research.

Measuring mouse retina response near the detection threshold to direct stimulation of photons with sub-poisson statistics

NASA Astrophysics Data System (ADS)

Tavala, Amir; Dovzhik, Krishna; Schicker, Klaus; Koschak, Alexandra; Zeilinger, Anton

Probing the visual system of human and animals at very low photon rate regime has recently attracted the quantum optics community. In an experiment on the isolated photoreceptor cells of Xenopus, the cell output signal was measured while stimulating it by pulses with sub-poisson distributed photons. The results showed single photon detection efficiency of 29 +/-4.7% [1]. Another behavioral experiment on human suggests a less detection capability at perception level with the chance of 0.516 +/-0.01 (i.e. slightly better than random guess) [2]. Although the species are different, both biological models and experimental observations with classical light stimuli expect that a fraction of single photon responses is filtered somewhere within the retina network and/or during the neural processes in the brain. In this ongoing experiment, we look for a quantitative answer to this question by measuring the output signals of the last neural layer of WT mouse retina using microelectrode arrays. We use a heralded downconversion single-photon source. We stimulate the retina directly since the eye lens (responsible for 20-50% of optical loss and scattering [2]) is being removed. Here, we demonstrate our first results that confirms the response to the sub-poisson distributied pulses. This project was supported by Austrian Academy of Sciences, SFB FoQuS F 4007-N23 funded by FWF and ERC QIT4QAD 227844 funded by EU Commission.

Testing a Poisson Counter Model for Visual Identification of Briefly Presented, Mutually Confusable Single Stimuli in Pure Accuracy Tasks

ERIC Educational Resources Information Center

Kyllingsbaek, Soren; Markussen, Bo; Bundesen, Claus

2012-01-01

The authors propose and test a simple model of the time course of visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks. The model implies that during stimulus analysis, tentative categorizations that stimulus i belongs to category j are made at a constant Poisson rate, v(i, j). The analysis is…

Renewal processes based on generalized Mittag-Leffler waiting times

NASA Astrophysics Data System (ADS)

Cahoy, Dexter O.; Polito, Federico

2013-03-01

The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized the standard and fractional Poisson processes through the waiting time distribution, and showed their relations to an integral operator with a generalized Mittag-Leffler function in the kernel. The waiting times of the proposed renewal processes have the generalized Mittag-Leffler and stretched-squashed Mittag-Leffler distributions. Note that the generalizations naturally provide greater flexibility in modeling real-life renewal processes. Algorithms to simulate sample paths and to estimate the model parameters are derived. Note also that these procedures are necessary to make these models more usable in practice. State probabilities and other qualitative or quantitative features of the models are also discussed.

Simulation on Poisson and negative binomial models of count road accident modeling

NASA Astrophysics Data System (ADS)

Sapuan, M. S.; Razali, A. M.; Zamzuri, Z. H.; Ibrahim, K.

2016-11-01

Accident count data have often been shown to have overdispersion. On the other hand, the data might contain zero count (excess zeros). The simulation study was conducted to create a scenarios which an accident happen in T-junction with the assumption the dependent variables of generated data follows certain distribution namely Poisson and negative binomial distribution with different sample size of n=30 to n=500. The study objective was accomplished by fitting Poisson regression, negative binomial regression and Hurdle negative binomial model to the simulated data. The model validation was compared and the simulation result shows for each different sample size, not all model fit the data nicely even though the data generated from its own distribution especially when the sample size is larger. Furthermore, the larger sample size indicates that more zeros accident count in the dataset.

Nonlocal Poisson-Fermi double-layer models: Effects of nonuniform ion sizes on double-layer structure

NASA Astrophysics Data System (ADS)

Xie, Dexuan; Jiang, Yi

2018-05-01

This paper reports a nonuniform ionic size nonlocal Poisson-Fermi double-layer model (nuNPF) and a uniform ionic size nonlocal Poisson-Fermi double-layer model (uNPF) for an electrolyte mixture of multiple ionic species, variable voltages on electrodes, and variable induced charges on boundary segments. The finite element solvers of nuNPF and uNPF are developed and applied to typical double-layer tests defined on a rectangular box, a hollow sphere, and a hollow rectangle with a charged post. Numerical results show that nuNPF can significantly improve the quality of the ionic concentrations and electric fields generated from uNPF, implying that the effect of nonuniform ion sizes is a key consideration in modeling the double-layer structure.

Performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data.

PubMed

Yelland, Lisa N; Salter, Amy B; Ryan, Philip

2011-10-15

Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.

Changes in alcohol consumption in the 50- to 64-year-old European economically active population during an economic crisis.

PubMed

Bosque-Prous, Marina; Kunst, Anton E; Brugal, M Teresa; Espelt, Albert

2017-08-01

The aim was to compare alcohol drinking patterns in economically active people aged 50-64 years before the last economic crisis (2006) and during the crisis (2013). Cross-sectional study with data from 25 479 economically active people aged 50-64 years resident in 11 European countries who participated in wave 2 or wave 5 of the SHARE project (2006 and 2013). The outcome variables were hazardous drinking, abstention in previous 3 months and the weekly average number of drinks per drinker. The prevalence ratios of hazardous drinking and abstention, comparing the prevalence in 2013 vs. 2006, were estimated with Poisson regression models with robust variance, and the changes in the number of drinks per week with Poisson regression models. The prevalence of hazardous drinking decreased among both men (PR = 0.75; 95%CI = 0.63-0.92) and women (PR = 0.91; 95%CI = 0.72-1.15), although the latter decrease was smaller and not statistically significant. The proportion of abstainers increased among both men (PR = 1.11; 95%CI = 0.99-1.29) and women (PR = 1.18; 95%CI = 1.07-1.30), although the former increase was smaller and not statistically significant. The weekly average number of drinks per drinker decreased in men and women. The decreases in consumption were larger in Italy and Spain. From 2006 to 2013, the amount of alcohol consumed by late working age drinkers decreased in Europe, with more pronounced declines in the countries hardest hit by the economic crisis. © The Author 2017. Published by Oxford University Press on behalf of the European Public Health Association. All rights reserved.

Initial evaluation of discrete orthogonal basis reconstruction of ECT images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moody, E.B.; Donohue, K.D.

1996-12-31

Discrete orthogonal basis restoration (DOBR) is a linear, non-iterative, and robust method for solving inverse problems for systems characterized by shift-variant transfer functions. This simulation study evaluates the feasibility of using DOBR for reconstructing emission computed tomographic (ECT) images. The imaging system model uses typical SPECT parameters and incorporates the effects of attenuation, spatially-variant PSF, and Poisson noise in the projection process. Sample reconstructions and statistical error analyses for a class of digital phantoms compare the DOBR performance for Hartley and Walsh basis functions. Test results confirm that DOBR with either basis set produces images with good statistical properties. Nomore » problems were encountered with reconstruction instability. The flexibility of the DOBR method and its consistent performance warrants further investigation of DOBR as a means of ECT image reconstruction.« less

Extended Poisson process modelling and analysis of grouped binary data.

PubMed

Faddy, Malcolm J; Smith, David M

2012-05-01

A simple extension of the Poisson process results in binomially distributed counts of events in a time interval. A further extension generalises this to probability distributions under- or over-dispersed relative to the binomial distribution. Substantial levels of under-dispersion are possible with this modelling, but only modest levels of over-dispersion - up to Poisson-like variation. Although simple analytical expressions for the moments of these probability distributions are not available, approximate expressions for the mean and variance are derived, and used to re-parameterise the models. The modelling is applied in the analysis of two published data sets, one showing under-dispersion and the other over-dispersion. More appropriate assessment of the precision of estimated parameters and reliable model checking diagnostics follow from this more general modelling of these data sets. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mixed Poisson distributions in exact solutions of stochastic autoregulation models.

PubMed

Iyer-Biswas, Srividya; Jayaprakash, C

2014-11-01

In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.

Seasonally adjusted birth frequencies follow the Poisson distribution.

PubMed

Barra, Mathias; Lindstrøm, Jonas C; Adams, Samantha S; Augestad, Liv A

2015-12-15

Variations in birth frequencies have an impact on activity planning in maternity wards. Previous studies of this phenomenon have commonly included elective births. A Danish study of spontaneous births found that birth frequencies were well modelled by a Poisson process. Somewhat unexpectedly, there were also weekly variations in the frequency of spontaneous births. Another study claimed that birth frequencies follow the Benford distribution. Our objective was to test these results. We analysed 50,017 spontaneous births at Akershus University Hospital in the period 1999-2014. To investigate the Poisson distribution of these births, we plotted their variance over a sliding average. We specified various Poisson regression models, with the number of births on a given day as the outcome variable. The explanatory variables included various combinations of years, months, days of the week and the digit sum of the date. The relationship between the variance and the average fits well with an underlying Poisson process. A Benford distribution was disproved by a goodness-of-fit test (p < 0.01). The fundamental model with year and month as explanatory variables is significantly improved (p < 0.001) by adding day of the week as an explanatory variable. Altogether 7.5% more children are born on Tuesdays than on Sundays. The digit sum of the date is non-significant as an explanatory variable (p = 0.23), nor does it increase the explained variance. INERPRETATION: Spontaneous births are well modelled by a time-dependent Poisson process when monthly and day-of-the-week variation is included. The frequency is highest in summer towards June and July, Friday and Tuesday stand out as particularly busy days, and the activity level is at its lowest during weekends.

Transcriptional dynamics with time-dependent reaction rates

NASA Astrophysics Data System (ADS)

Nandi, Shubhendu; Ghosh, Anandamohan

2015-02-01

Transcription is the first step in the process of gene regulation that controls cell response to varying environmental conditions. Transcription is a stochastic process, involving synthesis and degradation of mRNAs, that can be modeled as a birth-death process. We consider a generic stochastic model, where the fluctuating environment is encoded in the time-dependent reaction rates. We obtain an exact analytical expression for the mRNA probability distribution and are able to analyze the response for arbitrary time-dependent protocols. Our analytical results and stochastic simulations confirm that the transcriptional machinery primarily act as a low-pass filter. We also show that depending on the system parameters, the mRNA levels in a cell population can show synchronous/asynchronous fluctuations and can deviate from Poisson statistics.

Stage-structured transmission of phocine distemper virus in the Dutch 2002 outbreak

PubMed Central

Klepac, Petra; Pomeroy, Laura W.; Bjørnstad, Ottar N.; Kuiken, Thijs; Osterhaus, Albert D.M.E.; Rijks, Jolianne M.

2009-01-01

Heterogeneities in transmission among hosts can be very important in shaping infectious disease dynamics. In mammals with strong social organization, such heterogeneities are often structured by functional stage: juveniles, subadults and adults. We investigate the importance of such stage-related heterogeneities in shaping the 2002 phocine distemper virus (PDV) outbreak in the Dutch Wadden Sea, when more than 40 per cent of the harbour seals were killed. We do this by comparing the statistical fit of a hierarchy of models with varying transmission complexity: homogeneous versus heterogeneous mixing and density- versus frequency-dependent transmission. We use the stranding data as a proxy for incidence and use Poisson likelihoods to estimate the ‘who acquires infection from whom’ (WAIFW) matrix. Statistically, the model with strong heterogeneous mixing and density-dependent transmission was found to best describe the transmission dynamics. However, patterns of incidence support a model of frequency-dependent transmission among adults and juveniles. Based on the maximum-likelihood WAIFW matrix estimates, we use the next-generation formalism to calculate an R0 between 2 and 2.5 for the Dutch 2002 PDV epidemic. PMID:19364743

Comparison of RF spectrum prediction methods for dynamic spectrum access

NASA Astrophysics Data System (ADS)

Kovarskiy, Jacob A.; Martone, Anthony F.; Gallagher, Kyle A.; Sherbondy, Kelly D.; Narayanan, Ram M.

2017-05-01

Dynamic spectrum access (DSA) refers to the adaptive utilization of today's busy electromagnetic spectrum. Cognitive radio/radar technologies require DSA to intelligently transmit and receive information in changing environments. Predicting radio frequency (RF) activity reduces sensing time and energy consumption for identifying usable spectrum. Typical spectrum prediction methods involve modeling spectral statistics with Hidden Markov Models (HMM) or various neural network structures. HMMs describe the time-varying state probabilities of Markov processes as a dynamic Bayesian network. Neural Networks model biological brain neuron connections to perform a wide range of complex and often non-linear computations. This work compares HMM, Multilayer Perceptron (MLP), and Recurrent Neural Network (RNN) algorithms and their ability to perform RF channel state prediction. Monte Carlo simulations on both measured and simulated spectrum data evaluate the performance of these algorithms. Generalizing spectrum occupancy as an alternating renewal process allows Poisson random variables to generate simulated data while energy detection determines the occupancy state of measured RF spectrum data for testing. The results suggest that neural networks achieve better prediction accuracy and prove more adaptable to changing spectral statistics than HMMs given sufficient training data.

LD-SPatt: large deviations statistics for patterns on Markov chains.

PubMed

Nuel, G

2004-01-01

Statistics on Markov chains are widely used for the study of patterns in biological sequences. Statistics on these models can be done through several approaches. Central limit theorem (CLT) producing Gaussian approximations are one of the most popular ones. Unfortunately, in order to find a pattern of interest, these methods have to deal with tail distribution events where CLT is especially bad. In this paper, we propose a new approach based on the large deviations theory to assess pattern statistics. We first recall theoretical results for empiric mean (level 1) as well as empiric distribution (level 2) large deviations on Markov chains. Then, we present the applications of these results focusing on numerical issues. LD-SPatt is the name of GPL software implementing these algorithms. We compare this approach to several existing ones in terms of complexity and reliability and show that the large deviations are more reliable than the Gaussian approximations in absolute values as well as in terms of ranking and are at least as reliable as compound Poisson approximations. We then finally discuss some further possible improvements and applications of this new method.

Compound estimation procedures in reliability

NASA Technical Reports Server (NTRS)

Barnes, Ron

1990-01-01

At NASA, components and subsystems of components in the Space Shuttle and Space Station generally go through a number of redesign stages. While data on failures for various design stages are sometimes available, the classical procedures for evaluating reliability only utilize the failure data on the present design stage of the component or subsystem. Often, few or no failures have been recorded on the present design stage. Previously, Bayesian estimators for the reliability of a single component, conditioned on the failure data for the present design, were developed. These new estimators permit NASA to evaluate the reliability, even when few or no failures have been recorded. Point estimates for the latter evaluation were not possible with the classical procedures. Since different design stages of a component (or subsystem) generally have a good deal in common, the development of new statistical procedures for evaluating the reliability, which consider the entire failure record for all design stages, has great intuitive appeal. A typical subsystem consists of a number of different components and each component has evolved through a number of redesign stages. The present investigations considered compound estimation procedures and related models. Such models permit the statistical consideration of all design stages of each component and thus incorporate all the available failure data to obtain estimates for the reliability of the present version of the component (or subsystem). A number of models were considered to estimate the reliability of a component conditioned on its total failure history from two design stages. It was determined that reliability estimators for the present design stage, conditioned on the complete failure history for two design stages have lower risk than the corresponding estimators conditioned only on the most recent design failure data. Several models were explored and preliminary models involving bivariate Poisson distribution and the Consael Process (a bivariate Poisson process) were developed. Possible short comings of the models are noted. An example is given to illustrate the procedures. These investigations are ongoing with the aim of developing estimators that extend to components (and subsystems) with three or more design stages.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

PubMed

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Studying Resist Stochastics with the Multivariate Poisson Propagation Model

DOE PAGES

Naulleau, Patrick; Anderson, Christopher; Chao, Weilun; ...

2014-01-01

Progress in the ultimate performance of extreme ultraviolet resist has arguably decelerated in recent years suggesting an approach to stochastic limits both in photon counts and material parameters. Here we report on the performance of a variety of leading extreme ultraviolet resist both with and without chemical amplification. The measured performance is compared to stochastic modeling results using the Multivariate Poisson Propagation Model. The results show that the best materials are indeed nearing modeled performance limits.

Physical properties of biophotons and their biological functions.

PubMed

Chang, Jiin-Ju

2008-05-01

Biophotons (BPHs) are weak photons within or emitted from living organisms. The intensities of BPHs range from a few to several hundred photons s(-1) x cm(-2). BPH emission originates from a de-localized coherent electromagnetic field within the living organisms and is regulated by the field. In this paper based on the experimental results of Poisson and sub-Poisson distributions of photocount statistics, the coherent properties of BPHs and their functions in cell communication are described. Discussions are made on functions which BPHs may play in DNA and proteins functioning including the process of DNA replication, protein synthesis and cell signalling and in oxidative phosporylation and photosynthesis.

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.

PubMed

Chen, Duan

2017-11-01

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

Optimizing the maximum reported cluster size in the spatial scan statistic for ordinal data.

PubMed

Kim, Sehwi; Jung, Inkyung

2017-01-01

The spatial scan statistic is an important tool for spatial cluster detection. There have been numerous studies on scanning window shapes. However, little research has been done on the maximum scanning window size or maximum reported cluster size. Recently, Han et al. proposed to use the Gini coefficient to optimize the maximum reported cluster size. However, the method has been developed and evaluated only for the Poisson model. We adopt the Gini coefficient to be applicable to the spatial scan statistic for ordinal data to determine the optimal maximum reported cluster size. Through a simulation study and application to a real data example, we evaluate the performance of the proposed approach. With some sophisticated modification, the Gini coefficient can be effectively employed for the ordinal model. The Gini coefficient most often picked the optimal maximum reported cluster sizes that were the same as or smaller than the true cluster sizes with very high accuracy. It seems that we can obtain a more refined collection of clusters by using the Gini coefficient. The Gini coefficient developed specifically for the ordinal model can be useful for optimizing the maximum reported cluster size for ordinal data and helpful for properly and informatively discovering cluster patterns.

Optimizing the maximum reported cluster size in the spatial scan statistic for ordinal data

PubMed Central

Kim, Sehwi

2017-01-01

The spatial scan statistic is an important tool for spatial cluster detection. There have been numerous studies on scanning window shapes. However, little research has been done on the maximum scanning window size or maximum reported cluster size. Recently, Han et al. proposed to use the Gini coefficient to optimize the maximum reported cluster size. However, the method has been developed and evaluated only for the Poisson model. We adopt the Gini coefficient to be applicable to the spatial scan statistic for ordinal data to determine the optimal maximum reported cluster size. Through a simulation study and application to a real data example, we evaluate the performance of the proposed approach. With some sophisticated modification, the Gini coefficient can be effectively employed for the ordinal model. The Gini coefficient most often picked the optimal maximum reported cluster sizes that were the same as or smaller than the true cluster sizes with very high accuracy. It seems that we can obtain a more refined collection of clusters by using the Gini coefficient. The Gini coefficient developed specifically for the ordinal model can be useful for optimizing the maximum reported cluster size for ordinal data and helpful for properly and informatively discovering cluster patterns. PMID:28753674

Statistical image reconstruction from correlated data with applications to PET

PubMed Central

Alessio, Adam; Sauer, Ken; Kinahan, Paul

2008-01-01

Most statistical reconstruction methods for emission tomography are designed for data modeled as conditionally independent Poisson variates. In reality, due to scanner detectors, electronics and data processing, correlations are introduced into the data resulting in dependent variates. In general, these correlations are ignored because they are difficult to measure and lead to computationally challenging statistical reconstruction algorithms. This work addresses the second concern, seeking to simplify the reconstruction of correlated data and provide a more precise image estimate than the conventional independent methods. In general, correlated variates have a large non-diagonal covariance matrix that is computationally challenging to use as a weighting term in a reconstruction algorithm. This work proposes two methods to simplify the use of a non-diagonal covariance matrix as the weighting term by (a) limiting the number of dimensions in which the correlations are modeled and (b) adopting flexible, yet computationally tractable, models for correlation structure. We apply and test these methods with simple simulated PET data and data processed with the Fourier rebinning algorithm which include the one-dimensional correlations in the axial direction and the two-dimensional correlations in the transaxial directions. The methods are incorporated into a penalized weighted least-squares 2D reconstruction and compared with a conventional maximum a posteriori approach. PMID:17921576

Spontaneous action potentials and neural coding in unmyelinated axons.

PubMed

O'Donnell, Cian; van Rossum, Mark C W

2015-04-01

The voltage-gated Na and K channels in neurons are responsible for action potential generation. Because ion channels open and close in a stochastic fashion, spontaneous (ectopic) action potentials can result even in the absence of stimulation. While spontaneous action potentials have been studied in detail in single-compartment models, studies on spatially extended processes have been limited. The simulations and analysis presented here show that spontaneous rate in unmyelinated axon depends nonmonotonically on the length of the axon, that the spontaneous activity has sub-Poisson statistics, and that neural coding can be hampered by the spontaneous spikes by reducing the probability of transmitting the first spike in a train.

Three statistical models for estimating length of stay.

PubMed Central

Selvin, S

1977-01-01

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program. PMID:914532

Three statistical models for estimating length of stay.

PubMed

Selvin, S

1977-01-01

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program.

Characterization of x-ray framing cameras for the National Ignition Facility using single photon pulse height analysis.

PubMed

Holder, J P; Benedetti, L R; Bradley, D K

2016-11-01

Single hit pulse height analysis is applied to National Ignition Facility x-ray framing cameras to quantify gain and gain variation in a single micro-channel plate-based instrument. This method allows the separation of gain from detectability in these photon-detecting devices. While pulse heights measured by standard-DC calibration methods follow the expected exponential distribution at the limit of a compound-Poisson process, gain-gated pulse heights follow a more complex distribution that may be approximated as a weighted sum of a few exponentials. We can reproduce this behavior with a simple statistical-sampling model.

Analysis of field size distributions, LACIE test sites 5029, 5033, and 5039, Anhwei Province, People's Republic of China

NASA Technical Reports Server (NTRS)

Podwysocki, M. H.

1976-01-01

A study was made of the field size distributions for LACIE test sites 5029, 5033, and 5039, People's Republic of China. Field lengths and widths were measured from LANDSAT imagery, and field area was statistically modeled. Field size parameters have log-normal or Poisson frequency distributions. These were normalized to the Gaussian distribution and theoretical population curves were made. When compared to fields in other areas of the same country measured in the previous study, field lengths and widths in the three LACIE test sites were 2 to 3 times smaller and areas were smaller by an order of magnitude.

Study of non-Hodgkin's lymphoma mortality associated with industrial pollution in Spain, using Poisson models

PubMed Central

Ramis, Rebeca; Vidal, Enrique; García-Pérez, Javier; Lope, Virginia; Aragonés, Nuria; Pérez-Gómez, Beatriz; Pollán, Marina; López-Abente, Gonzalo

2009-01-01

Background Non-Hodgkin's lymphomas (NHLs) have been linked to proximity to industrial areas, but evidence regarding the health risk posed by residence near pollutant industries is very limited. The European Pollutant Emission Register (EPER) is a public register that furnishes valuable information on industries that release pollutants to air and water, along with their geographical location. This study sought to explore the relationship between NHL mortality in small areas in Spain and environmental exposure to pollutant emissions from EPER-registered industries, using three Poisson-regression-based mathematical models. Methods Observed cases were drawn from mortality registries in Spain for the period 1994–2003. Industries were grouped into the following sectors: energy; metal; mineral; organic chemicals; waste; paper; food; and use of solvents. Populations having an industry within a radius of 1, 1.5, or 2 kilometres from the municipal centroid were deemed to be exposed. Municipalities outside those radii were considered as reference populations. The relative risks (RRs) associated with proximity to pollutant industries were estimated using the following methods: Poisson Regression; mixed Poisson model with random provincial effect; and spatial autoregressive modelling (BYM model). Results Only proximity of paper industries to population centres (>2 km) could be associated with a greater risk of NHL mortality (mixed model: RR:1.24, 95% CI:1.09–1.42; BYM model: RR:1.21, 95% CI:1.01–1.45; Poisson model: RR:1.16, 95% CI:1.06–1.27). Spatial models yielded higher estimates. Conclusion The reported association between exposure to air pollution from the paper, pulp and board industry and NHL mortality is independent of the model used. Inclusion of spatial random effects terms in the risk estimate improves the study of associations between environmental exposures and mortality. The EPER could be of great utility when studying the effects of industrial pollution on the health of the population. PMID:19159450

p-brane actions and higher Roytenberg brackets

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2013-02-01

Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma models and corresponding dual string and p-brane models. We find that higher generalizations of the algebraic structures due to Dorfman, Roytenberg and Courant play an important role and establish their relation to Nambu-Poisson structures.

Pattern analysis of community health center location in Surabaya using spatial Poisson point process

NASA Astrophysics Data System (ADS)

Kusumaningrum, Choriah Margareta; Iriawan, Nur; Winahju, Wiwiek Setya

2017-11-01

Community health center (puskesmas) is one of the closest health service facilities for the community, which provide healthcare for population on sub-district level as one of the government-mandated community health clinics located across Indonesia. The increasing number of this puskesmas does not directly comply the fulfillment of basic health services needed in such region. Ideally, a puskesmas has to cover up to maximum 30,000 people. The number of puskesmas in Surabaya indicates an unbalance spread in all of the area. This research aims to analyze the spread of puskesmas in Surabaya using spatial Poisson point process model in order to get the effective location of Surabaya's puskesmas which based on their location. The results of the analysis showed that the distribution pattern of puskesmas in Surabaya is non-homogeneous Poisson process and is approched by mixture Poisson model. Based on the estimated model obtained by using Bayesian mixture model couple with MCMC process, some characteristics of each puskesmas have no significant influence as factors to decide the addition of health center in such location. Some factors related to the areas of sub-districts have to be considered as covariate to make a decision adding the puskesmas in Surabaya.

A physiologically based nonhomogeneous Poisson counter model of visual identification.

PubMed

Christensen, Jeppe H; Markussen, Bo; Bundesen, Claus; Kyllingsbæk, Søren

2018-04-30

A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects that are mutually confusable and hard to see. The model assumes that the visual system's initial sensory response consists in tentative visual categorizations, which are accumulated by leaky integration of both transient and sustained components comparable with those found in spike density patterns of early sensory neurons. The sensory response (tentative categorizations) feeds independent Poisson counters, each of which accumulates tentative object categorizations of a particular type to guide overt identification performance. We tested the model's ability to predict the effect of stimulus duration on observed distributions of responses in a nonspeeded (pure accuracy) identification task with eight response alternatives. The time courses of correct and erroneous categorizations were well accounted for when the event-rates of competing Poisson counters were allowed to vary independently over time in a way that mimicked the dynamics of receptive field selectivity as found in neurophysiological studies. Furthermore, the initial sensory response yielded theoretical hazard rate functions that closely resembled empirically estimated ones. Finally, supplied with a Naka-Rushton type contrast gain control, the model provided an explanation for Bloch's law. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Gene regulation and noise reduction by coupling of stochastic processes

NASA Astrophysics Data System (ADS)

Ramos, Alexandre F.; Hornos, José Eduardo M.; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Gene regulation and noise reduction by coupling of stochastic processes

PubMed Central

Hornos, José Eduardo M.; Reinitz, John

2015-01-01

Here we characterize the low noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the the two gene states depends on protein number. This fact has a very important implication: there exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction. PMID:25768447

Gene regulation and noise reduction by coupling of stochastic processes.

PubMed

Ramos, Alexandre F; Hornos, José Eduardo M; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Determination of oral mucosal Poisson's ratio and coefficient of friction from in-vivo contact pressure measurements.

PubMed

Chen, Junning; Suenaga, Hanako; Hogg, Michael; Li, Wei; Swain, Michael; Li, Qing

2016-01-01

Despite their considerable importance to biomechanics, there are no existing methods available to directly measure apparent Poisson's ratio and friction coefficient of oral mucosa. This study aimed to develop an inverse procedure to determine these two biomechanical parameters by utilizing in vivo experiment of contact pressure between partial denture and beneath mucosa through nonlinear finite element (FE) analysis and surrogate response surface (RS) modelling technique. First, the in vivo denture-mucosa contact pressure was measured by a tactile electronic sensing sheet. Second, a 3D FE model was constructed based on the patient CT images. Third, a range of apparent Poisson's ratios and the coefficients of friction from literature was considered as the design variables in a series of FE runs for constructing a RS surrogate model. Finally, the discrepancy between computed in silico and measured in vivo results was minimized to identify the best matching Poisson's ratio and coefficient of friction. The established non-invasive methodology was demonstrated effective to identify such biomechanical parameters of oral mucosa and can be potentially used for determining the biomaterial properties of other soft biological tissues.

Fractional Brownian motion and long term clinical trial recruitment

PubMed Central

Zhang, Qiang; Lai, Dejian

2015-01-01

Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations. PMID:26347306

Fractional Brownian motion and long term clinical trial recruitment.

PubMed

Zhang, Qiang; Lai, Dejian

2011-05-01

Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations.

surrosurv: An R package for the evaluation of failure time surrogate endpoints in individual patient data meta-analyses of randomized clinical trials.

PubMed

Rotolo, Federico; Paoletti, Xavier; Michiels, Stefan

2018-03-01

Surrogate endpoints are attractive for use in clinical trials instead of well-established endpoints because of practical convenience. To validate a surrogate endpoint, two important measures can be estimated in a meta-analytic context when individual patient data are available: the R indiv 2 or the Kendall's τ at the individual level, and the R trial 2 at the trial level. We aimed at providing an R implementation of classical and well-established as well as more recent statistical methods for surrogacy assessment with failure time endpoints. We also intended incorporating utilities for model checking and visualization and data generating methods described in the literature to date. In the case of failure time endpoints, the classical approach is based on two steps. First, a Kendall's τ is estimated as measure of individual level surrogacy using a copula model. Then, the R trial 2 is computed via a linear regression of the estimated treatment effects; at this second step, the estimation uncertainty can be accounted for via measurement-error model or via weights. In addition to the classical approach, we recently developed an approach based on bivariate auxiliary Poisson models with individual random effects to measure the Kendall's τ and treatment-by-trial interactions to measure the R trial 2 . The most common data simulation models described in the literature are based on: copula models, mixed proportional hazard models, and mixture of half-normal and exponential random variables. The R package surrosurv implements the classical two-step method with Clayton, Plackett, and Hougaard copulas. It also allows to optionally adjusting the second-step linear regression for measurement-error. The mixed Poisson approach is implemented with different reduced models in addition to the full model. We present the package functions for estimating the surrogacy models, for checking their convergence, for performing leave-one-trial-out cross-validation, and for plotting the results. We illustrate their use in practice on individual patient data from a meta-analysis of 4069 patients with advanced gastric cancer from 20 trials of chemotherapy. The surrosurv package provides an R implementation of classical and recent statistical methods for surrogacy assessment of failure time endpoints. Flexible simulation functions are available to generate data according to the methods described in the literature. Copyright © 2017 Elsevier B.V. All rights reserved.

Alpha, delta and theta rhythms in a neural net model. Comparison with MEG data.

PubMed

Kotini, A; Anninos, P

2016-01-07

The aim of this study is to provide information regarding the comparison of a neural model to MEG measurements. Our study population consisted of 10 epileptic patients and 10 normal subjects. The epileptic patients had high MEG amplitudes characterized with θ (4-7 Hz) or δ (2-3 Hz) rhythms and absence of α-rhythm (8-13 Hz). The statistical analysis of such activities corresponded to Poisson distribution. Conversely, the MEG from normal subjects had low amplitudes, higher frequencies and presence of α-rhythm (8-13 Hz). Such activities were not synchronized and their distributions were Gauss. These findings were in agreement with our theoretical neural model. The comparison of the neural network with MEG data provides information about the status of brain function in epileptic and normal states. Copyright © 2015 Elsevier Ltd. All rights reserved.

Accident prediction model for public highway-rail grade crossings.

PubMed

Lu, Pan; Tolliver, Denver

2016-05-01

Considerable research has focused on roadway accident frequency analysis, but relatively little research has examined safety evaluation at highway-rail grade crossings. Highway-rail grade crossings are critical spatial locations of utmost importance for transportation safety because traffic crashes at highway-rail grade crossings are often catastrophic with serious consequences. The Poisson regression model has been employed to analyze vehicle accident frequency as a good starting point for many years. The most commonly applied variations of Poisson including negative binomial, and zero-inflated Poisson. These models are used to deal with common crash data issues such as over-dispersion (sample variance is larger than the sample mean) and preponderance of zeros (low sample mean and small sample size). On rare occasions traffic crash data have been shown to be under-dispersed (sample variance is smaller than the sample mean) and traditional distributions such as Poisson or negative binomial cannot handle under-dispersion well. The objective of this study is to investigate and compare various alternate highway-rail grade crossing accident frequency models that can handle the under-dispersion issue. The contributions of the paper are two-fold: (1) application of probability models to deal with under-dispersion issues and (2) obtain insights regarding to vehicle crashes at public highway-rail grade crossings. Copyright © 2016 Elsevier Ltd. All rights reserved.

Formulation of the Multi-Hit Model With a Non-Poisson Distribution of Hits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassiliev, Oleg N., E-mail: Oleg.Vassiliev@albertahealthservices.ca

2012-07-15

Purpose: We proposed a formulation of the multi-hit single-target model in which the Poisson distribution of hits was replaced by a combination of two distributions: one for the number of particles entering the target and one for the number of hits a particle entering the target produces. Such an approach reflects the fact that radiation damage is a result of two different random processes: particle emission by a radiation source and interaction of particles with matter inside the target. Methods and Materials: Poisson distribution is well justified for the first of the two processes. The second distribution depends on howmore » a hit is defined. To test our approach, we assumed that the second distribution was also a Poisson distribution. The two distributions combined resulted in a non-Poisson distribution. We tested the proposed model by comparing it with previously reported data for DNA single- and double-strand breaks induced by protons and electrons, for survival of a range of cell lines, and variation of the initial slopes of survival curves with radiation quality for heavy-ion beams. Results: Analysis of cell survival equations for this new model showed that they had realistic properties overall, such as the initial and high-dose slopes of survival curves, the shoulder, and relative biological effectiveness (RBE) In most cases tested, a better fit of survival curves was achieved with the new model than with the linear-quadratic model. The results also suggested that the proposed approach may extend the multi-hit model beyond its traditional role in analysis of survival curves to predicting effects of radiation quality and analysis of DNA strand breaks. Conclusions: Our model, although conceptually simple, performed well in all tests. The model was able to consistently fit data for both cell survival and DNA single- and double-strand breaks. It correctly predicted the dependence of radiation effects on parameters of radiation quality.« less

Information transmission in hippocampal CA1 neuron models in the presence of poisson shot noise: the case of periodic sub-threshold spike trains.

PubMed

Kawaguchi, Minato; Mino, Hiroyuki; Durand, Dominique M

2006-01-01

This article presents an analysis of the information transmission of periodic sub-threshold spike trains in a hippocampal CA1 neuron model in the presence of a homogeneous Poisson shot noise. In the computer simulation, periodic sub-threshold spike trains were presented repeatedly to the midpoint of the main apical branch, while the homogeneous Poisson shot noise was applied to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the inter spike intervals were generated and then the probability, p(T), of the inter-spike interval histogram corresponding to the spike interval, r, of the periodic input spike trains was estimated to obtain an index of information transmission. In the present article, it is shown that at a specific amplitude of the homogeneous Poisson shot noise, p(T) was found to be maximized, as well as the possibility to encode the periodic sub-threshold spike trains became greater. It was implied that setting the amplitude of the homogeneous Poisson shot noise to the specific values which maximize the information transmission might contribute to efficiently encoding the periodic sub-threshold spike trains by utilizing the stochastic resonance.

Signal and noise modeling in confocal laser scanning fluorescence microscopy.

PubMed

Herberich, Gerlind; Windoffer, Reinhard; Leube, Rudolf E; Aach, Til

2012-01-01

Fluorescence confocal laser scanning microscopy (CLSM) has revolutionized imaging of subcellular structures in biomedical research by enabling the acquisition of 3D time-series of fluorescently-tagged proteins in living cells, hence forming the basis for an automated quantification of their morphological and dynamic characteristics. Due to the inherently weak fluorescence, CLSM images exhibit a low SNR. We present a novel model for the transfer of signal and noise in CLSM that is both theoretically sound as well as corroborated by a rigorous analysis of the pixel intensity statistics via measurement of the 3D noise power spectra, signal-dependence and distribution. Our model provides a better fit to the data than previously proposed models. Further, it forms the basis for (i) the simulation of the CLSM imaging process indispensable for the quantitative evaluation of CLSM image analysis algorithms, (ii) the application of Poisson denoising algorithms and (iii) the reconstruction of the fluorescence signal.

Mathematics make microbes beautiful, beneficial, and bountiful.

PubMed

Jungck, John R

2012-01-01

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning. Copyright © 2012 Elsevier Inc. All rights reserved.

Dengue hemorrhagic fever and typhoid fever association based on spatial standpoint using scan statistics in DKI Jakarta

NASA Astrophysics Data System (ADS)

Hervind, Widyaningsih, Y.

2017-07-01

Concurrent infection with multiple infectious agents may occur in one patient, it appears frequently in dengue hemorrhagic fever (DHF) and typhoid fever. This paper depicted association between DHF and typhoid based on spatial point of view. Since paucity of data regarding dengue and typhoid co-infection, data that be used are the number of patients of those diseases in every district (kecamatan) in Jakarta in 2014 and 2015 obtained from Jakarta surveillance website. Poisson spatial scan statistics is used to detect DHF and typhoid hotspots area district in Jakarta separately. After obtain the hotspot, Fisher's exact test is applied to validate association between those two diseases' hotspot. The result exhibit hotspots of DHF and typhoid are located around central Jakarta. The further analysis used Poisson space-time scan statistics to reveal the hotspot in term of spatial and time. DHF and typhoid fever more likely occurr from January until May in the area which is relatively similar with pure spatial result. Preventive action could be done especially in the hotspot areas and it is required further study to observe the causes based on characteristics of the hotspot area.

Generalized master equations for non-Poisson dynamics on networks.

PubMed

Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Generalized master equations for non-Poisson dynamics on networks

NASA Astrophysics Data System (ADS)

Hoffmann, Till; Porter, Mason A.; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Weber's law implies neural discharge more regular than a Poisson process.

PubMed

Kang, Jing; Wu, Jianhua; Smerieri, Anteo; Feng, Jianfeng

2010-03-01

Weber's law is one of the basic laws in psychophysics, but the link between this psychophysical behavior and the neuronal response has not yet been established. In this paper, we carried out an analysis on the spike train statistics when Weber's law holds, and found that the efferent spike train of a single neuron is less variable than a Poisson process. For population neurons, Weber's law is satisfied only when the population size is small (< 10 neurons). However, if the population neurons share a weak correlation in their discharges and individual neuronal spike train is more regular than a Poisson process, Weber's law is true without any restriction on the population size. Biased competition attractor network also demonstrates that the coefficient of variation of interspike interval in the winning pool should be less than one for the validity of Weber's law. Our work links Weber's law with neural firing property quantitatively, shedding light on the relation between psychophysical behavior and neuronal responses.

DQE as detection probability of the radiation detectors

NASA Astrophysics Data System (ADS)

Zanella, Giovanni

2008-02-01

In this paper it is shown that quantum efficiency (DQE), as commonly defined for imaging detectors, can be extended to all radiation detectors with the meaning of detection probability, if Poisson statistics applies. This unified approach is possible in time-domain at zero spatial-frequency.

Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

Tong, Howell

1995-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study

Imaging Analysis of the Hard X-Ray Telescope ProtoEXIST2 and New Techniques for High-Resolution Coded-Aperture Telescopes

NASA Technical Reports Server (NTRS)

Hong, Jaesub; Allen, Branden; Grindlay, Jonathan; Barthelmy, Scott D.

2016-01-01

Wide-field (greater than or approximately equal to 100 degrees squared) hard X-ray coded-aperture telescopes with high angular resolution (greater than or approximately equal to 2 minutes) will enable a wide range of time domain astrophysics. For instance, transient sources such as gamma-ray bursts can be precisely localized without the assistance of secondary focusing X-ray telescopes to enable rapid followup studies. On the other hand, high angular resolution in coded-aperture imaging introduces a new challenge in handling the systematic uncertainty: the average photon count per pixel is often too small to establish a proper background pattern or model the systematic uncertainty in a timescale where the model remains invariant. We introduce two new techniques to improve detection sensitivity, which are designed for, but not limited to, a high-resolution coded-aperture system: a self-background modeling scheme which utilizes continuous scan or dithering operations, and a Poisson-statistics based probabilistic approach to evaluate the significance of source detection without subtraction in handling the background. We illustrate these new imaging analysis techniques in high resolution coded-aperture telescope using the data acquired by the wide-field hard X-ray telescope ProtoEXIST2 during a high-altitude balloon flight in fall 2012. We review the imaging sensitivity of ProtoEXIST2 during the flight, and demonstrate the performance of the new techniques using our balloon flight data in comparison with a simulated ideal Poisson background.

A Poisson approach to the validation of failure time surrogate endpoints in individual patient data meta-analyses.

PubMed

Rotolo, Federico; Paoletti, Xavier; Burzykowski, Tomasz; Buyse, Marc; Michiels, Stefan

2017-01-01

Surrogate endpoints are often used in clinical trials instead of well-established hard endpoints for practical convenience. The meta-analytic approach relies on two measures of surrogacy: one at the individual level and one at the trial level. In the survival data setting, a two-step model based on copulas is commonly used. We present a new approach which employs a bivariate survival model with an individual random effect shared between the two endpoints and correlated treatment-by-trial interactions. We fit this model using auxiliary mixed Poisson models. We study via simulations the operating characteristics of this mixed Poisson approach as compared to the two-step copula approach. We illustrate the application of the methods on two individual patient data meta-analyses in gastric cancer, in the advanced setting (4069 patients from 20 randomized trials) and in the adjuvant setting (3288 patients from 14 randomized trials).

Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.

PubMed

Hougaard, P; Lee, M L; Whitmore, G A

1997-12-01

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction

NASA Technical Reports Server (NTRS)

Cohen, A. C.

1971-01-01

A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.

Noise parameter estimation for poisson corrupted images using variance stabilization transforms.

PubMed

Jin, Xiaodan; Xu, Zhenyu; Hirakawa, Keigo

2014-03-01

Noise is present in all images captured by real-world image sensors. Poisson distribution is said to model the stochastic nature of the photon arrival process and agrees with the distribution of measured pixel values. We propose a method for estimating unknown noise parameters from Poisson corrupted images using properties of variance stabilization. With a significantly lower computational complexity and improved stability, the proposed estimation technique yields noise parameters that are comparable in accuracy to the state-of-art methods.

Modeling number of claims and prediction of total claim amount

NASA Astrophysics Data System (ADS)

Acar, Aslıhan Şentürk; Karabey, Uǧur

2017-07-01

In this study we focus on annual number of claims of a private health insurance data set which belongs to a local insurance company in Turkey. In addition to Poisson model and negative binomial model, zero-inflated Poisson model and zero-inflated negative binomial model are used to model the number of claims in order to take into account excess zeros. To investigate the impact of different distributional assumptions for the number of claims on the prediction of total claim amount, predictive performances of candidate models are compared by using root mean square error (RMSE) and mean absolute error (MAE) criteria.

Variance to mean ratio, R(t), for poisson processes on phylogenetic trees.

PubMed

Goldman, N

1994-09-01

The ratio of expected variance to mean, R(t), of numbers of DNA base substitutions for contemporary sequences related by a "star" phylogeny is widely seen as a measure of the adherence of the sequences' evolution to a Poisson process with a molecular clock, as predicted by the "neutral theory" of molecular evolution under certain conditions. A number of estimators of R(t) have been proposed, all predicted to have mean 1 and distributions based on the chi 2. Various genes have previously been analyzed and found to have values of R(t) far in excess of 1, calling into question important aspects of the neutral theory. In this paper, I use Monte Carlo simulation to show that the previously suggested means and distributions of estimators of R(t) are highly inaccurate. The analysis is applied to star phylogenies and to general phylogenetic trees, and well-known gene sequences are reanalyzed. For star phylogenies the results show that Kimura's estimators ("The Neutral Theory of Molecular Evolution," Cambridge Univ. Press, Cambridge, 1983) are unsatisfactory for statistical testing of R(t), but confirm the accuracy of Bulmer's correction factor (Genetics 123: 615-619, 1989). For all three nonstar phylogenies studied, attained values of all three estimators of R(t), although larger than 1, are within their true confidence limits under simple Poisson process models. This shows that lineage effects can be responsible for high estimates of R(t), restoring some limited confidence in the molecular clock and showing that the distinction between lineage and molecular clock effects is vital.(ABSTRACT TRUNCATED AT 250 WORDS)

EM Adaptive LASSO—A Multilocus Modeling Strategy for Detecting SNPs Associated with Zero-inflated Count Phenotypes

PubMed Central

Mallick, Himel; Tiwari, Hemant K.

2016-01-01

Count data are increasingly ubiquitous in genetic association studies, where it is possible to observe excess zero counts as compared to what is expected based on standard assumptions. For instance, in rheumatology, data are usually collected in multiple joints within a person or multiple sub-regions of a joint, and it is not uncommon that the phenotypes contain enormous number of zeroes due to the presence of excessive zero counts in majority of patients. Most existing statistical methods assume that the count phenotypes follow one of these four distributions with appropriate dispersion-handling mechanisms: Poisson, Zero-inflated Poisson (ZIP), Negative Binomial, and Zero-inflated Negative Binomial (ZINB). However, little is known about their implications in genetic association studies. Also, there is a relative paucity of literature on their usefulness with respect to model misspecification and variable selection. In this article, we have investigated the performance of several state-of-the-art approaches for handling zero-inflated count data along with a novel penalized regression approach with an adaptive LASSO penalty, by simulating data under a variety of disease models and linkage disequilibrium patterns. By taking into account data-adaptive weights in the estimation procedure, the proposed method provides greater flexibility in multi-SNP modeling of zero-inflated count phenotypes. A fast coordinate descent algorithm nested within an EM (expectation-maximization) algorithm is implemented for estimating the model parameters and conducting variable selection simultaneously. Results show that the proposed method has optimal performance in the presence of multicollinearity, as measured by both prediction accuracy and empirical power, which is especially apparent as the sample size increases. Moreover, the Type I error rates become more or less uncontrollable for the competing methods when a model is misspecified, a phenomenon routinely encountered in practice. PMID:27066062

EM Adaptive LASSO-A Multilocus Modeling Strategy for Detecting SNPs Associated with Zero-inflated Count Phenotypes.

PubMed

Mallick, Himel; Tiwari, Hemant K

2016-01-01

Count data are increasingly ubiquitous in genetic association studies, where it is possible to observe excess zero counts as compared to what is expected based on standard assumptions. For instance, in rheumatology, data are usually collected in multiple joints within a person or multiple sub-regions of a joint, and it is not uncommon that the phenotypes contain enormous number of zeroes due to the presence of excessive zero counts in majority of patients. Most existing statistical methods assume that the count phenotypes follow one of these four distributions with appropriate dispersion-handling mechanisms: Poisson, Zero-inflated Poisson (ZIP), Negative Binomial, and Zero-inflated Negative Binomial (ZINB). However, little is known about their implications in genetic association studies. Also, there is a relative paucity of literature on their usefulness with respect to model misspecification and variable selection. In this article, we have investigated the performance of several state-of-the-art approaches for handling zero-inflated count data along with a novel penalized regression approach with an adaptive LASSO penalty, by simulating data under a variety of disease models and linkage disequilibrium patterns. By taking into account data-adaptive weights in the estimation procedure, the proposed method provides greater flexibility in multi-SNP modeling of zero-inflated count phenotypes. A fast coordinate descent algorithm nested within an EM (expectation-maximization) algorithm is implemented for estimating the model parameters and conducting variable selection simultaneously. Results show that the proposed method has optimal performance in the presence of multicollinearity, as measured by both prediction accuracy and empirical power, which is especially apparent as the sample size increases. Moreover, the Type I error rates become more or less uncontrollable for the competing methods when a model is misspecified, a phenomenon routinely encountered in practice.

Poisson Noise Removal in Spherical Multichannel Images: Application to Fermi data

NASA Astrophysics Data System (ADS)

Schmitt, Jérémy; Starck, Jean-Luc; Fadili, Jalal; Digel, Seth

2012-03-01

The Fermi Gamma-ray Space Telescope, which was launched by NASA in June 2008, is a powerful space observatory which studies the high-energy gamma-ray sky [5]. Fermi's main instrument, the Large Area Telescope (LAT), detects photons in an energy range between 20MeV and >300 GeV. The LAT is much more sensitive than its predecessor, the energetic gamma ray experiment telescope (EGRET) telescope on the Compton Gamma-ray Observatory, and is expected to find several thousand gamma-ray point sources, which is an order of magnitude more than its predecessor EGRET [13]. Even with its relatively large acceptance (∼2m2 sr), the number of photons detected by the LAT outside the Galactic plane and away from intense sources is relatively low and the sky overall has a diffuse glow from cosmic-ray interactions with interstellar gas and low energy photons that makes a background against which point sources need to be detected. In addition, the per-photon angular resolution of the LAT is relatively poor and strongly energy dependent, ranging from>10° at 20MeV to ∼0.1° above 100 GeV. Consequently, the spherical photon count images obtained by Fermi are degraded by the fluctuations on the number of detected photons. This kind of noise is strongly signal dependent : on the brightest parts of the image like the galactic plane or the brightest sources, we have a lot of photons per pixel, and so the photon noise is low. Outside the galactic plane, the number of photons per pixel is low, which means that the photon noise is high. Such a signal-dependent noise cannot be accurately modeled by a Gaussian distribution. The basic photon-imaging model assumes that the number of detected photons at each pixel location is Poisson distributed. More specifically, the image is considered as a realization of an inhomogeneous Poisson process. This statistical noise makes the source detection more difficult, consequently it is highly desirable to have an efficient denoising method for spherical Poisson data. Several techniques have been proposed in the literature to estimate Poisson intensity in 2-dimensional (2D). A major class of methods adopt a multiscale Bayesian framework specifically tailored for Poisson data [18], independently initiated by Timmerman and Nowak [23] and Kolaczyk [14]. Lefkimmiaits et al. [15] proposed an improved Bayesian framework for analyzing Poisson processes, based on a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities in adjacent scales are modeled as mixtures of conjugate parametric distributions. Another approach includes preprocessing the count data by a variance stabilizing transform(VST) such as theAnscombe [4] and the Fisz [10] transforms, applied respectively in the spatial [8] or in the wavelet domain [11]. The transform reforms the data so that the noise approximately becomes Gaussian with a constant variance. Standard techniques for independent identically distributed Gaussian noise are then used for denoising. Zhang et al. [25] proposed a powerful method called multiscale (MS-VST). It consists in combining a VST with a multiscale transform (wavelets, ridgelets, or curvelets), yielding asymptotically normally distributed coefficients with known variances. The interest of using a multiscale method is to exploit the sparsity properties of the data : the data are transformed into a domain in which it is sparse, and, as the noise is not sparse in any transform domain, it is easy to separate it from the signal. When the noise is Gaussian of known variance, it is easy to remove it with a high thresholding in the wavelet domain. The choice of the multiscale transform depends on the morphology of the data. Wavelets represent more efficiently regular structures and isotropic singularities, whereas ridgelets are designed to represent global lines in an image, and curvelets represent efficiently curvilinear contours. Significant coefficients are then detected with binary hypothesis testing, and the final estimate is reconstructed with an iterative scheme. In Ref

Dynamics of moment neuronal networks.

PubMed

Feng, Jianfeng; Deng, Yingchun; Rossoni, Enrico

2006-04-01

A theoretical framework is developed for moment neuronal networks (MNNs). Within this framework, the behavior of the system of spiking neurons is specified in terms of the first- and second-order statistics of their interspike intervals, i.e., the mean, the variance, and the cross correlations of spike activity. Since neurons emit and receive spike trains which can be described by renewal--but generally non-Poisson--processes, we first derive a suitable diffusion-type approximation of such processes. Two approximation schemes are introduced: the usual approximation scheme (UAS) and the Ornstein-Uhlenbeck scheme. It is found that both schemes approximate well the input-output characteristics of spiking models such as the IF and the Hodgkin-Huxley models. The MNN framework is then developed according to the UAS scheme, and its predictions are tested on a few examples.

Two-state Markov-chain Poisson nature of individual cellphone call statistics

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier

2016-07-01

Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.

Impact of Homeland Security Alert level on calls to a law enforcement peer support hotline.

PubMed

Omer, Saad B; Barnett, Daniel J; Castellano, Cherie; Wierzba, Rachel K; Hiremath, Girish S; Balicer, Ran D; Everly, George S

2007-01-01

The Homeland Security Advisory System (HSAS) was established by the Department of Homeland Security to communicate the risk of a terrorist event. In order to explore the potential psychological impacts of HSAS we analyzed the effects of terror alerts on the law enforcement community. We used data from the New Jersey Cop 2 Cop crisis intervention hotline. Incidence Rate Ratios--interpreted as average relative increases in the daily number of calls to the Cop 2 Cop hotline during an increased alert period--were computed from Poisson models. The hotline received a total of 4,145 initial calls during the study period. The mean daily number of calls was higher during alert level elevation compared to prior 7 days (7.68 vs. 8.00). In the Poisson regression analysis, the Incidence Rate Ratios of number of calls received during elevated alert levels compared to the reference period of seven days preceding each change in alert were close to 1, with confidence intervals crossing 1 (i.e. not statistically significant) for all lag periods evaluated. This investigation, in the context of New Jersey law enforcement personnel, does not support the concern that elevating the alert status places undue stress upon alert recipients.

A study of adverse birth outcomes and agricultural land use practices in Missouri.

PubMed

Almberg, Kirsten S; Turyk, Mary; Jones, Rachael M; Anderson, Robert; Graber, Judith; Banda, Elizabeth; Waller, Lance A; Gibson, Roger; Stayner, Leslie T

2014-10-01

Missouri is an agriculturally intensive state, primarily growing corn and soybeans with additional rice and cotton farming in some southeastern counties. Communities located in close proximity to pesticide-treated fields are known to have increased exposure to pesticides and may be at increased risk of adverse birth outcomes. The study aims were to assess the relationship between county-level measures of crop-specific agricultural production and adverse birth outcomes in Missouri and to evaluate the most appropriate statistical methodologies for doing so. Potential associations between county level data on the densities of particular crops and low birth weight and preterm births were examined in Missouri between 2004-2006. Covariates considered as potential confounders and effect modifiers included gender, maternal race/ethnicity, maternal age at delivery, maternal smoking, access to prenatal care, quarter of birth, county median household income, and population density. These data were analyzed using both standard Poisson regression models as well as models allowing for temporal and spatial correlation of the data. There was no evidence of an association between corn, soybean, or wheat densities with low birth weight or preterm births. Significant positive associations between both rice and cotton density were observed with both low birth weight and preterm births. Model results were consistent using Poisson and alternative models accounting for spatial and temporal variability. The associations of rice and cotton with low birth weight and preterm births warrant further investigation. Study limitations include the ecological study design and limited available covariate information. Copyright © 2014 Elsevier Inc. All rights reserved.

Estimating the empirical probability of submarine landslide occurrence

USGS Publications Warehouse

Geist, Eric L.; Parsons, Thomas E.; Mosher, David C.; Shipp, Craig; Moscardelli, Lorena; Chaytor, Jason D.; Baxter, Christopher D. P.; Lee, Homa J.; Urgeles, Roger

2010-01-01

The empirical probability for the occurrence of submarine landslides at a given location can be estimated from age dates of past landslides. In this study, tools developed to estimate earthquake probability from paleoseismic horizons are adapted to estimate submarine landslide probability. In both types of estimates, one has to account for the uncertainty associated with age-dating individual events as well as the open time intervals before and after the observed sequence of landslides. For observed sequences of submarine landslides, we typically only have the age date of the youngest event and possibly of a seismic horizon that lies below the oldest event in a landslide sequence. We use an empirical Bayes analysis based on the Poisson-Gamma conjugate prior model specifically applied to the landslide probability problem. This model assumes that landslide events as imaged in geophysical data are independent and occur in time according to a Poisson distribution characterized by a rate parameter λ. With this method, we are able to estimate the most likely value of λ and, importantly, the range of uncertainty in this estimate. Examples considered include landslide sequences observed in the Santa Barbara Channel, California, and in Port Valdez, Alaska. We confirm that given the uncertainties of age dating that landslide complexes can be treated as single events by performing statistical test of age dates representing the main failure episode of the Holocene Storegga landslide complex.

Soft network materials with isotropic negative Poisson's ratios over large strains.

PubMed

Liu, Jianxing; Zhang, Yihui

2018-01-31

Auxetic materials with negative Poisson's ratios have important applications across a broad range of engineering areas, such as biomedical devices, aerospace engineering and automotive engineering. A variety of design strategies have been developed to achieve artificial auxetic materials with controllable responses in the Poisson's ratio. The development of designs that can offer isotropic negative Poisson's ratios over large strains can open up new opportunities in emerging biomedical applications, which, however, remains a challenge. Here, we introduce deterministic routes to soft architected materials that can be tailored precisely to yield the values of Poisson's ratio in the range from -1 to 1, in an isotropic manner, with a tunable strain range from 0% to ∼90%. The designs rely on a network construction in a periodic lattice topology, which incorporates zigzag microstructures as building blocks to connect lattice nodes. Combined experimental and theoretical studies on broad classes of network topologies illustrate the wide-ranging utility of these concepts. Quantitative mechanics modeling under both infinitesimal and finite deformations allows the development of a rigorous design algorithm that determines the necessary network geometries to yield target Poisson ratios over desired strain ranges. Demonstrative examples in artificial skin with both the negative Poisson's ratio and the nonlinear stress-strain curve precisely matching those of the cat's skin and in unusual cylindrical structures with engineered Poisson effect and shape memory effect suggest potential applications of these network materials.

Updating a Classic: "The Poisson Distribution and the Supreme Court" Revisited

ERIC Educational Resources Information Center

Cole, Julio H.

2010-01-01

W. A. Wallis studied vacancies in the US Supreme Court over a 96-year period (1837-1932) and found that the distribution of the number of vacancies per year could be characterized by a Poisson model. This note updates this classic study.

Maximum likelihood-based analysis of single-molecule photon arrival trajectories

NASA Astrophysics Data System (ADS)

Hajdziona, Marta; Molski, Andrzej

2011-02-01

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 103 photons. When the intensity levels are well-separated and 104 photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

A Hierarchical Poisson Log-Normal Model for Network Inference from RNA Sequencing Data

PubMed Central

Gallopin, Mélina; Rau, Andrea; Jaffrézic, Florence

2013-01-01

Gene network inference from transcriptomic data is an important methodological challenge and a key aspect of systems biology. Although several methods have been proposed to infer networks from microarray data, there is a need for inference methods able to model RNA-seq data, which are count-based and highly variable. In this work we propose a hierarchical Poisson log-normal model with a Lasso penalty to infer gene networks from RNA-seq data; this model has the advantage of directly modelling discrete data and accounting for inter-sample variance larger than the sample mean. Using real microRNA-seq data from breast cancer tumors and simulations, we compare this method to a regularized Gaussian graphical model on log-transformed data, and a Poisson log-linear graphical model with a Lasso penalty on power-transformed data. For data simulated with large inter-sample dispersion, the proposed model performs better than the other methods in terms of sensitivity, specificity and area under the ROC curve. These results show the necessity of methods specifically designed for gene network inference from RNA-seq data. PMID:24147011

Distribution-free Inference of Zero-inated Binomial Data for Longitudinal Studies.

PubMed

He, H; Wang, W J; Hu, J; Gallop, R; Crits-Christoph, P; Xia, Y L

2015-10-01

Count reponses with structural zeros are very common in medical and psychosocial research, especially in alcohol and HIV research, and the zero-inflated poisson (ZIP) and zero-inflated negative binomial (ZINB) models are widely used for modeling such outcomes. However, as alcohol drinking outcomes such as days of drinkings are counts within a given period, their distributions are bounded above by an upper limit (total days in the period) and thus inherently follow a binomial or zero-inflated binomial (ZIB) distribution, rather than a Poisson or zero-inflated Poisson (ZIP) distribution, in the presence of structural zeros. In this paper, we develop a new semiparametric approach for modeling zero-inflated binomial (ZIB)-like count responses for cross-sectional as well as longitudinal data. We illustrate this approach with both simulated and real study data.

Do bacterial cell numbers follow a theoretical Poisson distribution? Comparison of experimentally obtained numbers of single cells with random number generation via computer simulation.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2016-12-01

We investigated a bacterial sample preparation procedure for single-cell studies. In the present study, we examined whether single bacterial cells obtained via 10-fold dilution followed a theoretical Poisson distribution. Four serotypes of Salmonella enterica, three serotypes of enterohaemorrhagic Escherichia coli and one serotype of Listeria monocytogenes were used as sample bacteria. An inoculum of each serotype was prepared via a 10-fold dilution series to obtain bacterial cell counts with mean values of one or two. To determine whether the experimentally obtained bacterial cell counts follow a theoretical Poisson distribution, a likelihood ratio test between the experimentally obtained cell counts and Poisson distribution which parameter estimated by maximum likelihood estimation (MLE) was conducted. The bacterial cell counts of each serotype sufficiently followed a Poisson distribution. Furthermore, to examine the validity of the parameters of Poisson distribution from experimentally obtained bacterial cell counts, we compared these with the parameters of a Poisson distribution that were estimated using random number generation via computer simulation. The Poisson distribution parameters experimentally obtained from bacterial cell counts were within the range of the parameters estimated using a computer simulation. These results demonstrate that the bacterial cell counts of each serotype obtained via 10-fold dilution followed a Poisson distribution. The fact that the frequency of bacterial cell counts follows a Poisson distribution at low number would be applied to some single-cell studies with a few bacterial cells. In particular, the procedure presented in this study enables us to develop an inactivation model at the single-cell level that can estimate the variability of survival bacterial numbers during the bacterial death process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Spatio-energetic cross talk in photon counting detectors: Detector model and correlated Poisson data generator.

PubMed

Taguchi, Katsuyuki; Polster, Christoph; Lee, Okkyun; Stierstorfer, Karl; Kappler, Steffen

2016-12-01

An x-ray photon interacts with photon counting detectors (PCDs) and generates an electron charge cloud or multiple clouds. The clouds (thus, the photon energy) may be split between two adjacent PCD pixels when the interaction occurs near pixel boundaries, producing a count at both of the pixels. This is called double-counting with charge sharing. (A photoelectric effect with K-shell fluorescence x-ray emission would result in double-counting as well). As a result, PCD data are spatially and energetically correlated, although the output of individual PCD pixels is Poisson distributed. Major problems include the lack of a detector noise model for the spatio-energetic cross talk and lack of a computationally efficient simulation tool for generating correlated Poisson data. A Monte Carlo (MC) simulation can accurately simulate these phenomena and produce noisy data; however, it is not computationally efficient. In this study, the authors developed a new detector model and implemented it in an efficient software simulator that uses a Poisson random number generator to produce correlated noisy integer counts. The detector model takes the following effects into account: (1) detection efficiency; (2) incomplete charge collection and ballistic effect; (3) interaction with PCDs via photoelectric effect (with or without K-shell fluorescence x-ray emission, which may escape from the PCDs or be reabsorbed); and (4) electronic noise. The correlation was modeled by using these two simplifying assumptions: energy conservation and mutual exclusiveness. The mutual exclusiveness is that no more than two pixels measure energy from one photon. The effect of model parameters has been studied and results were compared with MC simulations. The agreement, with respect to the spectrum, was evaluated using the reduced χ 2 statistics or a weighted sum of squared errors, χ red 2 (≥1), where χ red 2 =1 indicates a perfect fit. The model produced spectra with flat field irradiation that qualitatively agree with previous studies. The spectra generated with different model and geometry parameters allowed for understanding the effect of the parameters on the spectrum and the correlation of data. The agreement between the model and MC data was very strong. The mean spectra with 90 keV and 140 kVp agreed exceptionally well: χ red 2 values were 1.049 with 90 keV data and 1.007 with 140 kVp data. The degrees of cross talk (in terms of the relative increase from single pixel irradiation to flat field irradiation) were 22% with 90 keV and 19% with 140 kVp for MC simulations, while they were 21% and 17%, respectively, for the model. The covariance was in strong agreement qualitatively, although it was overestimated. The noisy data generation was very efficient, taking less than a CPU minute as opposed to CPU hours for MC simulators. The authors have developed a novel, computationally efficient PCD model that takes into account double-counting and resulting spatio-energetic correlation between PCD pixels. The MC simulation validated the accuracy.

Toward negative Poisson's ratio composites: Investigation of the auxetic behavior of fibrous networks

NASA Astrophysics Data System (ADS)

Tatlier, Mehmet Seha

Random fibrous can be found among natural and synthetic materials. Some of these random fibrous networks possess negative Poisson's ratio and they are extensively called auxetic materials. The governing mechanisms behind this counter intuitive property in random networks are yet to be understood and this kind of auxetic material remains widely under-explored. However, most of synthetic auxetic materials suffer from their low strength. This shortcoming can be rectified by developing high strength auxetic composites. The process of embedding auxetic random fibrous networks in a polymer matrix is an attractive alternate route to the manufacture of auxetic composites, however before such an approach can be developed, a methodology for designing fibrous networks with the desired negative Poisson's ratios must first be established. This requires an understanding of the factors which bring about negative Poisson's ratios in these materials. In this study, a numerical model is presented in order to investigate the auxetic behavior in compressed random fiber networks. Finite element analyses of three-dimensional stochastic fiber networks were performed to gain insight into the effects of parameters such as network anisotropy, network density, and degree of network compression on the out-of-plane Poisson's ratio and Young's modulus. The simulation results suggest that the compression is the critical parameter that gives rise to negative Poisson's ratio while anisotropy significantly promotes the auxetic behavior. This model can be utilized to design fibrous auxetic materials and to evaluate feasibility of developing auxetic composites by using auxetic fibrous networks as the reinforcing layer.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Irreversible thermodynamics of Poisson processes with reaction.

PubMed

Méndez, V; Fort, J

1999-11-01

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.

The Poisson Random Process. Applications of Probability Theory to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 340.

ERIC Educational Resources Information Center

Wilde, Carroll O.

The Poisson probability distribution is seen to provide a mathematical model from which useful information can be obtained in practical applications. The distribution and some situations to which it applies are studied, and ways to find answers to practical questions are noted. The unit includes exercises and a model exam, and provides answers to…

A Poisson-like closed-form expression for the steady-state wealth distribution in a kinetic model of gambling

NASA Astrophysics Data System (ADS)

Garcia, Jane Bernadette Denise M.; Esguerra, Jose Perico H.

2017-08-01

An approximate but closed-form expression for a Poisson-like steady state wealth distribution in a kinetic model of gambling was formulated from a finite number of its moments, which were generated from a βa,b(x) exchange distribution. The obtained steady-state wealth distributions have tails which are qualitatively similar to those observed in actual wealth distributions.

Estimating the Depth of the Navy Recruiting Market

DTIC Science & Technology

2016-09-01

recommend that NRC make use of the Poisson regression model in order to determine high-yield ZIP codes for market depth. 14. SUBJECT...recommend that NRC make use of the Poisson regression model in order to determine high-yield ZIP codes for market depth. vi THIS PAGE INTENTIONALLY LEFT...DEPTH OF THE NAVY RECRUITING MARKET by Emilie M. Monaghan September 2016 Thesis Advisor: Lyn R. Whitaker Second Reader: Jonathan K. Alt

Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.

PubMed

Sahin, Buyukdagli; Ralf, Blossey

2014-07-16

We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

Drug Adverse Event Detection in Health Plan Data Using the Gamma Poisson Shrinker and Comparison to the Tree-based Scan Statistic

PubMed Central

Brown, Jeffrey S.; Petronis, Kenneth R.; Bate, Andrew; Zhang, Fang; Dashevsky, Inna; Kulldorff, Martin; Avery, Taliser R.; Davis, Robert L.; Chan, K. Arnold; Andrade, Susan E.; Boudreau, Denise; Gunter, Margaret J.; Herrinton, Lisa; Pawloski, Pamala A.; Raebel, Marsha A.; Roblin, Douglas; Smith, David; Reynolds, Robert

2013-01-01

Background: Drug adverse event (AE) signal detection using the Gamma Poisson Shrinker (GPS) is commonly applied in spontaneous reporting. AE signal detection using large observational health plan databases can expand medication safety surveillance. Methods: Using data from nine health plans, we conducted a pilot study to evaluate the implementation and findings of the GPS approach for two antifungal drugs, terbinafine and itraconazole, and two diabetes drugs, pioglitazone and rosiglitazone. We evaluated 1676 diagnosis codes grouped into 183 different clinical concepts and four levels of granularity. Several signaling thresholds were assessed. GPS results were compared to findings from a companion study using the identical analytic dataset but an alternative statistical method—the tree-based scan statistic (TreeScan). Results: We identified 71 statistical signals across two signaling thresholds and two methods, including closely-related signals of overlapping diagnosis definitions. Initial review found that most signals represented known adverse drug reactions or confounding. About 31% of signals met the highest signaling threshold. Conclusions: The GPS method was successfully applied to observational health plan data in a distributed data environment as a drug safety data mining method. There was substantial concordance between the GPS and TreeScan approaches. Key method implementation decisions relate to defining exposures and outcomes and informed choice of signaling thresholds. PMID:24300404

A Generalized QMRA Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2016-10-01

Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single-hit dose-response models are the most commonly used dose-response models in QMRA. Denoting PI(d) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, PI(d|α,β,r*), is proposed in which the minimum number of organisms required for causing infection, K min , is not fixed, but a random variable following a geometric distribution with parameter 0

Multiparameter linear least-squares fitting to Poisson data one count at a time

NASA Technical Reports Server (NTRS)

Wheaton, Wm. A.; Dunklee, Alfred L.; Jacobsen, Allan S.; Ling, James C.; Mahoney, William A.; Radocinski, Robert G.

1995-01-01

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Poisson sigma models, reduction and nonlinear gauge theories

NASA Astrophysics Data System (ADS)

Signori, Daniele

This dissertation comprises two main lines of research. Firstly, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories. Secondly, we give a field theoretic interpretation of the of the BRST (Becchi-Rouet-Stora-Tyutin) and BFV (Batalin-Fradkin-Vilkovisky) methods for the reduction of coisotropic submanifolds of Poisson manifolds. The generalized Poisson sigma models that we define are related to the quantization deformation problems of coisotropic submanifolds using homotopical algebras.

Comparing meta-analysis and ecological-longitudinal analysis in time-series studies. A case study of the effects of air pollution on mortality in three Spanish cities

PubMed Central

Saez, M; Figueiras, A; Ballester, F; Perez-Hoyos, S; Ocana, R; Tobias, A

2001-01-01

STUDY OBJECTIVE—The objective of this paper is to introduce a different approach, called the ecological-longitudinal, to carrying out pooled analysis in time series ecological studies. Because it gives a larger number of data points and, hence, increases the statistical power of the analysis, this approach, unlike conventional ones, allows the complementation of aspects such as accommodation of random effect models, of lags, of interaction between pollutants and between pollutants and meteorological variables, that are hardly implemented in conventional approaches.
DESIGN—The approach is illustrated by providing quantitative estimates of the short-term effects of air pollution on mortality in three Spanish cities, Barcelona, Valencia and Vigo, for the period 1992-1994. Because the dependent variable was a count, a Poisson generalised linear model was first specified. Several modelling issues are worth mentioning. Firstly, because the relations between mortality and explanatory variables were non-linear, cubic splines were used for covariate control, leading to a generalised additive model, GAM. Secondly, the effects of the predictors on the response were allowed to occur with some lag. Thirdly, the residual autocorrelation, because of imperfect control, was controlled for by means of an autoregressive Poisson GAM. Finally, the longitudinal design demanded the consideration of the existence of individual heterogeneity, requiring the consideration of mixed models.
MAIN RESULTS—The estimates of the relative risks obtained from the individual analyses varied across cities, particularly those associated with sulphur dioxide. The highest relative risks corresponded to black smoke in Valencia. These estimates were higher than those obtained from the ecological-longitudinal analysis. Relative risks estimated from this latter analysis were practically identical across cities, 1.00638 (95% confidence intervals 1.0002, 1.0011) for a black smoke increase of 10 µg/m3 and 1.00415 (95% CI 1.0001, 1.0007) for a increase of 10 µg/m3 of sulphur dioxide. Because the statistical power is higher than in the individual analysis more interactions were statistically significant, especially those among air pollutants and meteorological variables.
CONCLUSIONS—Air pollutant levels were related to mortality in the three cities of the study, Barcelona, Valencia and Vigo. These results were consistent with similar studies in other cities, with other multicentric studies and coherent with both, previous individual, for each city, and multicentric studies for all three cities.


Keywords: air pollution; mortality; longitudinal studies PMID:11351001

Factor-Analysis Methods for Higher-Performance Neural Prostheses

PubMed Central

Santhanam, Gopal; Yu, Byron M.; Gilja, Vikash; Ryu, Stephen I.; Afshar, Afsheen; Sahani, Maneesh; Shenoy, Krishna V.

2009-01-01

Neural prostheses aim to provide treatment options for individuals with nervous-system disease or injury. It is necessary, however, to increase the performance of such systems before they can be clinically viable for patients with motor dysfunction. One performance limitation is the presence of correlated trial-to-trial variability that can cause neural responses to wax and wane in concert as the subject is, for example, more attentive or more fatigued. If a system does not properly account for this variability, it may mistakenly interpret such variability as an entirely different intention by the subject. We report here the design and characterization of factor-analysis (FA)–based decoding algorithms that can contend with this confound. We characterize the decoders (classifiers) on experimental data where monkeys performed both a real reach task and a prosthetic cursor task while we recorded from 96 electrodes implanted in dorsal premotor cortex. The decoder attempts to infer the underlying factors that comodulate the neurons' responses and can use this information to substantially lower error rates (one of eight reach endpoint predictions) by ≲75% (e.g., ∼20% total prediction error using traditional independent Poisson models reduced to ∼5%). We also examine additional key aspects of these new algorithms: the effect of neural integration window length on performance, an extension of the algorithms to use Poisson statistics, and the effect of training set size on the decoding accuracy of test data. We found that FA-based methods are most effective for integration windows >150 ms, although still advantageous at shorter timescales, that Gaussian-based algorithms performed better than the analogous Poisson-based algorithms and that the FA algorithm is robust even with a limited amount of training data. We propose that FA-based methods are effective in modeling correlated trial-to-trial neural variability and can be used to substantially increase overall prosthetic system performance. PMID:19297518

Normal and compound poisson approximations for pattern occurrences in NGS reads.

PubMed

Zhai, Zhiyuan; Reinert, Gesine; Song, Kai; Waterman, Michael S; Luan, Yihui; Sun, Fengzhu

2012-06-01

Next generation sequencing (NGS) technologies are now widely used in many biological studies. In NGS, sequence reads are randomly sampled from the genome sequence of interest. Most computational approaches for NGS data first map the reads to the genome and then analyze the data based on the mapped reads. Since many organisms have unknown genome sequences and many reads cannot be uniquely mapped to the genomes even if the genome sequences are known, alternative analytical methods are needed for the study of NGS data. Here we suggest using word patterns to analyze NGS data. Word pattern counting (the study of the probabilistic distribution of the number of occurrences of word patterns in one or multiple long sequences) has played an important role in molecular sequence analysis. However, no studies are available on the distribution of the number of occurrences of word patterns in NGS reads. In this article, we build probabilistic models for the background sequence and the sampling process of the sequence reads from the genome. Based on the models, we provide normal and compound Poisson approximations for the number of occurrences of word patterns from the sequence reads, with bounds on the approximation error. The main challenge is to consider the randomness in generating the long background sequence, as well as in the sampling of the reads using NGS. We show the accuracy of these approximations under a variety of conditions for different patterns with various characteristics. Under realistic assumptions, the compound Poisson approximation seems to outperform the normal approximation in most situations. These approximate distributions can be used to evaluate the statistical significance of the occurrence of patterns from NGS data. The theory and the computational algorithm for calculating the approximate distributions are then used to analyze ChIP-Seq data using transcription factor GABP. Software is available online (www-rcf.usc.edu/∼fsun/Programs/NGS_motif_power/NGS_motif_power.html). In addition, Supplementary Material can be found online (www.liebertonline.com/cmb).

QCAD simulation and optimization of semiconductor double quantum dots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nielsen, Erik; Gao, Xujiao; Kalashnikova, Irina

2013-12-01

We present the Quantum Computer Aided Design (QCAD) simulator that targets modeling quantum devices, particularly silicon double quantum dots (DQDs) developed for quantum qubits. The simulator has three di erentiating features: (i) its core contains nonlinear Poisson, e ective mass Schrodinger, and Con guration Interaction solvers that have massively parallel capability for high simulation throughput, and can be run individually or combined self-consistently for 1D/2D/3D quantum devices; (ii) the core solvers show superior convergence even at near-zero-Kelvin temperatures, which is critical for modeling quantum computing devices; (iii) it couples with an optimization engine Dakota that enables optimization of gate voltagesmore » in DQDs for multiple desired targets. The Poisson solver includes Maxwell- Boltzmann and Fermi-Dirac statistics, supports Dirichlet, Neumann, interface charge, and Robin boundary conditions, and includes the e ect of dopant incomplete ionization. The solver has shown robust nonlinear convergence even in the milli-Kelvin temperature range, and has been extensively used to quickly obtain the semiclassical electrostatic potential in DQD devices. The self-consistent Schrodinger-Poisson solver has achieved robust and monotonic convergence behavior for 1D/2D/3D quantum devices at very low temperatures by using a predictor-correct iteration scheme. The QCAD simulator enables the calculation of dot-to-gate capacitances, and comparison with experiment and between solvers. It is observed that computed capacitances are in the right ballpark when compared to experiment, and quantum con nement increases capacitance when the number of electrons is xed in a quantum dot. In addition, the coupling of QCAD with Dakota allows to rapidly identify which device layouts are more likely leading to few-electron quantum dots. Very efficient QCAD simulations on a large number of fabricated and proposed Si DQDs have made it possible to provide fast feedback for design comparison and optimization.« less

Void statistics, scaling, and the origins of large-scale structure

NASA Technical Reports Server (NTRS)

Fry, J. N.; Giovanelli, Riccardo; Haynes, Martha P.; Melott, Adrian L.; Scherrer, Robert J.

1989-01-01

The probability that a volume of the universe of given size and shape spaced at random will be void of galaxies is used here to study various models of the origin of cosmological structures. Numerical simulations are conducted on hot-particle and cold-particle-modulated inflationary models with and without biasing, on isothermal or initially Poisson models, and on models where structure is seeded by loops of cosmic string. For the Pisces-Perseus redshift compilation of Giovanelli and Haynes (1985), it is found that hierarchical scaling is obeyed for subsamples constructed with different limiting magnitudes and subsamples taken at random. This result confirms that the hierarchical ansatz holds valid to high order and supports the idea that structure in the observed universe evolves by a regular process from an almost Gaussian primordial state. Neutrino models without biasing show the effect of a strong feature in the initial power spectrum. Cosmic string models do not agree well with the galaxy data.

Characterisation of chlorophyll a solubilised in sodium lauryl sulphate micelles

NASA Astrophysics Data System (ADS)

Mukherjee, T.; Sapre, A. V.; Mittal, Jai P.

1980-01-01

Poisson statistics has been applied to the problem of solubilisation of chlorophyll a in sodium lauryl sulphate micelles. Dilution experiments have been carried out to support the finding that each unit of chlorophyll a contributing to the 740 nm band contains just one chlorophyll a molecule.

Imfit: A Fast, Flexible Program for Astronomical Image Fitting

NASA Astrophysics Data System (ADS)

Erwin, Peter

2014-08-01

Imift is an open-source astronomical image-fitting program specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. Its object-oriented design allows new types of image components (2D surface-brightness functions) to be easily written and added to the program. Image functions provided with Imfit include Sersic, exponential, and Gaussian galaxy decompositions along with Core-Sersic and broken-exponential profiles, elliptical rings, and three components that perform line-of-sight integration through 3D luminosity-density models of disks and rings seen at arbitrary inclinations. Available minimization algorithms include Levenberg-Marquardt, Nelder-Mead simplex, and Differential Evolution, allowing trade-offs between speed and decreased sensitivity to local minima in the fit landscape. Minimization can be done using the standard chi^2 statistic (using either data or model values to estimate per-pixel Gaussian errors, or else user-supplied error images) or the Cash statistic; the latter is particularly appropriate for cases of Poisson data in the low-count regime. The C++ source code for Imfit is available under the GNU Public License.

Ion flux through membrane channels--an enhanced algorithm for the Poisson-Nernst-Planck model.

PubMed

Dyrka, Witold; Augousti, Andy T; Kotulska, Malgorzata

2008-09-01

A novel algorithmic scheme for numerical solution of the 3D Poisson-Nernst-Planck model is proposed. The algorithmic improvements are universal and independent of the detailed physical model. They include three major steps: an adjustable gradient-based step value, an adjustable relaxation coefficient, and an optimized segmentation of the modeled space. The enhanced algorithm significantly accelerates the speed of computation and reduces the computational demands. The theoretical model was tested on a regular artificial channel and validated on a real protein channel-alpha-hemolysin, proving its efficiency. (c) 2008 Wiley Periodicals, Inc.

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

Forecasting a winner for Malaysian Cup 2013 using soccer simulation model

NASA Astrophysics Data System (ADS)

Yusof, Muhammad Mat; Fauzee, Mohd Soffian Omar; Latif, Rozita Abdul

2014-07-01

This paper investigates through soccer simulation the calculation of the probability for each team winning Malaysia Cup 2013. Our methodology used here is we predict the outcomes of individual matches and then we simulate the Malaysia Cup 2013 tournament 5000 times. As match outcomes are always a matter of uncertainty, statistical model, in particular a double Poisson model is used to predict the number of goals scored and conceded for each team. Maximum likelihood estimation is use to measure the attacking strength and defensive weakness for each team. Based on our simulation result, LionXII has a higher probability in becoming the winner, followed by Selangor, ATM, JDT and Kelantan. Meanwhile, T-Team, Negeri Sembilan and Felda United have lower probabilities to win Malaysia Cup 2013. In summary, we find that the probability for each team becominga winner is small, indicating that the level of competitive balance in Malaysia Cup 2013 is quite high.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287; Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu

2014-01-15

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.

Mapping species abundance by a spatial zero-inflated Poisson model: a case study in the Wadden Sea, the Netherlands.

PubMed

Lyashevska, Olga; Brus, Dick J; van der Meer, Jaap

2016-01-01

The objective of the study was to provide a general procedure for mapping species abundance when data are zero-inflated and spatially correlated counts. The bivalve species Macoma balthica was observed on a 500×500 m grid in the Dutch part of the Wadden Sea. In total, 66% of the 3451 counts were zeros. A zero-inflated Poisson mixture model was used to relate counts to environmental covariates. Two models were considered, one with relatively fewer covariates (model "small") than the other (model "large"). The models contained two processes: a Bernoulli (species prevalence) and a Poisson (species intensity, when the Bernoulli process predicts presence). The model was used to make predictions for sites where only environmental data are available. Predicted prevalences and intensities show that the model "small" predicts lower mean prevalence and higher mean intensity, than the model "large". Yet, the product of prevalence and intensity, which might be called the unconditional intensity, is very similar. Cross-validation showed that the model "small" performed slightly better, but the difference was small. The proposed methodology might be generally applicable, but is computer intensive.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data.

PubMed

Rodrigues, Josemar; Cancho, Vicente G; de Castro, Mário; Balakrishnan, N

2012-12-01

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis--latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

A spatial scan statistic for survival data based on Weibull distribution.

PubMed

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

The spatial scan statistic has been developed as a geographical cluster detection analysis tool for different types of data sets such as Bernoulli, Poisson, ordinal, normal and exponential. We propose a scan statistic for survival data based on Weibull distribution. It may also be used for other survival distributions, such as exponential, gamma, and log normal. The proposed method is applied on the survival data of tuberculosis patients for the years 2004-2005 in Nainital district of Uttarakhand, India. Simulation studies reveal that the proposed method performs well for different survival distribution functions. Copyright © 2013 John Wiley & Sons, Ltd.

Nonparametric estimation of the heterogeneity of a random medium using compound Poisson process modeling of wave multiple scattering.

PubMed

Le Bihan, Nicolas; Margerin, Ludovic

2009-07-01

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using compound Poisson processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.

Origin of the correlations between exit times in pedestrian flows through a bottleneck

NASA Astrophysics Data System (ADS)

Nicolas, Alexandre; Touloupas, Ioannis

2018-01-01

Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these features thanks to simple models that we develop and analyse quantitatively. We disprove the idea that anticorrelations between successive time gaps (i.e. an alternation between shorter ones and longer ones) are a hallmark of a zipper-like intercalation of pedestrian lines and show that they simply result from the possibility that pedestrians from distinct ‘lines’ or directions cross the bottleneck within a short time interval. A second feature concerns the bursts of escapes, i.e. egresses that come in fast succession. Despite the ubiquity of exponential distributions of burst sizes, entailed by a Poisson process, we argue that anomalous (power-law) statistics arise if the bottleneck is nearly congested, albeit only in a tiny portion of parameter space. The generality of the proposed mechanisms implies that similar statistical features should also be observed for other types of particulate flows.

Application of hotspot detection using spatial scan statistic: Study of criminality in Indonesia

NASA Astrophysics Data System (ADS)

Runadi, Taruga; Widyaningsih, Yekti

2017-03-01

According to the police registered data, the number of criminal cases tends to fluctuate during 2011 to 2013. It means there is no significant reduction cases number of criminal acts during that period. Local government needs to observe whether their area was a high risk of criminal case. The objectives of this study are to detect hotspot area of certain criminal cases using spatial scan statistic. This study analyzed the data of 22 criminal types cases based on province in Indonesia that occurred during 2013. The data was obtained from Badan Pusat Statistik (BPS) that was released in 2014. Hotspot detection was performed according to the likelihood ratio of the Poisson model using SaTScanTM software and then mapped using R. The spatial scan statistic method successfully detected provinces that was categorized as hotspot for 22 crime types cases being analyzed with p-value less than 0.05. The local governments of province that were detected as hotspot area of certain crime cases should provide more attention to improve security quality.

Effects of Heterogeniety on Spatial Pattern Analysis of Wild Pistachio Trees in Zagros Woodlands, Iran

NASA Astrophysics Data System (ADS)

Erfanifard, Y.; Rezayan, F.

2014-10-01

Vegetation heterogeneity biases second-order summary statistics, e.g., Ripley's K-function, applied for spatial pattern analysis in ecology. Second-order investigation based on Ripley's K-function and related statistics (i.e., L- and pair correlation function g) is widely used in ecology to develop hypothesis on underlying processes by characterizing spatial patterns of vegetation. The aim of this study was to demonstrate effects of underlying heterogeneity of wild pistachio (Pistacia atlantica Desf.) trees on the second-order summary statistics of point pattern analysis in a part of Zagros woodlands, Iran. The spatial distribution of 431 wild pistachio trees was accurately mapped in a 40 ha stand in the Wild Pistachio & Almond Research Site, Fars province, Iran. Three commonly used second-order summary statistics (i.e., K-, L-, and g-functions) were applied to analyse their spatial pattern. The two-sample Kolmogorov-Smirnov goodness-of-fit test showed that the observed pattern significantly followed an inhomogeneous Poisson process null model in the study region. The results also showed that heterogeneous pattern of wild pistachio trees biased the homogeneous form of K-, L-, and g-functions, demonstrating a stronger aggregation of the trees at the scales of 0-50 m than actually existed and an aggregation at scales of 150-200 m, while regularly distributed. Consequently, we showed that heterogeneity of point patterns may bias the results of homogeneous second-order summary statistics and we also suggested applying inhomogeneous summary statistics with related null models for spatial pattern analysis of heterogeneous vegetations.

Hierarchical dose response of E. coli O157:H7 from human outbreaks incorporating heterogeneity in exposure.

PubMed

Teunis, P F M; Ogden, I D; Strachan, N J C

2008-06-01

The infectivity of pathogenic microorganisms is a key factor in the transmission of an infectious disease in a susceptible population. Microbial infectivity is generally estimated from dose-response studies in human volunteers. This can only be done with mildly pathogenic organisms. Here a hierarchical Beta-Poisson dose-response model is developed utilizing data from human outbreaks. On the lowest level each outbreak is modelled separately and these are then combined at a second level to produce a group dose-response relation. The distribution of foodborne pathogens often shows strong heterogeneity and this is incorporated by introducing an additional parameter to the dose-response model, accounting for the degree of overdispersion relative to Poisson distribution. It was found that heterogeneity considerably influences the shape of the dose-response relationship and increases uncertainty in predicted risk. This uncertainty is greater than previously reported surrogate and outbreak models using a single level of analysis. Monte Carlo parameter samples (alpha, beta of the Beta-Poisson model) can be readily incorporated in risk assessment models built using tools such as S-plus and @ Risk.

Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

NASA Astrophysics Data System (ADS)

Hincks, Ian; Granade, Christopher; Cory, David G.

2018-01-01

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

Incidence trend and risk factors for campylobacter infections in humans in Norway

PubMed Central

Sandberg, Marianne; Nygård, Karin; Meldal, Hege; Valle, Paul Steinar; Kruse, Hilde; Skjerve, Eystein

2006-01-01

Background The objectives of the study were to evaluate whether the increase in incidence of campylobacteriosis observed in humans in Norway from 1995 to 2001 was statistically significant and whether different biologically plausible risk factors were associated with the incidence of campylobacteriosis in the different counties in Norway. Methods To model the incidence of domestically acquired campylobacteriosis from 1995 to 2001, a population average random effect poisson model was applied (the trend model). To case data and assumed risk-factor/protective data such as sale of chicken, receiving treated drinking water, density of dogs and grazing animals, occupation of people in the municipalities and climatic factors from 2000 and 2001, an equivalent model accounting for geographical clustering was applied (the ecological model). Results The increase in incidence of campylobacteriosis in humans in Norway from 1995 to 2001 was statistically significant from 1998. Treated water was a protective factor against Campylobacter infections in humans with an IRR of 0.78 per percentage increase in people supplied. The two-level modelling technique showed no evidence of clustering of campylobacteriosis in any particular county. Aggregation of data on municipality level makes interpretation of the results at the individual level difficult. Conclusion The increase in incidence of Campylobacter infections in humans from 1995 to 2001 was statistically significant from 1998. Treated water was a protective factor against Campylobacter infections in humans with an IRR of 0.78 per percentage increase in people supplied. Campylobacter infections did not appear to be clustered in any particular county in Norway. PMID:16827925

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Sparse representation and dictionary learning penalized image reconstruction for positron emission tomography.

PubMed

Chen, Shuhang; Liu, Huafeng; Shi, Pengcheng; Chen, Yunmei

2015-01-21

Accurate and robust reconstruction of the radioactivity concentration is of great importance in positron emission tomography (PET) imaging. Given the Poisson nature of photo-counting measurements, we present a reconstruction framework that integrates sparsity penalty on a dictionary into a maximum likelihood estimator. Patch-sparsity on a dictionary provides the regularization for our effort, and iterative procedures are used to solve the maximum likelihood function formulated on Poisson statistics. Specifically, in our formulation, a dictionary could be trained on CT images, to provide intrinsic anatomical structures for the reconstructed images, or adaptively learned from the noisy measurements of PET. Accuracy of the strategy with very promising application results from Monte-Carlo simulations, and real data are demonstrated.

NON-HOMOGENEOUS POISSON PROCESS MODEL FOR GENETIC CROSSOVER INTERFERENCE.

PubMed

Leu, Szu-Yun; Sen, Pranab K

2014-01-01

The genetic crossover interference is usually modeled with a stationary renewal process to construct the genetic map. We propose two non-homogeneous, also dependent, Poisson process models applied to the known physical map. The crossover process is assumed to start from an origin and to occur sequentially along the chromosome. The increment rate depends on the position of the markers and the number of crossover events occurring between the origin and the markers. We show how to obtain parameter estimates for the process and use simulation studies and real Drosophila data to examine the performance of the proposed models.

An investigation of stress wave propagation in a shear deformable nanobeam based on modified couple stress theory

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, Majid; Shariati, Mahmoud

2016-04-01

This paper presents a new investigation for propagation of stress wave in a nanobeam based on modified couple stress theory. Using Euler-Bernoulli beam theory, Timoshenko beam theory, and Reddy beam theory, the effect of shear deformation is investigated. This nonclassical model contains a material length scale parameter to capture the size effect and the Poisson effect is incorporated in the current model. Governing equations of motion are obtained by Hamilton's principle and solved explicitly. This solution leads to obtain two phase velocities for shear deformable beams in different directions. Effects of shear deformation, material length scale parameter, and Poisson's ratio on the behavior of these phase velocities are investigated and discussed. The results also show a dual behavior for phase velocities against Poisson's ratio.