Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels

Valid and efficient imprecise-probabilistic inference with partial priors, III. Marginalization

As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics have yet to solve the problem. Fortunately, the two mainstream frameworks aren't the only options. This series of papers rigorously develops a new and very general inferential model (IM) framework for imprecise-probabilistic statistical inference that is provably valid and efficient, while simultaneously accommodating incomplete or partial prior information about the relevant unknowns when it's available. The present paper, Part III in the series, tackles the marginal inference problem. Part II showed that, for parametric models, the likelihood function naturally plays a central role and, here, when nuisance parameters are present, the same principles suggest that the profile likelihood is the key player. When the likelihood factors nicely, so that the interest and nuisance parameters are perfectly separated, the valid and efficient profile-based marginal IM solution is immediate. But even when the likelihood doesn't factor nicely, the same profile-based solution remains valid and leads to efficiency gains. This is demonstrated in several examples, including the famous Behrens--Fisher and gamma mean problems, where I claim the proposed IM solution is the best solution available. Remarkably, the same profiling-based construction offers validity guarantees in the prediction and non-parametric inference problems. Finally, I show how a broader view of this new IM construction can handle non-parametric inference on risk minimizers and makes a connection between non-parametric IMs and conformal prediction.Comment: Follow-up to arXiv:2211.14567. Feedback welcome at https://researchers.one/articles/23.09.0000

Beyond probabilities: A possibilistic framework to interpret ensemble predictions and fuse imperfect sources of information

AbstractEnsemble forecasting is widely used in medium‐range weather predictions to account for the uncertainty that is inherent in the numerical prediction of high‐dimensional, nonlinear systems with high sensitivity to initial conditions. Ensemble forecasting allows one to sample possible future scenarios in a Monte‐Carlo‐like approximation through small strategical perturbations of the initial conditions, and in some cases stochastic parametrization schemes of the atmosphere–ocean dynamical equations. Results are generally interpreted in a probabilistic manner by turning the ensemble into a predictive probability distribution. Yet, due to model bias and dispersion errors, this interpretation is often not reliable and statistical postprocessing is needed to reach probabilistic calibration. This is all the more true for extreme events which, for dynamical reasons, cannot generally be associated with a significant density of ensemble members. In this work we propose a novel approach: a possibilistic interpretation of ensemble predictions, taking inspiration from possibility theory. This framework allows us to integrate in a consistent manner other imperfect sources of information, such as the insight about the system dynamics provided by the analogue method. We thereby show that probability distributions may not be the best way to extract the valuable information contained in ensemble prediction systems, especially for large lead times. Indeed, shifting to possibility theory provides more meaningful results without the need to resort to additional calibration, while maintaining or improving skills. Our approach is tested on an imperfect version of the Lorenz '96 model, and results for extreme event prediction are compared against those given by a standard probabilistic ensemble dressing

A possibilistic framework for constraint-based metabolic flux analysis

<p>Abstract</p> <p>Background</p> <p>Constraint-based models allow the calculation of the metabolic flux states that can be exhibited by cells, standing out as a powerful analytical tool, but they do not determine which of these are likely to be existing under given circumstances. Typical methods to perform these predictions are (a) flux balance analysis, which is based on the assumption that cell behaviour is optimal, and (b) metabolic flux analysis, which combines the model with experimental measurements.</p> <p>Results</p> <p>Herein we discuss a possibilistic framework to perform metabolic flux estimations using a constraint-based model and a set of measurements. The methodology is able to handle inconsistencies, by considering sensors errors and model imprecision, to provide rich and reliable flux estimations. The methodology can be cast as linear programming problems, able to handle thousands of variables with efficiency, so it is suitable to deal with large-scale networks. Moreover, the possibilistic estimation does not attempt necessarily to predict the actual fluxes with precision, but rather to exploit the available data – even if those are scarce – to distinguish possible from impossible flux states in a gradual way.</p> <p>Conclusion</p> <p>We introduce a possibilistic framework for the estimation of metabolic fluxes, which is shown to be flexible, reliable, usable in scenarios lacking data and computationally efficient.</p

An informational distance for estimating the faithfulness of a possibility distribution, viewed as a family of probability distributions, with respect to data

International audienceAn acknowledged interpretation of possibility distributions in quantitative possibility theory is in terms of families of probabilities that are upper and lower bounded by the associated possibility and necessity measures. This paper proposes an informational distance function for possibility distributions that agrees with the above-mentioned view of possibility theory in the continuous and in the discrete cases. Especially, we show that, given a set of data following a probability distribution, the optimal possibility distribution with respect to our informational distance is the distribution obtained as the result of the probability-possibility transformation that agrees with the maximal specificity principle. It is also shown that when the optimal distribution is not available due to representation bias, maximizing this possibilistic informational distance provides more faithful results than approximating the probability distribution and then applying the probability-possibility transformation. We show that maximizing the possibilistic informational distance is equivalent to minimizing the squared distance to the unknown optimal possibility distribution. Two advantages of the proposed informational distance function is that (i) it does not require the knowledge of the shape of the probability distribution that underlies the data, and (ii) it amounts to sum up the elementary terms corresponding to the informational distance between the considered possibility distribution and each piece of data. We detail the particular case of triangular and trapezoidal possibility distributions and we show that any unimodal unknown probability distribution can be faithfully upper approximated by a triangular distribution obtained by optimizing the possibilistic informational distance

Naive possibilistic classifiers for imprecise or uncertain numerical data

International audienceIn real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in the presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered dataset. We consider two types of uncertainty: (i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and (ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data

Properties Analysis of Inconsistency-based Possibilistic Similarity Measures

International audienceThis paper deals with the problem of measuring the similarity degree between two normalized possibility distributions encoding preferences or uncertain knowledge. Many exist- ing de nitions of possibilistic similarity indexes aggregate pairwise distances between each situation in possibility distributions. This paper goes one step further, and discusses de nitions of possibilistic similarity measures that include inconsistency degrees between possibility distribu- tions. In particular, we propose a postulate-based analysis of similarity indexes which extends the basic ones that have been recently proposed in a literature