Probabilistic Data Analysis Research Articles

Ajuste de las distribuciones GVE, LOG y PAG con momentos L de orden mayor

The probabilistic analysis of extreme hydrological data aims to estimate reliable predictions associated with high return periods. The LH or higher-order moments can characterize in a more efficient way the right tail of the probability distribution function (PDF), by giving more importance to large data values. The undesirable influence of the sample's small quantities is reduced by using the LH moments in the estimation of predictions. This paper briefly describes the theory of L moments, as a basis for its generalization, which leads to the LH moments, proposed in 1997 by Wang Q.J. By means of the L and LH moments methods, the equations that allow the estimation of the three fitting parameters of the PDF: General Extreme Values (GEV), Generalized Logistics (GLO) and Generalized Pareto (GPA) are cited. A numerical application to the 21 available records annual floods of Hydrological Region No. 10 (Sinaloa) is performed, contrasting its results based on the standard error of fit (SEF). The analysis of results showed that the GPA distribution leads to the best fittings. It can be highlighted that LH moments are a good choice to abate the SEF in the three distributions used.

<italic>Why so many people</italic>? Explaining Nonhabitual Transport Overcrowding With Internet Data

Public transport smartcard data can be used for detection of large crowds. By comparing statistics on habitual behavior (e.g., average by time of day), one can specifically identify nonhabitual crowds, which are often very problematic for transport systems. While habitual overcrowding (e.g., peak hour) is well understood both by traffic managers and travelers, nonhabitual overcrowding hotspots can become even more disruptive and unpleasant because they are generally unexpected. By quickly understanding such cases, a transport manager can react and mitigate transport system disruptions. We propose a probabilistic data analysis model that breaks each nonhabitual overcrowding hotspot into a set of explanatory components. The potential explanatory components are initially retrieved from social networks and special events websites and then processed through text-analysis techniques. Finally, for each such component, the probabilistic model estimates a specific share in the total overcrowding counts. We first validate with synthetic data and then test our model with real data from the public transport system (EZLink) of Singapore, focused on three case study areas. We demonstrate that it is able to generate explanations that are intuitively plausible and consistent both locally (correlation coefficient, i.e., CC, from 85% to 99% for the three areas) and globally (CC from 41.2% to 83.9%). This model is directly applicable to any other domain sensitive to crowd formation due to large social events (e.g., communications, water, energy, waste).

Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method.

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.

Observations of the inner radiation belt: CRAND and trapped solar protons

AbstractMeasurements of inner radiation belt protons have been made by the Van Allen Probes Relativistic Electron‐Proton Telescopes as a function of kinetic energy (24 to 76 MeV), equatorial pitch angle, and magnetic L shell, during late 2013 and early 2014. A probabilistic data analysis method reduces background from contamination by higher‐energy protons. Resulting proton intensities are compared to predictions of a theoretical radiation belt model. Then trapped protons originating both from cosmic ray albedo neutron decay (CRAND) and from trapping of solar protons are evident in the measured distributions. An observed double‐peaked distribution in L is attributed, based on the model comparison, to a gap in the occurrence of solar proton events during the 2007 to 2011 solar minimum. Equatorial pitch angle distributions show that trapped solar protons are confined near the magnetic equator but that CRAND protons can reach low altitudes. Narrow pitch angle distributions near the outer edge of the inner belt are characteristic of proton trapping limits.

Optimal performance of charged particle telescopes in space

A Bayesian probabilistic data analysis method for energetic proton and ion data from charged particle telescopes in space is described. The telescope is assumed to consist of only a series of planar silicon detectors with graduated thicknesses. The method is based on a range-straggling function and makes optimal use of energy loss measurements in each detector. It provides accurate incidence angle estimates for particles stopping in the telescope, allowing accurate element identification and possible isotope identification. It also provides energy estimates for high-energy particles going through the telescope without stopping. Examples are shown for simulated telescope design performance tests and application to real space-particle data.

Toward a neurometric foundation for probabilistic independent component analysis of fMRI data

Improved fMRI data analysis methods hold promise for breakthroughs in cognitive and affective neuroscience. Group probabilistic independent component analysis (pICA), such as that implemented by MELODIC (Beckmann & Smith IEEE Transactions on Medical Imaging 23:137-152, 2004), is one popular technique that typifies this development. Recently pICA has been proposed to be a reliable method for studying connectivity networks (Zuo et al. NeuroImage 49:2163-2177, 2010); however, there is no "standard" way to complete a pICA, and the full impact of the options on neurometric properties of resulting components is unknown. In the present study, we sought to assess the robustness, reproducibility, and within-subject test-retest reliability of ICA in two data sets: The first included 30 subjects imaged 3 weeks apart while completing a cognitive control task, and the second included 27 subjects imaged 9 months apart during rest. In addition to examining the impact of analytic parameters on the neurometrics, this study was the first to simultaneously investigate within-subject reliability of ICA-derived components from rest and task fMRI data. Results suggested that for both task and rest, meta-level analyses using 25 subject orders optimized robustness of the components. The impact of dimensionality and voxel threshold for components was subsequently examined regarding properties of reproducibility and within-subject retest reliability. Component thresholds between 0.2 and 0.6 of the maximum value optimized reproducibility across multiple dimensionalities and produced generally fair to moderate reliability estimates (Cicchetti & Sparrow American Journal of Mental Deficiency 86:127-137, 1981). These guidelines strengthen the foundation for this data-driven approach to fMRI analysis by providing prescriptive findings and a descriptive set of neurometrics for resting-state and task fMRI.

Spatial probability distribution of future volcanic eruptions at El Hierro Island (Canary Islands, Spain)

The 2011 submarine eruption that took place in the proximity of El Hierro Island (Canary Islands, Spain) has raised the need to identify the most likely future emission zones even on volcanoes characterized by low frequency activity. Here, we propose a probabilistic method to build the susceptibility map of El Hierro, i.e. the spatial distribution of vent opening for future eruptions, based on the probabilistic analysis of volcano-structural data of the Island collected through new fieldwork measurements, bathymetric information, as well as analysis of geological maps, orthophotos and aerial photographs. These data have been divided into different datasets and converted into separate and weighted probability density functions, which were included in a non-homogeneous Poisson process to produce the volcanic susceptibility map. The most likely area to host new eruptions in El Hierro is in the south-western part of the West rift. High probability locations are also found in the Northeast and South rifts, and along the submarine parts of the rifts. This map represents the first effort to deal with the volcanic hazard at El Hierro and can be a support tool for decision makers in land planning, emergency measures and civil defense actions.

Dynamic Wheel Loads of High-Speed Rail at Speeds Greater than 400 km/h

The high-speed rail (HSR) line in South Korea has been in service since 2004 with a maximum design speed and operating speed of 350 km/h and 300 km/h, respectively. Recently, South Korea developed a high-speed electric multiple unit (HEMU-430X, 430-km/h eXperiment) with a maximum design speed and operating speed of 430 km/h and 400 km/h, respectively; the government was waiting for a trial run on a conventional HSR line. This study tried to predict wheel load fluctuation (WLF), one of the key factors affecting acceleration to speeds over 400 km/h. For WLFs to be understood accurately in the high-speed range greater than 400 km/h, field running tests were performed twice with the KTX-Sancheon trains on the Gyeongbu high-speed line. The trains traveled between Gwangmyeong and Daejeon at maximum running speeds of 302 and 335 km/h, respectively, and WLFs were measured with a telemetry system (radio data transmitter and receiver system) at varying speeds. On the basis of probabilistic data analysis with a Gaussian function, the WLF (σ/Pst) normalized nondimensional parameter at speeds of 400 km/h and 500 km/h was modeled into quadratic functions. The WLFs at speeds of 400 km/h and 500 km/h were predicted to be 0.356 and 0.512, respectively. In addition, impacts from structures that greatly affected WLFs, such as turnouts, transition zones, and loose sleepers, were evaluated quantitatively. Of those, turnouts had the greatest impacts on the WLFs.

Probabilistic Model of the Multiaxial Low-Cycle Fatigue Life Prediction

First, several widely used models of the multiaxial low-cycle fatigue life prediction based on the critical plane approach were presented in this paper, and the predicted results of these models for a medium carbon steel under the condition of multiaxial low-cycle fatigue loading were compared. Second, the stochastic expressions and probability density function curves of the fatigue performance parameters were obtained by probabilistic analysis of the medium carbon steel fatigue data. Finally, the probabilistic model of the multiaxial fatigue life prediction was simulated by Monte Carlo Method, which should provide a basis for the reliability analysis of engineering components subjected to the multiaxial complex loads.

Joint Modelling of Confounding Factors and Prominent Genetic Regulators Provides Increased Accuracy in Genetical Genomics Studies

Expression quantitative trait loci (eQTL) studies are an integral tool to investigate the genetic component of gene expression variation. A major challenge in the analysis of such studies are hidden confounding factors, such as unobserved covariates or unknown subtle environmental perturbations. These factors can induce a pronounced artifactual correlation structure in the expression profiles, which may create spurious false associations or mask real genetic association signals. Here, we report PANAMA (Probabilistic ANAlysis of genoMic dAta), a novel probabilistic model to account for confounding factors within an eQTL analysis. In contrast to previous methods, PANAMA learns hidden factors jointly with the effect of prominent genetic regulators. As a result, this new model can more accurately distinguish true genetic association signals from confounding variation. We applied our model and compared it to existing methods on different datasets and biological systems. PANAMA consistently performs better than alternative methods, and finds in particular substantially more trans regulators. Importantly, our approach not only identifies a greater number of associations, but also yields hits that are biologically more plausible and can be better reproduced between independent studies. A software implementation of PANAMA is freely available online at http://ml.sheffield.ac.uk/qtl/.

Accurate modeling of confounding variation in eQTL studies leads to a great increase in power to detect trans-regulatory effects

AbstractExpression quantitative trait loci (eQTL) studies are an integral tool to investigate the genetic component of gene expression variation. A major challenge in the analysis of such studies are hidden confounding factors, such as unobserved covariates or unknown environmental influences. These factors can induce a pronounced artifactual correlation structure in the expression profiles, which may create spurious false associations or mask real genetic association signals.Here, we report PANAMA (Probabilistic ANAlysis of genoMic dAta), a novel probabilistic model to account for confounding factors within an eQTL analysis. In contrast to previous methods, PANAMA learns hidden factors jointly with the effect of prominent genetic regulators. As a result, PANAMA can more accurately distinguish between true genetic association signals and confounding variation.We applied our model and compared it to existing methods on a variety of datasets and biological systems. PANAMA consistently performs better than alternative methods, and finds in particular substantially more trans regulators. Importantly, PANAMA not only identified a greater number of associations, but also yields hits that are biologically more plausible and can be better reproduced between independent studies.

Probabilistic analysis of weather data for a hybrid solar/wind energy system

In this paper, a procedure for the probabilistic treatment of solar irradiance and wind speed data is reported as a method of evaluating, at a given site, the electric energy generated by both a photovoltaic system and a wind system. The aim of the proposed approach is twofold: first, to check if the real probability distribution functions (PDFs) of both clearness index and wind speed overlap with Hollands and Huget and Weibull PDFs, respectively; and then to find the parameters of these two distributions that best fit the real data. Further, using goodness-of-fit tests, these PDFs are compared with another set of very common PDFs, namely the Gordon and Reddy and Lognormal functions, respectively. The results inform the design of a pre-processing stage for the input of an algorithm that probabilistically optimizes the design of hybrid solar wind power systems. In this paper, the validity of the proposed procedure was tested using long-term meteorological data from Acireale (Italy). Copyright © 2010 John Wiley & Sons, Ltd.

Cognitive and Motor Loops of the Human Cerebro-cerebellar System

We applied fMRI and diffusion-weighted MRI to study the segregation of cognitive and motor functions in the human cerebro-cerebellar system. Our fMRI results show that a load increase in a nonverbal auditory working memory task is associated with enhanced brain activity in the parietal, dorsal premotor, and lateral prefrontal cortices and in lobules VII-VIII of the posterior cerebellum, whereas a sensory-motor control task activated the motor/somatosensory, medial prefrontal, and posterior cingulate cortices and lobules V/VI of the anterior cerebellum. The load-dependent activity in the crus I/II had a specific relationship with cognitive performance: This activity correlated negatively with load-dependent increase in RTs. This correlation between brain activity and RTs was not observed in the sensory-motor task in the activated cerebellar regions. Furthermore, probabilistic tractography analysis of the diffusion-weighted MRI data suggests that the tracts between the cerebral and the cerebellar areas exhibiting cognitive load-dependent and sensory-motor activity are mainly projected via separated pontine (feed-forward tracts) and thalamic (feedback tracts) nuclei. The tractography results also indicate that the crus I/II in the posterior cerebellum is linked with the lateral prefrontal areas activated by cognitive load increase, whereas the anterior cerebellar lobe is not. The current results support the view that cognitive and motor functions are segregated in the cerebellum. On the basis of these results and theories of the function of the cerebellum, we suggest that the posterior cerebellar activity during a demanding cognitive task is involved with optimization of the response speed.

A probabilistic approach to determine thermal process setting parameters: Application for commercial sterility of products

The objective of the probabilistic data analysis presented in this paper was to enable the thermal process to be set on actual data rather than on generic or conservative rules. The application was an ambient stable soup product, heated in a continuous UHT line. The data set comes from a decade of microbiological analysis: initial spore load and survival spore concentration after moderate heat-treatment (100°C for 15min and 110°C for 15min) have been enumerated in forty eight ingredients. The probabilistic analysis was carried out within a risk-based context, considering a Performance Objective, PO, set after the heat-treatment process and an initial spore contamination (H0) at the ingredient mixing step. The probabilistic analysis was based upon Bayesian inference, chosen for its flexibility when dealing with censored data (some values were reported as less than 1log cfu/g) and also for its ability to incorporate in the data analysis prior information. Beforehand, Z values around 10°C for aerobic bacterial spores, and log count error around 1 log, were assumed. The methodology and the results are reported using two ingredients (garlic and milk powder) illustrating the ‘not detected’ (censored data) issue and also the inter-ingredient variability. Indeed, Z was estimated to be 13.6°C (mean) for spores selected from garlic and 5.9°C for those selected from milk powder. Based upon a hypothetical soup recipe with these two ingredients, the sterilization value was estimated to be 13min (95th percentile). The potential use of similar methodology to design and set the sterilization value for the thermal process of future products, is discussed.

Extending the Nano-Positioning System (NPS)

Single-Pair Fluorescence Resonance Energy Transfer (FRET) experiments reveal structural and dynamic information about macro-molecules by monitoring the change in FRET efficiency between fluorescent dyes attached to a macro-molecule. The Nano-Positioning System (NPS) developed recently [1] uses data from several of such experiments to infer the position of a dye attached to protein sites unresolved by x-ray crystallography. Briefly, we perform probabilistic data analysis that allows us to calculate the distribution of possible dye positions in a simple and objective way without relying on ad-hoc procedures. Up to now NPS was limited to the triangulation of just one fluorescently labelled position based on FRET measurements to several other positions known from crystal structure [1,2]. Here, we discuss ways to extend the present model beyond this basic triangulation principle. In particular, we show how to gain three dimensional distance information by analysing triangulation networks where FRET is measured between arbitrary labelling sites in absence of other structural information. [1] A. Muschielok, J. Andrecka, A. Jawhari, F. Brückner, P. Cramer & J. Michaelis, Nat. Meth. 5, 965-971 (2008) [2] J. Andrecka, B. Treutlein, M.A. Izquierdo Arcusa, A. Muschielok, R. Lewis; A.C.M. Cheung, P. Cramer, and J. Michaelis, NAR doi:10.1093/nar/gkp601 (2009)

The Nano-Positioning System - A Fret-Based Tool for Macro-Molecular Structural Analysis

Single-Pair Fluorescence Resonance Energy Transfer (FRET) experiments reveal structural and dynamic information about macro-molecules by monitoring the change in FRET efficiency between fluorescent dyes attached to a macro-molecule. The Nano-Positioning System (NPS) developed recently [1] uses data from several of such experiments to infer the position of a dye attached to protein sites unresolved by x-ray crystallography.While triangulation, the basic underlying principle, is not new and has already been reported in this or a similar context [2,3], the NPS applies probabilistic data analysis to the problem. That allows us to calculate the distribution of possible dye positions in a simple and objective way without relying on ad-hoc procedures, while at the same time we account for various error sources that usually accompany FRET measurements, for instance dye orientation effects. We have applied the NPS to determine the position of the nascent RNA [1] as well as to map the pathway of the non-template and upstream DNA in yeast RNA polymerase II elongation complexes [4].[1] A. Muschielok, J. Andrecka, A. Jawhari, F. Bruckner, P. Cramer & J. Michaelis, Nat. Meth. 5, 965–971 (2008).[2] M. Margittai, J. Widengren, E. Schweinberger, G.F. Schrooder, S. Felekyan, E. Haustein, M. Konig, D. Fasshauer, H. Grubmuller, R. Jahn, and C. A. M. Seidel, PNAS 100, 15516–15521 (2003).[3] J.L. Knight, V. Mekler, J. Mukhopadhyay, R.H. Ebright, and R.M. Levy, Biophys. J. 88, 925–938 (2005).[4] J. Andrecka, B. Treutlein, M.A. Izquierdo Arcusa, A. Muschielok, R. Lewis; A.C.M. Cheung, P. Cramer, and J. Michaelis, NAR doi:10.1093/nar/gkp601 (2009).

Contour approximation of data: A duality theory

Given a dataset D partitioned in clusters, the joint distance function (JDF) J ( x ) at any point x is the harmonic mean of the distances between x and the cluster centers. The JDF is a continuous function, capturing the data points in its lower level sets (a property called contour approximation), and is a useful concept in probabilistic clustering and data analysis. In particular, contour approximation allows a compact representation of the data: for a dataset in R n with N points organized in K clusters, the JDF requires K centers and covariances (if Mahalanobis distances are used), for a total of Kn ( n + 3 ) / 2 parameters, and a considerable reduction of storage if N ≫ K , n . The JDF of the whole dataset, J ( D ) ≔ ∑ { J ( x ) : x ∈ D } , is a measure of the classifiability of the data, and can be used to determine the “right” number of clusters for D . A duality theory for the JDF J ( D ) is given, in analogy with Kuhn’s geometric duality theory for the Fermat–Weber location problem. The JDF J ( D ) is the optimal value of a primal problem (P), for which a dual problem (D) is given, with a sharp lower bound on J ( D ) .

A nano-positioning system for macromolecular structural analysis

Very often, the positions of flexible domains within macromolecules as well as within macromolecular complexes cannot be determined by standard structural biology methods. To overcome this problem, we developed a method that uses probabilistic data analysis to combine single-molecule measurements with X-ray crystallography data. The method determines not only the most likely position of a fluorescent dye molecule attached to the domain but also the complete three-dimensional probability distribution depicting the experimental uncertainty. With this approach, single-pair fluorescence resonance energy transfer measurements can now be used as a quantitative tool for investigating the position and dynamics of flexible domains within macromolecular complexes. We applied this method to find the position of the 5' end of the nascent RNA exiting transcription elongation complexes of yeast (Saccharomyces cerevisiae) RNA polymerase II and studied the influence of transcription factor IIB on the position of the RNA.

Probabilistic analysis of data interleaving for reed-solomon coding in BCMCS

In cdma2000 1xEV-DO Broadcast and Multicast Services (BCMCS), Reed-Solomon coding is applied to the layers above the turbo code, and is particularly effective in correcting long bursts of errors. An additional block interleaving mechanism improves the performance of RS coding by increasing the time diversity, to an extent controlled by the width of the error control block (ECB), which converts error bursts into random patterns. We propose and evaluate a performance model of RS coding under varying conditions of Rayleigh fading on the broadcast channel, within the levels of block interleaving that the BCMCS specification allows. Simulation results show that our model predicts the performance of RS coding accurately. This evaluation will allow a service provider to determine the most efficient RS code for their target service quality, that maximizes the effective data-rate and minimizes the energy required for the RS decoding process.

Probabilistic lithium beam data analysis

A probabilistic data analysis method was applied to analyze the spatially resolved beam emission intensities from the lithium beam diagnostic at ASDEX Upgrade. The method allows us to recover density profiles from the Li I emission profile with a spatial resolution of 5 mm and a temporal resolution of 50 µs. It is based on a probabilistic description of the measured data including absolutely calibrated measurement errors, a forward model for the simulation of the data given a density profile, and prior information about weak constraints on monotonicity. The density profile is parametrized by cubic spline polynomials. The method replaces the conventional approach applying an iterative (shooting) method to invert the density profile. The new probabilistic method allows us to analyze low-density profiles since there is no need to fulfil an inner boundary condition or to pre-smooth measured data because no direct inversion occurs. Consistent profile uncertainty measures are provided for different purposes. Profiles in the edge region can be fully explored for any plasma regime and the profile pedestal is accessible up to 0.8 × 1020 m−3. The advanced technique is demonstrated with low, medium and high density profiles at ASDEX Upgrade. The benefit of the achieved temporal resolution is shown with ELM resolved measurements. The dependence of the density profiles on electron temperature or impurity content is shown to be negligible.