Joint Conditional Probability Research Articles

三峡水库提前蓄水方案的优化选择

应用Copula函数构建了联合分布及条件概率分布，通过随机抽样方法模拟得到三峡水库9月份随机入库流量序列。建立了提前蓄水方案优选模型，计算并分析了8月下旬不同来水情景下，三峡水库9月份提前蓄水方案的优化选择。研究结果表明：若8月下旬来水为丰水，则9月下旬起蓄，月底均匀蓄水至166 m，较原设计方案，在不增加防洪风险的前提下，多年平均发电量可增加1.57亿kW∙h (1.46%)，弃水量减小10.72亿m3 (12.89%)；若来水为平水，则9月中旬起蓄，月底均匀蓄水至166 m，较原设计方案，在不增加防洪风险的前提下，多年平均发电量可增加3.45亿kW∙h (3.40%)，弃水量减小22.59亿m3 (34.19%)；若来水为枯水，通过加强实时监测，则可进一步提前至9月上旬起蓄，月底均匀蓄水至166 m，较原设计方案，在基本不增加防洪风险的前提下，多年平均发电量可增加5.50亿kW∙h (6.12%)，弃水量减小19.18亿m3 (51.89%)。 A joint distribution function and conditional probability distribution of this samples using copula was built and inflow series in September were obtained by stochastic simulation method. Furthermore, a refill operation optimization model of the Three Gorges Reservoir was established in this paper to derive the optimal refill scheme. The results show that the optimal refill scheme depends on the reservoir inflow in late August. In the wet year, refill begins in late September with storage level reaching 166 m on September 30 linearly. Comparing with designed scheme, the scheme can generate extra about 1.57 × 108 kW·h electrical energy (by 1.46%) and save 10.72 × 108 m3 water resources (by 12.89%) annually without increasing the flood control risk; In the normal year, refill begins in middle September with storage level reaching 166 m on September 30 linearly. Comparing with designed scheme, the scheme can generate extra about 3.45 × 108 kW·h electrical energy (by 3.40%) and save 22.59 × 108 m3 water resources (by 34.19%) annually without increasing the flood control risk; In the dry year, refill begins in early September with storage level reaching 166 m on September 30 linearly by strengthening real-time monitoring. Comparing with designed scheme, the scheme can generate extra about 5.50 × 108 kW·h electrical energy (by 6.12%) and save 19.18 × 108 m3 water resources (by 51.89%) annually without increasing the flood control risk.

Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method

We presented a new methodology for seismic reservoir characterization that combined advanced geostatistical methods with traditional geophysical models to provide fine-scale reservoir models of facies and reservoir properties, such as porosity and net-to-gross. The methodology we proposed was a stochastic inversion where we simultaneously obtained earth models of facies, rock properties, and elastic attributes. It is based on an iterative process where we generated a set of models of reservoir properties by using sequential simulations, calculated the corresponding elastic attributes through rock-physics relations, computed synthetic seismograms and, finally, compared these synthetic results with the real seismic amplitudes. The optimization is a stochastic technique, the probability perturbation method, that perturbs the probability distribution of the initial realization and allows obtaining a facies model consistent with all available data through a relatively small number of iterations. The probability perturbation approach uses the Tau model probabillistic method, which provides an analytical representation to combine single probabilistic information into a joint conditional probability. The advantages of probability perturbation method are that it transforms a 3D multiparameter optimization problem into a set of 1D optimization problems and it allowed us to include several probabilistic information through the Tau model. The method was tested on a synthetic case where we generated a set of pseudologs and the corresponding synthetic seismograms. We then applied the method to a real well profile, and finally extended it to a 2D seismic section. The application to the real reservoir study included data from three wells and partially stacked near and far seismic sections, and provided as a main result the set of optimized models of facies, and of the relevant petrophysical properties, to be the initial static reservoir models for fluid flow reservoir simulations.

Cross-Layer Design of Combining HARQ with Adaptive Modulation and Coding for Nakagami-m Fading Channels

In this paper, we propose a cross-layer design which combines adaptive modulation and coding (AMC) at the physical layer with a hybrid automatic repeat request (HARQ) protocol at the data link layer to minimize the packet error rate (PER) and maximize the spectral efficiency. By using Markov model to predict the channel condition of next frame according to the second order statistics characteristics of the former frame, we calculate the conditional probability density function and joint probability density function of signal to noise ratio (SNR). Further, we derive the packet error rate and average spectral efficiency in closed-form for transmission over Nakagami-m fading channels. Numerical results show that the proposed scheme can obtain lower PER and higher spectral efficiency c ompared with traditional HARQ protocol s. The cross-layer design scheme combing type-III HARQ with AMC can achieve the highest spectral efficiency and the lowest PER than type-I HARQ and type-II HARQ.

Multispectral texture characterization: application to computer aided diagnosis on prostatic tissue images

AbstractVarious approaches have been proposed in the literature for texture characterization of images. Some of them are based on statistical properties, others on fractal measures and some more on multi-resolution analysis. Basically, these approaches have been applied on mono-band images. However, most of them have been extended by including the additional information between spectral bands to deal with multi-band texture images. In this article, we investigate the problem of texture characterization for multi-band images. Therefore, we aim to add spectral information to classical texture analysis methods that only treat gray-level spatial variations. To achieve this goal, we propose a spatial and spectral gray level dependence method (SSGLDM) in order to extend the concept of gray level co-occurrence matrix (GLCM) by assuming the presence of texture joint information between spectral bands. Thus, we propose new multi-dimensional functions for estimating the second-order joint conditional probability density of spectral vectors. Theses functions can be represented in structure form which can help us to compute the occurrences while keeping the corresponding components of spectral vectors. In addition, new texture features measurements related to (SSGLDM) which define the multi-spectral image properties are proposed. Extensive experiments have been carried out on 624 textured multi-spectral images for use in prostate cancer diagnosis and quantitative results showed the efficiency of this method compared to the GLCM. The results indicate a significant improvement in terms of global accuracy rate. Thus, the proposed approach can provide clinically useful information for discriminating pathological tissue from healthy tissue.

A probability model and sampling algorithm for the inter‐day stochastic traffic assignment problem

SUMMARYIn this study, we consider that inter‐day traffic flow fluctuations in a network are caused by stochastic travel behavior. We treat route traffic flows at each time interval as random variables. Therefore, the solution of the stochastic assignment problem should be the conditional joint probability distribution of the route flows given that the network is in stochastic user equilibrium. We formulate the conditional joint distribution and develop a Gibbs sampler to draw samples from the conditional joint distribution. The characteristics of the route flows at each time interval during the time horizon can be estimated on the basis of the simulated samples. Copyright © 2012 John Wiley & Sons, Ltd.

Test of Strain Behavior Model with Radon Anomaly in Seismogenic Area: A Bayesian Melding Approach

Mathematical models in seismo-geochemical monitoring offer powerful tools for the study and exploration of complex dynamics associated with discharge of radon as the indicator of change of intense-deformed conditions of seismogenic layers or blocks within the lithosphere. Seismic precursory model of radon gas emanation in the process of earthquake prediction research aims to find out the distinct anomaly variation necessary to correlate radon gas with processes of preparation and realization of tectonic earthquakes in long-term and short-term forecasts tectonic earthquakes. The study involves a radon gas volume analytic model to find the correlation of radon fluctuations to stress drop under compression and dilatation strain condition. Here, we present a mathematical inference by observing radon gas emanation prior to the occurrence of earthquake that may reduce the uncertainties in models and updating their probability distributions in a Bayesian deterministic model. Using Bayesian melding theorem, we implement an inferential framework to understand the process of preparation of tectonic earthquake and concurrent occurrence of radon discharge during a tectonic earthquake phenomena. Bayesian melding for deterministic simulation models was augmented to make use of prior knowledge on correlations between model inputs. The background porosity is used as a priori information for analyzing the block subjected to inelastic strain. It can be inferred that use of probabilistic framework involving exhalation of radon may provide a scenario of earthquake occurrences on recession of the curve that represents a qualitative pattern of radon activity concentration drop, indicating associated stress change within the causative seismogenic fault. Using evidence analysis, we propose a joint conditional probability framework model simulation to understand how a single fracture may be affected in response to an external load and radon anomaly change that can be used to detect the slip, a predictable nature of the causative fault in the subsurface rock.

Systemic Risk and Sovereign Debt in the Euro Area

We introduce a new measure of systemic risk, the change in the conditional joint probability of default, which assesses the effects of the interdependence in the financial system on the general default risk of sovereign debtors. We apply our measure to examine the fragility of the European financial system during the ongoing sovereign debt crisis. Our analysis documents an increase in systemic risk contributions in the euro area during the post-Lehman global recession and especially after the beginning of the euro area sovereign debt crisis. We also find a considerable potential for cascade effects from small to large euro area sovereigns. When we investigate the effect of sovereign default on the European Union banking system, we find that bigger banks, banks with riskier activities, with poor asset quality, and funding and liquidity constraints tend to be more vulnerable to a sovereign default. Surprisingly, an increase in leverage does not seem to influence systemic vulnerability.

Region-Level Motion-Based Foreground Segmentation Under a Bayesian Network

This paper presents a probabilistic approach for automatically segmenting foreground objects from a video sequence. In order to save computation time and be robust to noise effects, a region detection algorithm incorporating edge information is first proposed to identify the regions of interest, within which the spatial relationships are represented by a region adjacency graph. Next, we consider the motion of the foreground objects and, hence, utilize the temporal coherence property in the regions detected. Thus, the foreground segmentation problem is formulated as follows. Given two consecutive image frames and the segmentation result priorly obtained, we simultaneously estimate the motion vector field and the foreground segmentation mask in a mutually supporting manner by maximizing the conditional joint probability density function of these two elements. To represent the conditional joint probability density function in a compact form, a Bayesian network is adopted, which is derived to model the interdependency of these two elements. Experimental results for several video sequences are provided to demonstrate the effectiveness of the proposed approach.

Digital Image Analysis of Endoscopic Images of Diminutive Polyps

Purpose: Endoscopic digital images contain rich information on texture and color. There is increasing interest in differentiating tissue pathology based on the patterns of color and texture features of endoscopic images extracted by digital image analysis (DIA). Objective: In this study, we applied techniques of DIA to endoscopic images of diminutive polyps in order to identify the color and texture features of endoscopic images that may differentiate adenomatous polyps from hyperplastic polyps. Methods: Methods: Our endoscopic image database was searched to retrieve and store digital images of diminutive polyps with diagnosis confirmed by histopathology. Texture analysis was performed on multiple regions of interest (ROIs) digitally selected in these images using the MatLab image processing toolbox; the following texture parameters were extracted: histogram (first order statistics) run-length and co-occurrence matrix (measuring features of runs of pixels and distribution of pairs of pixels), gradient analysis (spatial distribution of pixels), auto-regressive analysis (measurement of local interaction amongst pixels of different grey level values) and also wavelet analysis (which measures parameters of spatial frequency). Principal component analysis (PCA) was used for data reduction, and an artificial neural network (NN) based predictive model was built, trained and validated using the extracted texture features for classification of adenomatous polyps from hyperplastic polyps. Results: Results: A total of 110 and 109 ROIs were selected from endoscopic images of 30 and 28 patients with diminutive adenomatous and hyperplastic polyps, respectively. The sensitivity and specificity of the multilayered perceptron neural network classification model were both 82% with an area under the receiver operating characteristic (ROC) curve of 0.87. Three types of features of pixel distribution had high discriminatory power: Kurtosis (measure of the steepness of the pixel distribution), angular second momentum and horizontal and vertical grey level non-uniformity (parameters estimating the second order joint conditional probability density functions of spatial distribution of two neighboring pixels) Conclusion: Conclusion: Results of this exploratory study suggest that the technique DIA may be a clinically useful adjunct for non-invasive automated diagnosis of diminutive colon polyps, particularly if available as a real-time application.

Using Bayesian Networks in reliability evaluation for an [formula omitted]-out-of- [formula omitted]:F distributed communication system

A Bayesian Network is a probability-based approach to infer or make decision in systems with stochastic parameters. It is used to model and predict the behaviour of a particular system. This prediction is based on the observed stochastic phenomena of the system. The main purpose of building a Bayesian Network is to estimate the certainty of unobservable (or costly observable) events called hypothesis variables. Bayesian Networks allow us to use the causal relationships and can then easily handle and predict a critical situation in distributed systems. The causal relationships are expressed as a joint conditional probability distribution to relate the different possible states of variables. We also say a situation is critical when, in spite of the failure of some components the system is still working but the next failure will cause a system failure. Most of the other models cannot give us an accurate prediction for such a critical situation, because they cannot recognize the correlations and relations between the events in the system. Bayesian Networks, however, can encode such dependencies. Furthermore, the table of conditional probabilities, which is the quantitative part of Bayesian Networks developed for reliability analysis, not only includes many straightforward probability functions, but also includes many 0s and 1s as the working or survival conditional probabilities. This can help us to simulate the model much faster in reliability studies. This paper shows how one may use Bayesian Networks as a statistical technique to develop a new approach to evaluate the reliability of an ( r , s ) -out-of- ( m , n ) : F system. An ( r , s ) -out-of- ( m , n ) : F system is a system that fails when at least an r × s matrix of its components fail.

Digital Image Analysis (DIA) Is a Useful Adjunct to Endosonographic Diagnosis of Submucosal Lesions (SML) of the Gastro-Intestinal Tract

Establishing definitive diagnosis of gastrointestinal SML remains a challenge. Information from EUS further delineates the lesions, but histologic data remain the gold standard. To enhance the diagnostic capability of EUS, with the hope to circumvent the need for tissue acquisition, EUS images were digitally analyzed using the technique described pervious by us to discern any parameters that can differentiate clinically significant lesions such as, gastrointestinal stromal cell tumors (GIST) and carcinoids from more benign lesions such as such as, lipoma. Objective: To evaluate the role of DIA of EUS images of SML. Methods: Patients with histopathologically confirmed SML who had undergone EUS evaluation were identified from our database. Representative regions of interest (ROIs) were digitally selected from their EUS images [Gastrointest Endosc 2006;63(5): AB 256, Gastrointest Endosc 2007;65(5):AB 103, & Das, Gastrointest Endosc 2008 (in press)]. Texture analyses were performed using histogram, run-length and co-occurrence matrix (measuring runs of pixels and distribution of pairs of pixels), gradient analysis (spatial distribution of pixels), auto-regressive analysis (measurement of local interaction amongst pixels of different grey level values) and also wavelet analysis (which measures parameters of spatial frequency). Results: A total of 106, 111 and 124 ROIs were selected from EUS images of 8, 10 and 28 patients with lipoma, carcinoids and GIST, respectively. Principal component analysis (PCA) was used for data reduction and later a neural network (ANN) based predictive model was built, trained and validated using the extracted texture features for classification. The performance characteristics of the ANN model in classifying lipoma, carcinoids and GIST is shown in Table. Three types of features of pixel distribution had high discriminatory power: Kurtosis (measure of the steepness of the pixel distribution), angular second momentum and horizontal and vertical grey level non-uniformity (parameters estimating the second order joint conditional probability density functions of spatial distribution of two neighboring pixels). Conclusion: DIA of texture features of EUS images is a useful non-invasive adjunct to endosonographic diagnosis of submucosal lesions. Tabled 1 SML Sensitivity Specificity PPV NPV AUC ∗ AUC of ROC curve. Lipoma 0.90 0.77 0.64 0.95 0.92 Carcinoid 0.79 0.81 0.67 0.89 0.86 GIST 0.81 0.79 0.74 0.86 0.89 ∗ AUC of ROC curve. Open table in a new tab

On the Multivariate Conditional Probability Density of a Vector Perturbed by Gaussian Noise

This correspondence examines the joint conditional probability density function (PDF) of the main variables (envelope, phase, and their eta-order time derivatives) of a time-varying random signal in the presence of additive Gaussian noise. The main variables are conditioned with respect to the given variables, which are the amplitude, phase, and their derivatives of the signal alone. We prove a theorem stating that some of the conditional PDFs of the main variables do not depend on some of the given variables. This theorem, together with Bayes's theorem, can substantially simplify the derivations of conditional PDFs and give alternative forms of them. Both theorems can also help in finding reasonable approximations, as we demonstrate for the phase and first time derivative of the envelope.

Probabilistic Prediction Models for Aggregate Quarry Siting

Weights-of-evidence (WofE) and logistic regression techniques were used in a GIS framework to predict the spatial likelihood (prospectivity) of crushed-stone aggregate quarry development. The joint conditional probability models, based on geology, transportation network, and population density variables, were defined using quarry location and time of development data for the New England States, North Carolina, and South Carolina, USA. The Quarry Operation models describe the distribution of active aggregate quarries, independent of the date of opening. The New Quarry models describe the distribution of aggregate quarries when they open. Because of the small number of new quarries developed in the study areas during the last decade, independent New Quarry models have low parameter estimate reliability. The performance of parameter estimates derived for Quarry Operation models, defined by a larger number of active quarries in the study areas, were tested and evaluated to predict the spatial likelihood of new quarry development. Population density conditions at the time of new quarry development were used to modify the population density variable in the Quarry Operation models to apply to new quarry development sites. The Quarry Operation parameters derived for the New England study area, Carolina study area, and the combined New England and Carolina study areas were all similar in magnitude and relative strength. The Quarry Operation model parameters, using the modified population density variables, were found to be a good predictor of new quarry locations. Both the aggregate industry and the land management community can use the model approach to target areas for more detailed site evaluation for quarry location. The models can be revised easily to reflect actual or anticipated changes in transportation and population features.

Digital Image Analysis (DIA) of EUS Images Accurately Differentiates Pancreatic Cancer (PC) from Chronic Pancreatitis (CP)

Changes of CP markedly degrades the accuracy of EUS in diagnosing PC. We previously reported (DDW 2006) DIA based on spatial distribution of ultrasound amplitude or grey-level pixels of EUS images as an approach to tissue characterization. Objective: We performed quantitative analysis of texture parameters of EUS images to evaluate if DIA can reliably distinguish PC from CP. Methods: Representative regions of interest (ROIs) were digitally selected from EUS images of patients with normal pancreas (group I), established CP (diagnosed by clinical features and multiple imaging modalities, group II) and histologically confirmed PC (group III,) and were analyzed with a DIA software. Texture analyses were performed using histogram, run-length and co-occurrence matrix (measuring runs of pixels and distribution of pairs of pixels), gradient analysis (spatial distribution of pixels), auto-regressive analysis (measurement of local interaction amongst pixels of different grey level values) and also wavelet analysis (which measures parameters of spatial frequency). Principal component analysis (PCA) was used for data reduction and later a neural network (NN) based predictive model was built, trained and validated using the extracted texture features for classification. Methods: A total of 110, 99 and 110 ROIs in Group I, II, III, respectively, were available for analysis and for each ROI, a total 256 statistical parameters were initially extracted and 11 features (representing 96% of initial eigenvalues) were retained subsequently by PCA. With a random selection of the half of the dataset, a multi-layered perceptron NN model was built, and trained using the 11 PCA selected parameters as input variables for prediction of PC and then the model was validated in the remainder of the dataset. The NN model had a very high classification performance in classifying ROIs representing PC with an area under Receiver Operating Characteristic Curve of 0.93 in the validation set. Three types of features of pixel distribution had high discriminatory power: Kurtosis (measure of the steepness of the pixel distribution), angular second momentum and horizontal and vertical grey level non-uniformity (parameters estimating the second order joint conditional probability density functions of spatial distribution of two neighboring pixels). Conclusion: DIA of texture features of EUS images is highly accurate in differentiating PC from CP and normal tissue, with performance characteristics similar to aspiration cytology. If real-time application of DIA achieves similar results, this technology can potentially eliminate the need for tissue aquisition.

Deciding Whether There is Statistical Independence or Not?

The study investigated how students assess statistical independence (SI). A sample of 98 students was available to the researcher. One group was probed on their understanding of statistical independence, a second group was given a proficiency test and a third group was presented a proof for statistical Independence. Interview data from the first two groups exposed student misconception on their understanding and assessment of SI. Those who judge the relation from a causal framework, tend to explore the "representativeness of the relation," if the relation is familiar, students judge it as being dependent; and if the relation is incidental, it is judged as being independent. The results indicate that student proficiency in the calculation and conceptual formalization of the joint probability and conditional probabilities are a prerequisite to the formalization of SI. The study proposes a continuous feedback to student responses through a conceptual mediated approach and use of formal algebra as a viable method to alter strongly held misconception of SI assessment.

Quantitative texture analysis of EUS images accurately differentiates pancreatic cancer from normal tissue and may obviate the need for EUS-FNA

Texture analysis as an approach to tissue characterization based on the two-dimensional spatial distribution of ultrasound amplitude or grey-level pixels within a region of interest (ROI) is well-established and have been used extensively in Radiology and echocardiography. Objective: We performed a quantitative statistical analysis of various texture parameters of EUS images in patients with histologically confirmed pancreatic adenocarcinoma to evaluate if such statistical techniques can reliably distinguish between malignant and normal pancreatic tissue. Methods: Linear endosonographic images of 22 patients who presented with pancreatic mass and underwent EUS guided FNA for establishing diagnosis of pancreatic adenocarcinoma were analyzed with an image analyzing software (ImageJ, NIH). Multiple ROIs were digitally selected both in the area of the malignant mass and normal pancreatic tissue by an experienced endosonographer. Texture analysis was performed using: histogram (first order statistics) run-length and co-occurrence matrix (measuring features of runs of pixels and distribution of pairs of pixels), gradient analysis (spatial distribution of pixels), auto-regressive analysis (measurement of local interaction amongst pixels of different grey level values) and also wavelet analysis (which measures parameters of spatial frequency). A neural network (NN) based predictive model was built, trained and validated using the extracted texture features for classification of malignant tissue from normal. Methods: A total of 70 ROIs representing malignant tissue and 110 representing normal pancreatic tissue was available for analysis and for each ROI, a total 256 statistical parameters were initially extracted and subsequently 10 best discriminating (based on highest Fisher's co-efficient) features were retained. Overall, 3 types of features had high discriminatory power: Kurtosis (which is a measure of the steepness of the pixel distribution), angular second momentum and horizontal and vertical grey level non-uniformity (parameters estimating the second order joint conditional probability density functions of spatial distribution of two neighboring pixels). Using a random selection of the half of the data set (90 ROIs), a multi-layered perceptron NN model was built, trained using the 10 features as input variables for prediction of malignant tissue and then the model was validated on the rest of the 90 ROIs. The NN model had a very high classification performance with an area under Receiver Operating Characteristic Curve of 0.91 (PPV of 80% and NPV 90%). Conclusion: Digital image analysis of texture features on EUS images is highly accurate in differentiating malignant from normal pancreatic tissue with performance characteristics similar to aspiration cytology.

Digital Image Analysis of EUS Images Accurately Differentiates Pancreatic Cancer from Normal Tissue and May Obviate the Need for EUS-FNA

Texture analysis as an approach to tissue characterization based on the two-dimensional spatial distribution of ultrasound grey-level pixels within a region of interest (ROI) is well-established and have been used extensively in Radiology and echocardiography. Objective: We performed a quantitative statistical analysis of various texture parameters of EUS images in patients with histologically confirmed pancreatic adenocarcinoma to evaluate if such statistical techniques can reliably distinguish between malignant and normal pancreatic tissue. Methods: Linear endosonographic images of 22 patients who presented with pancreatic mass and underwent EUS guided FNA for establishing diagnosis of pancreatic adenocarcinoma were analyzed with an image analyzing software (ImageJ, NIH). Multiple ROIs were digitally selected both in the area of the malignant mass and normal pancreatic tissue by an experienced endosonographer. Texture analysis was performed using : histogram (first order statistics) run-length and co-occurrence matrix (measuring features of runs of pixels and distribution of pairs of pixels), gradient analysis (spatial distribution of pixels) , auto-regressive analysis (measurement of local interaction amongst pixels of different grey level values) and also wavelet analysis (which measures parameters of spatial frequency). Methods: A total of 70 ROIs representing malignant tissue and 110 representing normal pancreatic tissue was available for analysis and for each ROI, a total 256 statistical parameters were initially extracted and subsequently 10 best discriminating (based on highest Fisher's co-efficient) features were retained. Overall, 3 types of features had high discriminatory power: Kurtosis (which is a measure of the steepness of the pixel distribution), angular second momentum and horizontal and vertical grey level non-uniformity (parameters estimating the second order joint conditional probability density functions of spatial distribution of two neighboring pixels). Using a random selection of the half of the data set (90 ROIs), a multi-layered perceptron neural network (NN) model was built and trained using the 10 features as input variables for prediction of malignant tissue and then the model was validated on the rest of the 90 ROIs. The NN model had a very high classification performance in differentiating malignant from normal tissue with an area under Receiver Operating Characteristic Curve of 0.91 (PPV of 80% and NPV 90%). Conclusion: Digital image analysis of texture features on EUS images is highly accurate in differentiating malignant from normal pancreatic tissue with performance characteristics similar to aspiration cytology.

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.

A Markov Chain‐Based Probability Vector Approach for Modeling Spatial Uncertainties of Soil Classes

Due to our imperfect knowledge of soil distributions acquired from field surveys, spatial uncertainties inevitably arise in mapping soils at unobserved locations. Providing spatial uncertainty information along with survey maps is crucial for risk assessment and decision‐making. This paper introduces a novel probability vector approach for spatial uncertainty modeling of soil classes based on an existing two‐dimensional Markov chain model for conditional simulation. The objective is to find an accurate and efficient way to represent spatial uncertainties that arise in mapping soil classes. Joint conditional probability distribution (JCPD) represented by a set of occurrence probability vectors (PVs) of soil classes is directly calculated from conditional Markov transition probabilities, rather than the conventional approximate estimation from a limited number of simulated realizations. By visualizing the calculated PVs, information reflecting spatial uncertainty of soil distribution can be quickly assessed. We hypothesize that these directly calculated PVs are equivalent to the PVs estimated from an infinite number of realizations and thus realizations visualized from the calculated PVs represent the spatial variation of soil distribution. This hypothesis is supported by simulation results showing that: (i) with increasing the number of realizations generated by the Markov chain model from 10 to 100 and to 1000, PVs estimated from these realizations gradually approach the calculated PVs; (ii) similar to simulated realizations, realizations visualized from calculated PVs also can reflect the spatial patterns of soil classes and approximately reproduce the complex indicator variograms of soil classes of the original soil map.

Validating forecasts of the joint probability density of bond yields: Can affine models beat random walk?

Most existing empirical studies on affine term structure models (ATSMs) have mainly focused on in-sample goodness-of-fit of historical bond yields and ignored out-of-sample forecast of future bond yields. Using an omnibus nonparametric procedure for density forecast evaluation in a continuous-time framework, we provide probably the first comprehensive empirical analysis of the out-of-sample performance of ATSMs in forecasting the joint conditional probability density of bond yields. We find that although the random walk models tend to have better forecasts for the conditional mean dynamics of bond yields, some ATSMs provide better forecasts for the joint probability density of bond yields. However, all ATSMs considered are still overwhelmingly rejected by our tests and fail to provide satisfactory density forecasts. There exists room for further improving density forecasts for bond yields by extending ATSMs.