Simulating a Gaussian random process by conditional PDF

In this paper, we present a proportionate-type normalized least mean square algorithm which operates by choosing adaptive gains at each time step in a manner designed to maximize the joint conditional probability that the next-step coefficient estimates reach their optimal values. We compare and show that the performance of the joint maximum conditional probability density function (PDF) one-step algorithm is superior to the proportionate normalized least mean square algorithm when operating on a sparse impulse response. We also show that the new algorithm is superior to a previously introduced algorithm which assumed that the conditional PDF could be represented by the product of the marginal conditional PDFs, i.e., that the weight deviations are mutually conditionally independent.

Probabilistic distribution coefficients ( Kds) in freshwater for radioisotopes of Ag, Am, Ba, Be, Ce, Co, Cs, I, Mn, Pu, Ra, Ru, Sb, Sr and Th – implications for uncertainty analysis of models simulating the transport of radionuclides in rivers

Background modelling is one of the main challenges in particle physics data analysis. Commonly employed strategies include the use of simulated events of the background processes, and the fitting of parametric background models to the observed data. However, reliable simulations are not always available or may be extremely costly to produce. As a result, in many cases uncertainties associated with the accuracy or sample size of the simulation are the limiting factor in the analysis sensitivity. At the same time, parametric models are limited by the a priori unknown functional form and parameter values of the background distribution. These issues become ever more pressing when large datasets become available, as it is already the case at the CERN Large Hadron Collider, and when studying exclusive signatures involving hadronic backgrounds.A widely applicable approach for non-parametric data-driven background modelling is proposed, which addresses these issues for a broad class of searches and measurements. It relies on a relaxed version of the event selection to estimate conditional probability density functions and two different techniques are discussed for its realisation. The first relies on ancestral sampling and uses data from a relaxed event selection to estimate a graph of conditional probability density functions of the variables used in the analysis, while accounting for significant correlations. A background model is then generated from events drawn from this graph, on which the full event selection is applied. In the second, a novel generative adversarial network is trained to estimate the joint probability density function of the variables used in the analysis. The training is performed on a relaxed event selection, which excludes the signal region, and the network is conditioned on a blinding variable. Subsequently, the conditional probability density function is interpolated into the signal region to model the background. The application of each method on a benchmark analysis and on ensemble tests is presented in detail, and the performance is discussed.

A new method for evaluating Borgonovo moment-independent importance measure with its application in an aircraft structure

This paper describes a method for evaluating the effectiveness of the route guidance system, which provides a driver with individual information to accomplish a trip under such objectives as the travel time saving, the fuel saving, the reduced air pollution and the reduced traffic accident etc.. In this paper the travel time saving is chosen as an evaluation criterion of this system. The travel time indicates the time required from a driver's specific origin (O) to his specific destination (D). Multiple routes may be chosen with each specific O-D, owing to his route choice criteria and to his trial and error. The route choice probability is defined, based on a traffic study of a driver's comprehension of road configuration. On the other hand, the travel time along the selected route is affected by the vehicular type, the traffic flow, the traffic regulation, the traffic signal and the weather etc.. In this paper the travel time is defined in terms of a conditional probability density function. The characteristics of the function are examined by a traffic study of travel time using an improved license matching technique.The probability density function of the travel time in the case of the specific O-D is composed of the route choice probability and the conditional probability density functions, mentioned above. Comparing the probability density function of a guided vehicle with that of a non-guided vehicle, a mathematical formula to calculate the amount of travel time saving is derived.

In this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences. Streamflow is assumed to be a Markov process with time dependence characterized by a multivariate probability density function. Kernel methods are used to estimate this multivariate density function. Simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function. This is a nonparametric method for the synthesis of streamflow that is data‐driven and avoids prior assumptions as to the form of dependence (e.g., linear or nonlinear) and the form of the probability density functions (e.g., Gaussian). We show, using synthetic examples with known underlying models, that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence. The effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the Beaver River in Utah.

Reliable long-term streamflow forecasting is invaluable for water resource planning and management which allocates water supply according to the demand of water users. It is necessary to get probabilistic forecasts to establish risk-based reservoir operation policies. Probabilistic forecasts may be useful for the users who assess and manage risks according to decision-making responding forecasting results. Probabilistic forecasting of seasonal inflow to Andong dam is performed and assessed using selected predictors from sea surface temperature and 500 hPa geopotential height data. Categorical probability forecast by Piechota's method and logistic regression analysis, and probability forecast by conditional probability density function are used to forecast seasonal inflow. Kernel density function is used in categorical probability forecast by Piechota's method and probability forecast by conditional probability density function. The results of categorical probability forecasts are assessed by Brier skill score. The assessment reveals that the categorical probability forecasts are better than the reference forecasts. The results of forecasts using conditional probability density function are assessed by qualitative approach and transformed categorical probability forecasts. The assessment of the forecasts which are transformed to categorical probability forecasts shows that the results of the forecasts by conditional probability density function are much better than those of the forecasts by Piechota's method and logistic regression analysis except for winter season data.

Starting from the linear Mori-Kubo generalized Langevin equation, conditional probability density functions are derived for independent dynamical variables of a general system under the action of (non-markovian) gaussian force or torque. The special techniques developed by Adelman (1976, 1977) for brownian oscillators are here extended to the general case. As applications of the general theory, angular momentum and orientational probability density functions are computed for models of molecular rotation in fluids. The rotational dynamics of each molecule is described by an itinerant oscillator/librator. The periodicity of spatial orientation is treated in terms of wrapped distributions, and hence the planar-reorientational counterpart of the translational self van Hove function is derived. It is shown that both momentum and orientational probability density functions can exhibit widely varying time-decay properties, which are directly interpretable in terms of the structure and dynamics of the molecular f...

MRI significantly improves the accuracy and reliability of target delineation in radiation therapy for certain tumors due to its superior soft tissue contrast compared to CT. A treatment planning process with MRI as the sole imaging modality will eliminate systematic CT/MRI co-registration errors, reduce cost and radiation exposure, and simplify clinical workflow. However, MRI lacks the key electron density information necessary for accurate dose calculation and generating reference images for patient setup. The purpose of this work is to develop a unifying method to derive electron density from standard T1-weighted MRI. We propose to combine both intensity and geometry information into a unifying probabilistic Bayesian framework for electron density mapping. For each voxel, we compute two conditional probability density functions (PDFs) of electron density given its: (1) T1-weighted MRI intensity, and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of the atlas and test patient. The two conditional PDFs containing intensity and geometry information are combined into a unifying posterior PDF, whose mean value corresponds to the optimal electron density value under the mean-square error criterion. We evaluated the algorithm’s accuracy of electron density mapping and its ability to detect bone in the head for eight patients, using an additional patient as the atlas or template. Mean absolute HU error between the estimated and true CT, as well as receiver operating characteristics for bone detection (HU > 200) were calculated. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 126, compared with 139 for deformable registration (p = 2 × 10−4), 283 for the intensity approach (p = 2 × 10−6) and 282 without density correction (p = 5 × 10−6). For 90% sensitivity in bone detection, the proposed method achieved a specificity of 86%, compared with 80, 11 and 10% using deformable registration, intensity and without density correction, respectively. Notably, the Bayesian approach was more robust against anatomical differences between patients, with a specificity of 62% in the worst case (patient), compared to 30% specificity in registration-based approach. In conclusion, the proposed unifying Bayesian method provides accurate electron density estimation and bone detection from MRI of the head with highly heterogeneous anatomy.

This paper presents a new framework for designing decentralized rank-1 pre-coders in MIMO interference channel. The proposed pre-coders aim to separate the received signal points corresponding to different bits into distinct clusters at every receiver. This is accomplished by minimizing the overlaps between conditional probability density functions (PDFs) given the sent bits, which is shown to be equivalent to maximizing the weighted Euclidean distance between the signal points. This formulation is shown to be synonymous to minimizing an upper bound to the probability of error or maximizing the approximated Bhattacharya distances of the conditional PDFs. When full channel state information (CSI) is given at all transmitters and receivers, our design is shown to offer significant performance gain over a wide range of SNR when compared to other pre-coder designs in the literature. We also extend our pre-coder design to the case when transmitters only have partial CSI in an arbitrary form. When the partial CSI is given in the form of quantized levels of channel coefficients, our design is shown to retain considerable performance gain as we partition the channel coefficients with finer resolutions.

The three-condition version of the uniform conditional state combustion model makes use of the mixture fraction, progress variable, and normalized total enthalpy as conditioning variables to build a three-dimensional conditional manifold for chemistry. In order to map the solution in conditional space into the flow domain, the joint Probability Density Function (PDF) of the conditioning variables needs to be modeled. In simulations, presumed functions (i.e., β-PDF for the mixture fraction and progress variable and δ-PDF for total enthalpy) are often used for modeling the marginal PDFs. In this work, the measurements from the Cambridge/Sandia burner are employed to obtain the marginal PDFs for the conditioning variables at various points in the reacting domain. The measurements are then combined from all positions in space to form conditional PDFs of the normalized total enthalpy for various values of the other two variables. In the vicinity of the flame brush, the marginal PDF of the normalized total enthalpy resembles a bimodal Gaussian distribution; nonetheless, the conditional PDFs for this variable are nearly Gaussian distributions. The correlation coefficients between the conditioning variables are also investigated, and the assumption of their statistical independence is examined. To consider the association between the conditioning variables for modeling, the copula concept is introduced, and the performances of three different copulas are tested. Furthermore, the statistical moments of the conditioning variables are computed from the experimental data at different points and are utilized for modeling the joint PDF of the conditioning variables from two different approaches that are compared.

An intensity-modulated Gaussian process {x(t)} is defined as the product of a non-negative stationary random process {σx(t)} and a stationary Gaussian process {z(t)} that is statistically independent of {σx(t)}. When such an intensity-modulated process is the excitation to a linear time-invariant system, the response process {y(t)}, conditioned on the excitation-modulating function σx(t), is a generally nonstationary Gaussian process. This property is used to develop an approximation to the probability density function (PDF) of the system response by assuming that the time-varying conditional response variance σ2y(t), conditioned on the excitation-modulating function σx(t), is governed by the gamma PDF. The resulting response process PDF is characterized by two parameters: the mean and variance of the conditional response variance σ2y(t). An alternative approximation to the response PDF, characterized by these same two parameters, is developed by using a Taylor’s series representation in the variable σ2y of the response PDF conditioned on σ2y. This latter PDF approximation is shown to be identical to the Gram–Charlier series of type A through terms involving the Hermite polynomial of degree 6. The two response PDF approximations are shown to give essentially identical results for values of the coefficient of variation of σ2y of one-half or less. Simple, easily evaluated expressions for the mean and variance of σ2y are derived in terms of measurable quantities by utilizing the assumption that fluctuations in σx(t) occur slowly in comparison with those of z(t).

Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks

The current North America Digital Cellular (NADC) standards suggest /spl pi//4-shifted-DQPSK as the modulation for the current digital mobile communications systems. The performance of differential quaternary-phase-shift-keying (DQPSK) receivers impaired by mixer imbalance and timing error is investigated. Expressions for the system bit error rate (BER) are obtained for channels free of fading and for frequency non-selective slow Rayleigh fading channels in the face of additive white Gaussian noise. To arrive at the desired expressions for the system BER, the conditional probability density function (PDF) of the phase angle between a pair of Gaussian random vectors is averaged over timing error and channel fading effects.

Bayesian model averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g., Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so‐called copula functions, into BMA. Here we introduce a copula‐embedded BMA (Cop‐BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop‐BMA, they are applied to hydrologic forecasts from different rainfall‐runoff and land‐surface models. We consider the streamflow observation and simulations for 10 river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop‐BMA application. It is also shown that the postprocessed forecasts have better correlation with observation after Cop‐BMA application.