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Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function $f(\mathbf{x}, \mathbf{v}; t)$. Adopting an alternative approach, previously proposed for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function $f(\mathbf{x}, \mathbf{v}; t)$. Adopting an alternative approach, previously proposed for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function $f(\mathbf{x}, \mathbf{v}; t)$. Adopting an alternative approach, previously proposed for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Explains the various techniques of PPM development, simulation and optimization. All the explanations are given with IT industry and usage of alternate techniques to build PPM to suit even smaller organizations. Application of Statistical, Probablistic and Simulation  models are elaborated.

Explains the various techniques of PPM development, simulation and optimization. All the explanations are given with IT industry and usage of alternate techniques to build PPM to suit even smaller organizations. Application of Statistical, Probablistic and Simulation  models are elaborated.

Explains the various techniques of PPM development, simulation and optimization. All the explanations are given with IT industry and usage of alternate techniques to build PPM to suit even smaller organizations. Application of Statistical, Probablistic and Simulation  models are elaborated.

Explains the various techniques of PPM development, simulation and optimization. All the explanations are given with IT industry and usage of alternate techniques to build PPM to suit even smaller organizations. Application of Statistical, Probablistic and Simulation  models are elaborated.

Explains the various techniques of PPM development, simulation and optimization. All the explanations are given with IT industry and usage of alternate techniques to build PPM to suit even smaller organizations. Application of Statistical, Probablistic and Simulation  models are elaborated.

Explains the various techniques of PPM development, simulation and optimization. All the explanations are given with IT industry and usage of alternate techniques to build PPM to suit even smaller organizations. Application of Statistical, Probablistic and Simulation  models are elaborated.

This work is designed to carry out the statistical modelling of the drying characteristics of unripe plantain (Musa paradisiaca) slices and to study the effect of drying temperature and slice thickness on drying characteristics. The test samples were dried in a laboratory scale oven dryer at varying temperatures of 700C, 800C and 900C, and different slice thicknesses of 2mm, 3mm and 4mm.The result obtained indicated that drying temperature and slice thickness had significant effect on drying rate and hence moisture profile. The moisture ratio – drying time data obtained were fitted to ten thin layer drying models. The fit quality obtained with each model was evaluated using statistical tests namely; coefficient of determination (R2 ), root mean square error (RMSE), reduced chi-square (X2 ), and standard error of estimate (SEE). Although most of the models fitted quite well to the experimental data, Page and Modified Page models showed the highest average R 2 and the lowest average RMSE, X 2 and SEE values. Page and modified Page models were selected and found suitable to represent the drying characteristics of unripe plantain slices and predict drying times.

A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary statistical model is defined. The parameters of the single experiments are functions of a hyperparameter, which defines the state of the system. There is a symmetry group acting on the hyperparameters, and for the induced action on the parameters of the single experiment a simple consistency property is assumed, called permissibility of the parametric function. The other assumptions needed are rather weak. The derivation relies partly on quantum logic, partly on a group representation of the hyperparameter group, where the invariant spaces are shown to be in 1-1 correspondence with the equivalence classes of permissible parametric functions. Planck's constant only plays a role connected to generators of unitary group representations.

RooStatsCms is an object oriented statistical framework based on the RooFit technology. Its scope is to allow the modelling, statistical analysis and combination of multiple search channels for new phenomena in High Energy Physics. It provides a variety of methods described in literature implemented as classes, whose design is oriented to the execution of multiple CPU intensive jobs on batch systems or on the Grid.

We describe results from the third stage of a project to build a statistical model for hurricane tracks. In the first stage we modelled the unconditional mean track. In the second stage we modelled the unconditional variance of fluctuations around the mean. Now we address the question of how to model the autocorrelations in the standardised fluctuations. We perform a thorough diagnostic analysis of these fluctuations, and fit a type of AR(1) model. We then assess the goodness of fit of this model in a number of ways, including an out-of-sample comparison with a simpler model, an in-sample residual analysis, and a comparison of simulated tracks from the model with the observed tracks. Broadly speaking, the model captures the behaviour of observed hurricane tracks. In detail, however, there are a number of systematic errors.

Usually one compares the accuracy of two competing classifiers via null hypothesis significance tests (nhst). Yet the nhst tests suffer from important shortcomings, which can be overcome by switching to Bayesian hypothesis testing. We propose a Bayesian hierarchical model which jointly analyzes the cross-validation results obtained by two classifiers on multiple data sets. It returns the posterior probability of the accuracies of the two classifiers being practically equivalent or significantly different. A further strength of the hierarchical model is that, by jointly analyzing the results obtained on all data sets, it reduces the estimation error compared to the usual approach of averaging the cross-validation results obtained on a given data set.

During the six-month period from 1 April 1991 to 30 September 1991 the following research papers in statistical modeling of software reliability appeared: (1) A Nonparametric Software Reliability Growth Model; (2) On the Use and the Performance of Software Reliability Growth Models; (3) Research and Development Issues in Software Reliability Engineering; (4) Special Issues on Software; and (5) Software Reliability and Safety.

The objective of this paper is to find the best-fit probability model for annual maximum rainfall data for Botswana for the period January 1901 to December 2012. The Kwiatkowski-Philips-Schmidt-Shin test of stationarity on the data shows that the time series is stationary. Based on visual inspection of the generalized quantile plot, three extreme value probability distributions are considered, belonging to the Gumbel and Frechet maximum domains of attraction: the gamma, lognormal and BurrXII. The maximum likelihood method is used to estimate the parameters of each distribution under study. The empirical CDF plots and Q-Q plots of the data show that the three models are highly competitive in terms of goodness-of-fit. Formal model assessment criteria, namely, the Anderson-Darling test and the Bayesian Information Criterion agree on the ranking of the three models: the lognormal distribution gives the best fit to the data followed closely by the gamma whilst the BurrXII distribution comes a distant third.

SciPy 2010 Day 2 Main Track 7 Statsmodels - Statistical Modelling in Python Skipper Seabold

ABS Research Paper: Exploration of state space modelling approaches for statistical impact measurment in ABS time series: The Labour Force Survey as a case study, Jun 2018

In astrophysical (inverse) regression problems it is an important task to decide whether a given parametric model describes the observational data sufficiently well or whether a non-parametric modelling becomes necessary. However, in contrast to common practice this cannot be decided by solely comparing the quality of fit due to possible over-fitting by the non-parametric method. Therefore, in this paper we present a resampling algorithm which allows to decide whether deviations between a parametric and a non-parametric model are systematic or due to noise. The algorithm is based on a statistical comparison of the corresponding residuals, under the assumption of the parametric model as well as under violation of this assumption. This yields a graphical tool for a robust decision making of parametric versus non-parametric modelling. Moreover, our approach can be used for the selection of the most proper model among several competitors (model selection). The methods are illustrated by the problem of recovering the luminosity density in the Milky Way [MW] from near-infrared [NIR] surface brightness data of the DIRBE experiment on board of the COBE satellite. Among the parametric models investigated one with 4-armed spiral structure performs best. In this model the Sagittarius-Carina arm and its counter-arm are significantly weaker than the other pair of arms. Furthermore, we find statistical evidence for an improvement over a range of parametric models with different spiral structure morphologies by a non-parametric model of Bissantz & Gerhard (2002).

To elucidate the non-trivial empirical statistical properties of fluctuations of a typical non-steady time series representing the appearance of words in blogs, we investigated approximately five billion Japanese blogs over a period of six years and analyse some corresponding mathematical models. First, we introduce a solvable non-steady extension of the random diffusion model, which can be deduced by modelling the behaviour of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

Electric vehicles (EVs) and particularly plug-in hybrid electric vehicles (PHEVs) are foreseen to become popular in the near future. Not only are they much more environmentally friendly than conventional internal combustion engine (ICE) vehicles, their fuel can also be catered from diverse energy sources and resources. However, they add significant load on the power grid as they become widespread. The characteristics of this extra load follow the patterns of people's driving behaviours. In particular, random parameters such as arrival time and driven distance of the vehicles determine their expected demand profile from the power grid. In this paper, we first present a model for uncoordinated charging power demand of PHEVs based on a stochastic process and accordingly we characterize the EV's expected daily power demand profile. Next, we adopt different distributions for the EV's charging time following some available empirical research data in the literature. Simulation results show that the EV's expected daily power demand profiles obtained under the uniform, Gaussian with positive support and Rician distributions for charging time are identical when the first and second order statistics of these distributions are the same. This gives us useful insights into the long-term planning for upgrading power systems' infrastructure to accommodate PHEVs. In addition, the results from this modelling can be incorporated into designing demand response (DR) algorithms and evaluating the available DR techniques more accurately.

Electric vehicles (EVs) and particularly plug-in hybrid electric vehicles (PHEVs) are foreseen to become popular in the near future. Not only are they much more environmentally friendly than conventional internal combustion engine (ICE) vehicles, their fuel can also be catered from diverse energy sources and resources. However, they add significant load on the power grid as they become widespread. The characteristics of this extra load follow the patterns of people's driving behaviours. In particular, random parameters such as arrival time and driven distance of the vehicles determine their expected demand profile from the power grid. In this paper, we first present a model for uncoordinated charging power demand of PHEVs based on a stochastic process and accordingly we characterize the EV's expected daily power demand profile. Next, we adopt different distributions for the EV's charging time following some available empirical research data in the literature. Simulation results show that the EV's expected daily power demand profiles obtained under the uniform, Gaussian with positive support and Rician distributions for charging time are identical when the first and second order statistics of these distributions are the same. This gives us useful insights into the long-term planning for upgrading power systems' infrastructure to accommodate PHEVs. In addition, the results from this modelling can be incorporated into designing demand response (DR) algorithms and evaluating the available DR techniques more accurately.

Electric vehicles (EVs) add significant load on the power grid as they become widespread. The characteristics of this extra load follow the patterns of people's driving behaviours. In particular, random parameters such as arrival time and charging time of the vehicles determine their expected charging demand profile from the power grid. In this paper, we first present a model for uncoordinated charging power demand of EVs based on a stochastic process and accordingly we characterize an EV's expected daily power demand profile. Next, we illustrate it for different charging time distributions through simulations. This gives us useful insights into the long-term planning for upgrading power systems' infrastructure to accommodate EVs. Then, we incorporate departure time as another random variable into this modelling and introduce an autonomous demand response (DR) technique to manage the EVs' charging demand. Our results show that, it is possible to accommodate a large number of EVs and achieve the same peak-to-average ratio (PAR) in daily aggregated power consumption of the grid as when there is no EV in the system. This peak value can be decreased further significantly when we add vehicle-to-grid (V2G) capability in the system.

The behaviour of spoken dialogue systems is traditionally determined by expert-coded rules. A new set of rules is therefore required for each new domain. Also, rule-based systems do not naturally deal with uncertainty in the input, which makes them sensitive to speech understanding errors. Finally, such systems do not improve over time. The partially observable Markov decision process (POMDP) has been proposed as an alternative model for dialogue. POMDPs can automatically be optimised to maximise the reward, a measure of success. They are robust to speech understanding errors, and can adapt to new data. A POMDP-based dialogue manager maintains a distribution over every possible dialogue state, the belief state. Based on that distribution, the system chooses the action that gives the highest expected reward. The main challenge with the POMDP-based approach, however, is to make it tractable to maintain the belief state and optimise the action selection. In this talk a methods will be presented to make POMDP-based dialogue management scalable and suitable for flexible real-world dialogue systems. ©2011 Microsoft Corporation. All rights reserved.

New experimental techniques in molecular biology make it possible to probe cellular processes in unprecedented detail. In particular, information on the activity profiles of genes is available from large scale microarray or reporter assay experiments. To infer detailed models for cellular processes poses formidable inference problems, if models beyond simple clustering or association graphs are envisaged.I will discuss some ideas and examples for the inference of static as well as dynamic models for gene regulation using a Bayesian model selection framework. The fact that most data sets are high dimensional but comparatively small suggests exploiting the simplicity and flexibility of Gaussian processes for modelling nonlinear relationships in dynamical models. ©2006 Microsoft Corporation. All rights reserved.

New experimental techniques in molecular biology make it possible to probe cellular processes in unprecedented detail. In particular, information on the activity profiles of genes is available from large scale microarray or reporter assay experiments. To infer detailed models for cellular processes poses formidable inference problems, if models beyond simple clustering or association graphs are envisaged.I will discuss some ideas and examples for the inference of static as well as dynamic models for gene regulation using a Bayesian model selection framework. The fact that most data sets are high dimensional but comparatively small suggests exploiting the simplicity and flexibility of Gaussian processes for modelling nonlinear relationships in dynamical models. ©2006 Microsoft Corporation. All rights reserved.

Multi-electrode arrays (MEA) are increasingly used to investigate spontaneous neuronal network activity. The recorded signals comprise several distinct components: Apart from artefacts without biological significance, one can distinguish between spikes (action potentials) and subthreshold fluctuations (local fields potentials). Here we aim to develop a theoretical model that allows for a compact and robust characterization of subthreshold fluctuations in terms of a Gaussian statistical field theory in two spatial and one temporal dimension. What is usually referred to as the driving noise in the context of statistical physics is here interpreted as a representation of the neural activity. Spatial and temporal correlations of this activity give valuable information about the connectivity in the neural tissue. We apply our methods on a dataset obtained from MEA-measurements in an acute hippocampal brain slice from a rat. Our main finding is that the empirical correlation functions indeed obey the logarithmic behaviour that is a general feature of theoretical models of this kind. We also find a clear correlation between the activity and the occurence of spikes. Another important insight is the importance of correcly separating out certain artefacts from the data before proceeding with the analysis.

The RooStatsCms (RSC) software framework allows analysis modelling and combination, statistical studies together with the access to sophisticated graphics routines for results visualisation. The goal of the project is to complement the existing analyses by means of their combination and accurate statistical studies.

With the influx of complex and detailed tracking data gathered from electronic tracking devices, the analysis of animal movement data has recently emerged as a cottage industry amongst biostatisticians. New approaches of ever greater complexity are continue to be added to the literature. In this paper, we review what we believe to be some of the most popular and most useful classes of statistical models used to analyze individual animal movement data. Specifically we consider discrete-time hidden Markov models, more general state-space models and diffusion processes. We argue that these models should be core components in the toolbox for quantitative researchers working on stochastic modelling of individual animal movement. The paper concludes by offering some general observations on the direction of statistical analysis of animal movement. There is a trend in movement ecology toward what are arguably overly-complex modelling approaches which are inaccessible to ecologists, unwieldy with large data sets or not based in mainstream statistical practice. Additionally, some analysis methods developed within the ecological community ignore fundamental properties of movement data, potentially leading to misleading conclusions about animal movement. Corresponding approaches, e.g. based on L\'evy walk-type models, continue to be popular despite having been largely discredited. We contend that there is a need for an appropriate balance between the extremes of either being overly complex or being overly simplistic, whereby the discipline relies on models of intermediate complexity that are usable by general ecologists, but grounded in well-developed statistical practice and efficient to fit to large data sets.

Econometrics is a branch of economics that utilizes statistical methods, mathematical models, and computational techniques to analyze and understand economic data. It combines economic theory, statistical analysis, and mathematical modeling to provide insights into economic phenomena and make predictions about future outcomes. In this essay, we will explore the key concepts and techniques in econometrics, its applications, and its significance in the field of economics. Econometrics is concerned with the development and application of statistical methods to analyze economic data. It aims to test economic theories, estimate economic relationships, and forecast future economic trends. The field of econometrics emerged in the early 20th century when economists realized the need to use statistical methods to analyze economic phenomena. The first step in econometric analysis is data collection. Economic data can be collected through various sources, such as surveys, administrative records, or publicly available datasets. Econometricians work with different types of data, including time series data, cross-sectional data, and panel data. Time series data captures observations of a variable over time, while cross-sectional data represents observations at a specific point in time. Panel data combines both time series and cross-sectional data by collecting observations on multiple entities over time. Econometric analysis relies on economic models that describe the relationships between economic variables. These models are based on certain assumptions about the behavior of individuals, firms, and markets. The most commonly used economic model in econometrics is the linear regression model, which assumes a linear relationship between the dependent variable and the independent variables. Linear regression is a fundamental technique in econometrics that estimates the relationship between a dependent variable and one or more independent variables. The estimated relationship is represented by an equation that specifies the effect of the independent variables on the dependent variable. The coefficients in the equation indicate the magnitude and direction of the relationship. Econometricians use various methods to estimate the coefficients, such as Ordinary Least Squares (OLS) estimation. Hypothesis testing is an essential part of econometric analysis. It involves formulating null and alternative hypotheses about the relationship between variables and testing these hypotheses using statistical tests. The most common hypothesis test in econometrics is the t-test, which assesses the significance of a coefficient in the regression model. The p-value obtained from the t-test helps determine whether the coefficient is statistically significant.  

Research Master Thesis project by Iris van der Wulp at Utrecht University

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases.

We describe results from the second stage of a project to build a statistical model for hurricane tracks. In the first stage we modelled the unconditional mean track. We now attempt to model the unconditional variance of fluctuations around the mean. The variance models we describe use a semi-parametric nearest neighbours approach in which the optimal averaging length-scale is estimated using a jack-knife out-of-sample fitting procedure. We test three different models. These models consider the variance structure of the deviations from the unconditional mean track to be isotropic, anisotropic but uncorrelated, and anisotropic and correlated, respectively. The results show that, of these models, the anisotropic correlated model gives the best predictions of the distribution of future positions of hurricanes.

We present a series of experiments focusing on the modelling of source-side context to improve Phrase-based Statistical Machine Translation. Statistical Machine Translation systems typically consist of a translation model and a language model. The former maps phrases in the source language to the target language, without regard for the context in which the source phrases occur. The latter models just the target language, and acts as a target-side model of context information after translation. We attempt to independently reproduce a line of existing research and test whether considering context information directly in the translation model has a positive effect on translation quality. We furthermore investigate various ways discriminative classifier-based models can be integrated into Statical Machine Translation. We will use proven techniques from Word Sense Disambiguation, effectively integrating these techniques in Statistical Machine Translation. Our approach is language-independent and knowledge-poor: we do not employ any explicit linguistic features computed by part-of-speech taggers, word sense disambiguation systems, supertaggers, or parsers, as used by previous work. We find only limited improvement of translation quality for certain formulaic corpora and conclude that explicit modelling of source-side context information does not add much to the data already implicitly available in the decode process.

We present a series of experiments focusing on the modelling of source-side context to improve Phrase-based Statistical Machine Translation. Statistical Machine Translation systems typically consist of a translation model and a language model. The former maps phrases in the source language to the target language, without regard for the context in which the source phrases occur. The latter models just the target language, and acts as a target-side model of context information after translation. We attempt to independently reproduce a line of existing research and test whether considering context information directly in the translation model has a positive effect on translation quality. We furthermore investigate various ways discriminative classifier-based models can be integrated into Statical Machine Translation. We will use proven techniques from Word Sense Disambiguation, effectively integrating these techniques in Statistical Machine Translation. Our approach is language-independent and knowledge-poor: we do not employ any explicit linguistic features computed by part-of-speech taggers, word sense disambiguation systems, supertaggers, or parsers, as used by previous work. We find only limited improvement of translation quality for certain formulaic corpora and conclude that explicit modelling of source-side context information does not add much to the data already implicitly available in the decode process.

We present a series of experiments focusing on the modelling of source-side context to improve Phrase-based Statistical Machine Translation. Statistical Machine Translation systems typically consist of a translation model and a language model. The former maps phrases in the source language to the target language, without regard for the context in which the source phrases occur. The latter models just the target language, and acts as a target-side model of context information after translation. We attempt to independently reproduce a line of existing research and test whether considering context information directly in the translation model has a positive effect on translation quality. We furthermore investigate various ways discriminative classifier-based models can be integrated into Statical Machine Translation. We will use proven techniques from Word Sense Disambiguation, effectively integrating these techniques in Statistical Machine Translation. Our approach is language-independent and knowledge-poor: we do not employ any explicit linguistic features computed by part-of-speech taggers, word sense disambiguation systems, supertaggers, or parsers, as used by previous work. We find only limited improvement of translation quality for certain formulaic corpora and conclude that explicit modelling of source-side context information does not add much to the data already implicitly available in the decode process.

There has been considerable recent interest in algorithms for finding communities in networks - groups of vertex within which connections are dense (frequent), but between which connections are sparser (rare). Most of the current literature advocates an heuristic approach to the removal of the edges (i.e., removing the links that are less significant using a well-designed function). In this article, we will investigate a technique for uncovering latent communities using a new modelling approach, based on how information spread within a network. It will prove to be easy to use, robust and scalable. It makes supplementary information related to the network/community structure (different communications, consecutive observations) easier to integrate. We will demonstrate the efficiency of our approach by providing some illustrating real-world applications, like the famous Zachary karate club, or the Amazon political books buyers network.

There has been considerable recent interest in algorithms for finding communities in networks - groups of vertex within which connections are dense (frequent), but between which connections are sparser (rare). Most of the current literature advocates an heuristic approach to the removal of the edges (i.e., removing the links that are less significant using a well-designed function). In this article, we will investigate a technique for uncovering latent communities using a new modelling approach, based on how information spread within a network. It will prove to be easy to use, robust and scalable. It makes supplementary information related to the network/community structure (different communications, consecutive observations) easier to integrate. We will demonstrate the efficiency of our approach by providing some illustrating real-world applications, like the famous Zachary karate club, or the Amazon political books buyers network.

The San Marcos and Comal Rivers, located in south Texas, support populations of five Federally listed or endangered species. Both rivers are fed by spring runs which are supplied by the Edwards aquifer which is currently in an overdraft condition. A major reduction or elimination of spring flows is considered a severe threat to the survival of these species. In order to preserve these species, the United States Fish and Wildlife Service (USF&WS) initiated a 5-year cooperative agreement with Utah State University to assess and quantify the instream flows necessary to protect these species. The research presented in this paper concentrates on the habitat needs and habitat utilization patterns of the fountain darter (Etheostoma fonticola) in the Comal River with the goals of generating a habitat occupancy equation, a population density equation, and developing a statistical methodology for handling similar situations. Field data collected on the Comal over a one year period contained. information on the physical, chemical, and vegetative environment as well as information on fish species composition and numbers. This data was systematically reduced, normalized, and then analyzed by various statistical techniques including principle component analysis, discriminate functions analysis, multiple regression analysis, and analyses of variance and covariance.

This article is from Trials , volume 14 . Abstract None

This paper proposes a new channel modelling method for powerline communications networks based on the multipath profile in the time domain. The new channel model is developed to be applied in a range of Powerline Communications (PLC) research topics such as impulse noise modelling, deployment and coverage studies, and communications theory analysis. To develop the methodology, channels are categorised according to their propagation distance and power delay profile. The statistical multipath parameters such as path arrival time, magnitude and interval for each category are analyzed to build the model. Each generated channel based on the proposed statistical model represents a different realisation of a PLC network. Simulation results in similar the time and frequency domains show that the proposed statistical modelling method, which integrates the impact of network topology presents the PLC channel features as the underlying transmission line theory model. Furthermore, two potential application scenarios are described to show the channel model is applicable to capacity analysis and correlated impulse noise modelling for PLC networks.

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

The last glacial period was punctuated by a series of abrupt climate shifts, the so-called Dansgaard-Oeschger (DO) events. The frequency of DO events varied in time, supposedly because of changes in background climate conditions. Here, the influence of external forcings on DO events is investigated with statistical modelling. We assume two types of simple stochastic dynamical systems models (double-well potential-type and oscillator-type), forced by the northern hemisphere summer insolation change and/or the global ice volume change. The model parameters are estimated by using the maximum likelihood method with the NGRIP Ca$^{2+}$ record. The stochastic oscillator model with at least the ice volume forcing reproduces well the sample autocorrelation function of the record and the frequency changes of warming transitions in the last glacial period across MISs 2, 3, and 4. The model performance is improved with the additional insolation forcing. The BIC scores also suggest that the ice volume forcing is relatively more important than the insolation forcing, though the strength of evidence depends on the model assumption. Finally, we simulate the average number of warming transitions in the past four glacial periods, assuming the model can be extended beyond the last glacial, and compare the result with an Iberian margin sea-surface temperature (SST) record (Martrat et al., Science, vol. 317, p. 502, 2007). The simulation result supports the previous observation that abrupt millennial-scale climate changes in the penultimate glacial (MIS 6) are less frequent than in the last glacial (MISs 2-4). On the other hand, it suggests that the number of abrupt millennial-scale climate changes in older glacial periods (MISs 6, 8, and 10) might be larger than inferred from the SST record.

We discuss how ensemble weather forecasts can be used, and highlight the advantages and disadvantages of two particular methods.

This paper describes several applications in astronomy and cosmology that are addressed using probabilistic modelling and statistical inference.

In this dissertation, an abstract formalism extending information geometry is introduced. This framework encompasses a broad range of modelling problems, including possible applications in machine learning and in the information theoretical foundations of quantum theory. Its purely geometrical foundations make no use of probability theory and very little assumptions about the data or the models are made. Starting only from a divergence function, a Riemannian geometrical structure consisting of a metric tensor and an affine connection is constructed and its properties are investigated. Also the relation to information geometry and in particular the geometry of exponential families of probability distributions is elucidated. It turns out this geometrical framework offers a straightforward way to determine whether or not a parametrised family of distributions can be written in exponential form. Apart from the main theoretical chapter, the dissertation also contains a chapter of examples illustrating the application of the formalism and its geometric properties, a brief introduction to differential geometry and a historical overview of the development of information geometry.

Online forums (synchronous and asynchronous) offer exciting data opportunities to analyze how people influence one another through their interactions. However, researchers must address several analytic difficulties involving the data (missing values, nested structure [messages within topics], non-sequential messages), outcome variables (discrete outcomes, rare instances, multiple outcome variables, similarities among nearby messages), and explanatory variables (sequences of explanatory variables, indirect mediation effects, false positives, and robustness of results). We explicate a method that addresses these difficulties (Statistical Discourse Analysis or SDA) and illustrate it on 1,330 asynchronous messages written and self-coded by 17 students during a 13-week online educational technology course. Both individual characteristics and message attributes were linked to participants' online messages. Men wrote more messages about their theories than women did. Moreover, some sequences of messages were more likely to precede other messages. For example, opinions were often followed by elaborations, which were often followed by theorizing.

As part of a project to develop more accurate estimates of the risks due to tropical cyclones, we describe a non-parametric method for the statistical simulation of the location of tropical cyclone genesis. The method avoids the use of arbitrary grid boxes, and the spatial smoothing of the historical data is constructed optimally according to a clearly defined merit function.

This paper describes the density-quantile function approach to statistical analysis of a sample as involving five phases requiring the study of various population raw and smoothed quantile and density-quantile functions.

This paper describes the density-quantile function approach to statistical analysis of a sample as involving five phases requiring the study of various population raw and smoothed quantile and density-quantile functions.