Simple Probabilistic Model Research Articles

Bayesian inversion of pressure diffusivity from microseismicity

We have considered the problem of using microseismic data to characterize the flow of injected fluid during hydraulic fracturing. We have developed a simple probabilistic physical model that directly ties the fluid pressure in the subsurface during the injection to observations of induced microseismicity. This tractable model includes key physical parameters that affect fluid pressure, rock failure, and seismic wave propagation. It is also amenable to a rigorous uncertainty quantification analysis of the forward model and the inversion. We have used this probabilistic rock failure model to invert for fluid pressure during injection from synthetically generated microseismicity and to quantify the uncertainty of this inversion. The results of our analysis can be used to assess the effectiveness of microseismic monitoring in a given experiment and even to suggest ways to improve the quality and value of monitoring.

Contributing factors to Koshava wind characteristics

ABSTRACTKoshava is a local wind usually observed in the cold part of the year over the large part of Serbia, parts of Romania, parts of Hungary, and east Croatia. The main characteristics of the Koshava wind are its high wind speed, southeasterly direction, persistence, and gustiness. This paper analyses the synoptic [Mediterranean cyclones (MCs) and Eurasian anticyclones (EAs)] as well as the mesoscale contributors to the Koshava wind. Time and spatial features of the pressure systems have been analysed using an automatic cyclone tracking scheme. The results show that the MCs and EAs that generate Koshava are approximately 1000 km away from the Koshava region. It is demonstrated that the strong anticyclones are the main trigger for the Koshava wind. Less than 3% of the Koshava winds occurred without the occurrence of either an anticyclone or a cyclone. The Synoptic Koshava Index (SKI), developed in this study and defined as the difference between the area‐averaged mean sea level pressures in the anticyclone and cyclone regions, has been shown to be a good indicator of the Koshava occurrence. Koshava has also been investigated from the perspective of the gap flow windstorm. The across‐mountain pressure difference, ΔP, is the most important mesoscale contributor to the Koshava characteristics. The across‐mountain potential temperature difference, Δθ, together with ΔP, can be successfully used to predict Koshava's occurrence. A simple (linear) probabilistic model for forecasting the Koshava mean hourly wind speed has been constructed. The results demonstrate that the occurrence of the Koshava wind can be predicted with the significantly higher accuracy than the Koshava mean hourly speed. The correlation between Koshava and winds at higher levels is small.

Verification of simple illuminance based measures for indication of discomfort glare from windows

Modern office buildings are often designed with highly glazed facades, with an intention of being sufficiently day lit. However, extensive daylight supply has its backside, as glare might be a considerable concern. From a building design perspective it is important to be able to make reasonable predictions of discomfort glare from windows already in the early design stage when decisions regarding the façade are taken. This study focus on verifying if simple illuminance based measures like vertical illuminance at eye level or horizontal illuminance at the desk are correlated with the perceived glare reported by 44 test subjects in a repeated measure design occupant survey and if the reported glare corresponds with the predictions from the simple Daylight Glare Probability (DGPs) model. Large individual variations were seen in the occupants' assessment of glare in the present study. Yet, the results confirm that there is a statistically significant correlation between both vertical eye illuminance and horizontal illuminance at the desk and the occupants' perception of glare in a perimeter zone office environment, which is promising evidence towards utilizing such simple measures for indication of discomfort glare in early building design. Further, the observed response indicate that the participants in the present study were more tolerant to low illuminance levels and more sensitive to high illuminance levels than the DGPs model would predict. More and larger studies are needed to confirm or enfeeble this latter finding.

Probabilistic prediction model for average bond strength at steel–concrete interface considering corrosion effect

Considerable numbers of reinforced concrete (RC) bridges in the US are structurally deficient mainly due to corrosion. Corrosion affects the structural integrity by deteriorating the material properties and the bond at the steel–concrete interface. Currently, the available bond strength models considering corrosion deterioration are either complex or developed based on the limited database. This paper proposes a simple probabilistic model of bond strength considering corrosion using multivariable regression based on a comprehensive database collected from the literature. The predictions are found to be accurate and unbiased when compared with the experimental results. Then, the proposed bond model is employed in the nonlinear finite element models of intact and corroded RC beams to investigate the importance of steel–concrete bond modeling on evaluating flexural behavior of the beams. Lastly, the minimum required development length for a given corrosion level is calculated and its sufficiency is investigated through a numerical analysis.

The maximal C3 self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses

In 1996, a set X of 20 trinucleotides is identified in genes of both prokaryotes and eukaryotes which has in average the highest occurrence in reading frame compared to the two shifted frames (Arquès and Michel, 1996). Furthermore, this set X has an interesting mathematical property as X is a maximal C3 self-complementary trinucleotide circular code (Arquès and Michel, 1996). In 2014, the number of trinucleotides in prokaryotic genes has been multiplied by a factor of 527. Furthermore, two new gene kingdoms of plasmids and viruses contain enough trinucleotide data to be analysed. The approach used in 1996 for identifying a preferential frame for a trinucleotide is quantified here with a new definition analysing the occurrence probability of a complementary/permutation (CP) trinucleotide set in a gene kingdom. Furthermore, in order to increase the statistical significance of results compared to those of 1996, the circular code X is studied on several gene taxonomic groups in a kingdom. Based on this new statistical approach, the circular code X is strengthened in genes of prokaryotes and eukaryotes, and now also identified in genes of plasmids. A subset of X with 18 or 16 trinucleotides is identified in genes of viruses. Furthermore, a simple probabilistic model based on the independent occurrence of trinucleotides in reading frame of genes explains the circular code frequencies and asymmetries observed in the shifted frames in all studied gene kingdoms. Finally, the developed approach allows to identify variant X codes in genes, i.e. trinucleotide codes which differ from X. In genes of bacteria, eukaryotes and plasmids, 14 among the 47 studied gene taxonomic groups (about 30%) have variant X codes. Seven variant X codes are identified with at least 16 trinucleotides of X. Two variant X codes XA in cyanobacteria and plasmids of cyanobacteria, and XD in birds are self-complementary, without permuted trinucleotides but non-circular. Five variant X codes XB in deinococcus, plasmids of chloroflexi and deinococcus, mammals and kinetoplasts, XC in elusimicrobia and apicomplexans, XE in fishes, XF in insects, and XG in basidiomycetes and plasmids of spirochaetes are C3 self-complementary circular. In genes of viruses, no variant X code is found.

Paradoxical probabilistic behavior for strongly correlated many-body classical systems

Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that each row is a list of n strongly correlated random variables. The correlations are preserved even when n→∞, since the standard central limit theorem does not hold for this array. We show that, if we choose a fixed number m<n of random variables of the nth row and trace over the other n−m variables, and then consider n→∞, the m chosen ones can, paradoxically, turn out to be independent. However, the scenario can be different if m increases with n. Finally, we suggest a possible experimental verification of our results near criticality of a second-order phase transition.

Long-term performance assessment and design of offshore structures

The design of an offshore structure is highly dependent on the operating environmental parameters, where a realistic statistical model of the latter is essential to produce a representative estimate of the performance and failure probability. Establishing an accurate model of the offshore environment can be a challenging task. The use of simple probabilistic models may lead to biased results in the stochastic structural analysis since the environmental impact to an existing offshore structure is associated with a wide range of inter-dependent factors. In this paper, the specification of long-term design loads for offshore structures considering multiple environmental factors is investigated where the dependency between several commonly used sea state parameters are instituted through a copula-based multivariate probabilistic model. Several copula functions, capable of modeling both linear and non-linear dependence structures, are considered. The developed multivariate model based on copula concept is compared with the available approaches in the literature using actual environmental data. The modeled sea state parameters are then utilized to characterize the sea load for the reliability analysis of a real jacket structure where the prediction of the long term load is derived in a discretized form. The applicability of this approach in a high dimensional multivariate problem is also discussed.

Probabilistic Path Queries in Path Networks: An Effective and Efficient Clustering Methods

Efficiently processing shortest path (SP) queries over stochastic networks attracted a lot of research attention as such queries are very popular in the emerging real world applications such as Intelligent Transportation Systems and communication networks whose edge weights can be modeled as a random variable. Some pervious works aim at finding the most likely SP (the path with largest probability to be SP), and others search the least-expected-weight path. In all these works, the definitions of the shortest path query are based on simple probabilistic models which can be converted into the multi-objective optimal issues on a weighted graph. Challenging problem, two algorithms, the PEEDR and the CPGS clustering algorithm. Reliable clusters are those which are not likely to be disconnected in the context of different instantiations of the uncertain graph. we provide a generalized reliability measurement from two basic intuitions (purity and size balance) to overcome the challenges from standard reliability criterion, and develop a novel k-means algorithm to solve the uncertain clustering problem

Impact of measurement dating inaccuracies in the monitoring of bulk flows

This paper discusses the negative impact of errors in the dating of information gathered across a distributed network of sensors to be treated by a centralized monitoring algorithm. In this contribution, an example of flow monitoring serves as basis for the analysis. We consider an estimator setup for loss detection. Using a simple probability model, we determine the variance of this estimator and show how it is impacted by the dating uncertainty. A mitigating solution is proposed. Further extensions are discussed.

Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater

On geological timescales there is a temperature dependent feedback that means that increased degassing of CO2 into the atmosphere leads to increased CO2 drawdown into rocks stabilizing Earth's climate. It is widely considered that this thermostat largely comes from continental chemical weathering. An alternative, or additional, feedback comes from dissolution of seafloor basalt in low-temperature (tens of °C), off-axis, hydrothermal systems. Carbonate minerals precipitated in these systems provide strong evidence that increased bottom water temperature (traced by their O-isotopic compositions) leads to increased basalt dissolution (traced by their Sr-isotopic compositions). Inversion of a simple probabilistic model of fluid–rock interaction allows us to determine the apparent activation energy of rock dissolution in these systems. The high value we find (92±7 kJmol−1) indicates a strong temperature dependence of rock dissolution. Because deep-ocean temperature is sensitive to global climate, and the fluid temperature in the upper oceanic crust is strongly influenced by bottom water temperature, increased global temperature must lead to increased basalt dissolution. In turn, through the generation of alkalinity by rock dissolution, this leads to a negative feedback on planetary warming; i.e. off-axis, hydrothermal systems play an important role in the planetary thermostat. Changes in the extent of rock dissolution, due to changes in bottom water temperature, also lead to changes in the flux of unradiogenic Sr into the ocean. The decreased flux of unradiogenic Sr into the ocean due to the cooling of ocean bottom water over the last 35 Myr is sufficient to explain most of the increase in seawater 87Sr/86Sr over this time.

Game, Set and Stats

Abstract Chris Gray makes the case for data analytics in tennis with a simple probability model for analysing the outcomes of matches

Inherent directionality explains the lack of feedback loops in empirical networks

We explore the hypothesis that the relative abundance of feedback loops in many empirical complex networks is severely reduced owing to the presence of an inherent global directionality. Aimed at quantifying this idea, we propose a simple probabilistic model in which a free parameter γ controls the degree of inherent directionality. Upon strengthening such directionality, the model predicts a drastic reduction in the fraction of loops which are also feedback loops. To test this prediction, we extensively enumerated loops and feedback loops in many empirical biological, ecological and socio-technological directed networks. We show that, in almost all cases, empirical networks have a much smaller fraction of feedback loops than network randomizations. Quite remarkably, this empirical finding is quantitatively reproduced, for all loop lengths, by our model by fitting its only parameter γ. Moreover, the fitted value of γ correlates quite well with another direct measurement of network directionality, performed by means of a novel algorithm. We conclude that the existence of an inherent network directionality provides a parsimonious quantitative explanation for the observed lack of feedback loops in empirical networks.

Autoimmunity and tumor immunology: two facets of a probabilistic immune system.

BackgroundThe immune system of vertebrates has evolved the ability to mount highly elaborate responses to a broad range of pathogen-driven threats. Accordingly, it is quite a challenge to understand how a primitive adaptive immune system that probably lacked much of its present complexity could provide its bearers with significant evolutionary advantage, and therefore, continue to be selected for.ResultsWe have developed a very simple model of the immune system that captures the probabilistic communication between its innate and adaptive components. Probabilistic communication arises specifically from the fact that antigen presenting cells collect and present a range of antigens from which the adaptive immune system must (probabilistically) identify its target. Our results show that although some degree of self-reactivity in the immune repertoire is unavoidable, the system is generally able to correctly target pathogens rather than self-antigens. Particular circumstances that impair correct targeting and that may lead to infection-induced autoimmunity can be predicted within this framework. Notably, the probabilistic immune system exhibits the remarkable ability to detect sudden increases in the abundance of rare self-antigens, which represents a first step towards developing anti-tumoral responses.ConclusionA simple probabilistic model of the communication between the innate and adaptive immune system provides a robust immune response, including targeting tumors, but at the price of being at risk of developing autoimmunity.

A simple probabilistic model to combine losses arising from the simultaneous occurrence of several hazards

A simple model is presented to combine, using a probabilistic approach, the losses arising from several hazards that are triggered simultaneously by the same event. The merits of the model are presented, demonstrating the intuitive appeal of this combination rule. Assuming that the losses due to individual hazards are conditionally independent random variables with known mean and variance, expressions are given to compute the mean and variance of the combined loss. Finally, an approximate method is given to construct the probability distribution of this combined loss.

Understanding disease mechanisms with models of signaling pathway activities.

BackgroundUnderstanding the aspects of the cell functionality that account for disease or drug action mechanisms is one of the main challenges in the analysis of genomic data and is on the basis of the future implementation of precision medicine.ResultsHere we propose a simple probabilistic model in which signaling pathways are separated into elementary sub-pathways or signal transmission circuits (which ultimately trigger cell functions) and then transforms gene expression measurements into probabilities of activation of such signal transmission circuits. Using this model, differential activation of such circuits between biological conditions can be estimated. Thus, circuit activation statuses can be interpreted as biomarkers that discriminate among the compared conditions. This type of mechanism-based biomarkers accounts for cell functional activities and can easily be associated to disease or drug action mechanisms. The accuracy of the proposed model is demonstrated with simulations and real datasets.ConclusionsThe proposed model provides detailed information that enables the interpretation disease mechanisms as a consequence of the complex combinations of altered gene expression values. Moreover, it offers a framework for suggesting possible ways of therapeutic intervention in a pathologically perturbed system.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-014-0121-3) contains supplementary material, which is available to authorized users.

Characterizing spiking in noisy type II neurons.

Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model.

English

We develop an efficient general-purpose blind/no-reference image quality assessment (IQA) algorithm using a natural scene statistics (NSS) model of discrete cosine transform (DCT) coefficients. The algorithm is computationally appealing, given the availability of platforms optimized for DCT computation. The approach relies on a simple Bayesian inference model to predict image quality scores given certain extracted features. The features are based on an NSS model of the image DCT coefficients. The estimated parameters of the model are utilized to form features that are indicative of perceptual quality. These features are used in a simple Bayesian inference approach to predict quality scores. The resulting algorithm, which we name BLIINDS-II, requires minimal training and adopts a simple probabilistic model for score prediction. Given the extracted features from a test image, the quality score that maximizes the probability of the empirically determined inference model is chosen as the predicted quality score of that image. When tested on the LIVE IQA database, BLIINDS-II is shown to correlate highly with human judgments of quality, at a level that is competitive with the popular SSIM index.

Local value difference metric

Value difference metric (VDM) is one of the widely used distance functions designed to work with nominal attributes. Research has indicated that the definition of VDM follows naturally from a simple probabilistic model called a naive Bayes (NB). NB assumes that all the attributes are independent given the class. To further improve the performance of NB, several techniques have been proposed. Among these, an effective technique is local learning. Because VDM has a close relationship with NB, in this paper, we propose a local learning method for VDM. The improved distance function is called local value difference metric (LVDM). When LVDM computes the distance between a test instance and each training instance, the conditional probabilities in VDM are estimated by counting from the neighborhood of the test instance only instead of from all the training data. A modified decision tree algorithm is proposed to determine the neighborhood of the test instance. The experimental results on 43 datasets downloaded from the University of California at Irvine (UCI) show that the proposed LVDM significantly outperforms VDM in terms of the class-probability estimation performance of distance-based learning algorithms.

Identification of chromosomal translocation hotspots via scan statistics.

The detection of genomic regions unusually rich in a given pattern is an important undertaking in the analysis of next-generation sequencing data. Recent studies of chromosomal translocations in activated B lymphocytes have identified regions that are frequently translocated to c-myc oncogene. A quantitative method for the identification of translocation hotspots was crucial to this study. Here we improve this analysis by using a simple probabilistic model and the framework provided by scan statistics to define the number and location of translocation breakpoint hotspots. A key feature of our method is that it provides a global chromosome-wide nominal control level to clustering, as opposed to previous methods based on local criteria. While being motivated by a specific application, the detection of unusual clusters is a widespread problem in bioinformatics. We expect our method to be useful in the analysis of data from other experimental approaches such as of ChIP-seq and 4C-seq. The analysis of translocations from B lymphocytes with the method described here reveals the presence of longer hotspots when compared with those defined previously. Further, we show that the hotspot size changes substantially in the absence of DNA repair protein 53BP1. When 53BP1 deficiency is combined with overexpression of activation-induced cytidine deaminase, the hotspot length increases even further. These changes are not detected by previous methods that use local significance criteria for clustering. Our method is also able to identify several exclusive translocation hotspots located in genes of known tumor supressors. The detection of translocation hotspots is done with hot_scan, a program implemented in R and Perl. Source code and documentation are freely available for download at https://github.com/itojal/hot_scan.

DEGREE OF DIFFICULTY AS THE OBJECTIVE OF CONTEST DESIGN

The compensation received by economic agents reflects their performance. Usually compensation reflects performance measured cardinally, but sometimes ordinal considerations play a role. It is well established that rewards — cardinal or ordinal — can rationally motivate contestants to put forth increased effort. We ask whether rewards, and in particular their cardinal or ordinal nature, can affect agents' strategies. Specifically, if level of effort is fixed and degree of difficulty is the only choice, what strategy is optimal? For example, in a high-jump competition, level of effort is not a meaningful variable; what is of interest is the choice of strategy — the height attempted, or degree of difficulty. We study how optimal strategies reflect reward structure, assuming that rewards may depend on level of difficulty, and go only to successful candidates, or only to candidates who succeed at more difficult tasks. Basing our conclusions in part on simple probabilistic models in which optimal choices can be determined analytically, we show how the structure of competitive rewards alters contestants' rational choices. We adopt a contest-design framework: What combinations of fixed and variable prizes cause contestants to select degrees of difficulty that maximize the contest designer's expected payoff? Our general conclusion is that competition can affect strategic choices, in magnitudes and even directions that are difficult to predict.