Non-parametric data-driven background modelling using conditional probabilities

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.

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.

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.

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

PurposeThe introduction of a linear safety factor to address peak local specific absorption rate (pSAR10g) uncertainties (eg, intersubject variation, modeling inaccuracies) bears one considerable drawback: It often results in over‐conservative scanning constraints. We present a more efficient approach to define a variable safety margin based on the conditional probability density function of the effectively obtained pSAR10g value, given the estimated pSAR10g value.MethodsThe conditional probability density function can be estimated from previously simulated data. A representative set of true and estimated pSAR10g samples was generated by means of our database of 23 subject‐specific models with an 8‐fractionated dipole array for prostate imaging at 7 T. The conditional probability density function was calculated for each possible estimated pSAR10g value and used to determine the corresponding safety margin with an arbitrary low probability of underestimation. This approach was applied to five state‐of‐the‐art local SAR estimation methods, namely: (1) using just the generic body model “Duke”; (2) using our model library to assess the maximum pSAR10g value over all models; (3) using the most representative “local SAR model”; (4) using the five most representative local SAR models; and (5) using a recently developed deep learning–based method.ResultsCompared with the more conventional safety factor, the conditional safety‐margin approach results in lower (up to 30%) mean overestimation for all investigated local SAR estimation methods.ConclusionThe proposed probabilistic approach for pSAR10g correction allows more accurate local SAR assessment with much lower overestimation, while a predefined level of underestimation is accepted (eg, 0.1%).

PurposeOne of the biggest problems in an R&D process is the acquisition of information about the structure dynamic loads, which are needed to reliably prove the structure's durability. This paper aims to present an innovative method for simulating stationary Gaussian random processes, which is based on the conditional probability density function (PDF) approach.Design/methodology/approachThe basic information on the structure dynamic loads is first obtained by short‐duration measurements on prototypes or the structure itself. These data are then used to simulate the expected structure load states during operations. A theoretical background is presented first, which is followed by the application of the method.FindingsThe results show that the spectral characteristics of the original and simulated Gaussian random processes are very similar, if the influential range of the conditional PDF is properly chosen.Practical implicationsThe method can be applied for simulating random loads of structures, and excitations of dynamic systems, for example.Originality/valueThe innovative simulation approach could be helpful to engineers in the early phases of the new product development process.

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

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...

The problem of cloud field recognition from the NOAA satellite data is urgent for solving not only meteorological problems but also for resource-ecological monitoring of the Earth's underlying surface associated with the detection of thunderstorm clouds, estimation of the liquid water content of clouds and the moisture of the soil, the degree of fire hazard, etc. To solve these problems, we used the AVHRR/NOAA video data that regularly displayed the situation in the territory. The complexity and extremely nonstationary character of problems to be solved call for the use of information of all spectral channels, mathematical apparatus of testing statistical hypotheses, and methods of pattern recognition and identification of the informative parameters. For a class of detection and pattern recognition problems, the average risk functional is a natural criterion for the quality and the information content of the synthesized decision rules. In this case, to solve efficiently the problem of identifying cloud field types, the informative parameters must be determined by minimization of this functional. Since the conditional probability density functions, representing mathematical models of stochastic patterns, are unknown, the problem of nonparametric reconstruction of distributions from the leaning samples arises. To this end, we used nonparametric estimates of distributions with the modified Epanechnikov kernel. The unknown parameters of these distributions were determined by minimization of the risk functional, which for the learning sample was substituted by the empirical risk. After the conditional probability density functions had been reconstructed for the examined hypotheses, a cloudiness type was identified using the Bayes decision rule.

The increased water demand and the increased capital construction costs of water resource development projects force engineers and water planners to utilize efficiently the existing and proposed water resources systems. Hence, it is considered necessary to find the optimum real time operating rules for systems of multiple reservoirs.Stochastic dynamic programming (SDP) has been used as the tool for deriving the real time operating rules for a system of multiple reservoirs, in preference to simulation analysis and linear programming. This is because the operation of the storages is considered as a sequential decision problem and dynamic programming is well suited to handle sequential, multi-period type decision problems. Further, the stochastic nature of streamflow is considered explicitly through a multivariate distribution for streamflow. The method theoretically produces the global optimum solution.The computational difficulties in terms of computer time and memory space have prohibited the realistic application of this method to systems of multiple reservoirs in the past. In this study, two methods have been introduced to reduce the computational difficulties of the method, thus making SDP more attractive to use in the derivation of the real time operating rules for a system of multiple reservoirs.The first method, the assumption of cross correlation of streamflow, reduces the number of states in the SDP method which reduces computer time and memory space. Further, it reduces the number of conditional probability estimates of streamflow which are used in recursive relation of the SDP algorithm. The second method, the “corridor” approach, reduces computer time involved in the SDP method by eliminating the computation of infeasible and/or inferior (suboptimal) solutions. These two methods have resulted in significant savings in the computer effort of the SDP method.The conditional probabilities of streamflow are computed by considering the hypervolume under the conditional probability density function between the integration limits using the computationally efficient Gaussian Legendre quadrature method. The conditional probability density function is derived from the historical streamflow data.Real time operating rules are expressed as a function of the storage volume(s) at the beginning of the current time interval and the forecast inflow into the storage(s) during the current time interval.The Melbourne water supply system is used as the example. The derived operating rules have been tested by operating a simulation model and the conclusion is made that the SDP method is a satisfactory technique for objectively deriving real time operating rules for a system of multiple reservoirs.Finally, a combined stochastic dynamic programming – statistical disaggregation approach is introduced to determine the real time operating rules for a system of multiple reservoirs where operational data are available. Releases from individual storages are a function of the total system storage volume and inflow. The method uses SDP to determine the release rules from the equivalent single reservoir of the multiple reservoir system; these releases are then disaggregated to individual releases using the statistical release disaggregation model whose parameters are derived from the historical operational data. The approach was used to derive real time operating rules for the Melbourne water supply system and the operating rules were validated using a simulation model of the system.

In this paper, we propose a robust incremental principal component analysis (IPCA) for stream data that can handle missing values on an ongoing basis. In the proposed IPCA, a missing value is substituted with the value estimated from a conditional probability density function. The conditional probability density functions are incrementally updated when new data are given. In the experiments, we evaluate the performance for both artificial and real data sets through the comparison with the two conventional approaches to handing missing values. We first investigate the estimation errors of missing values. The experimental results demonstrate that the proposed IPCA gives lower estimation errors compared to the other approaches. Next, we investigate the approximation accuracy of eigenvectors. The results show that the proposed IPCA has relatively good accuracy of eigenvectors not only for major components but also for minor components.

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.

We introduce a statistically-inspired class of loss functions for scoring predictive models of wildfire risk, quantifying how well a model fits observed fire occurrence. These loss functions are derived as a weighted generalization of Poisson process deviance; this generalization unifies various existing approaches in the statistical wildfire literature and suggests new approaches, enabling improvements by relaxing requirements of probabilistic independence, using more of the historical information, and giving more importance to the largest fires. Nontrivially, we apply these tools to calibrating the parameters of wildland fire Monte Carlo simulations, and in particular the joint distribution of ignitions and fire durations. We argue that such an integrated approach is more reliable than optimizing the distribution of ignitions in isolation, because it optimizes the end results of simulations. We also describe a fast algorithm for approximating the loss function on candidate distributions of ignitions and durations without having to repeatedly run new simulations: using a sample-reweighting approach, a calibration simulation is run once, and the family of possible ignition distributions is defined and explored after the fact. In particular, distribution mixtures can be used for ensembling fire behavior models, and fire durations can be modeled and calibrated either explicitly via a conditional probability density function, or implicitly via a parametric hazard function that represents containment effectiveness. Furthermore, this method enables the use of gradient-based optimization algorithms for finding the best-fitting parameters. This enables a workflow similar to fitting parametric statistical models. We call this approach Plug-in Reweighted Poisson Likelihood Optimization (PiRPLO).