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

Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments

In this doctoral dissertation characteristics of very large industrial real investments (VLIRI) are investigated and a special group of VLIRI is defined as giga-investments. The investment decision-making regarding to giga-investments is discussed from the points of view of discounted cash-flow based methods and real option valuation. Based on the bacground of establishing giga-investments, state-of-the-art in capital budgeting (including real options) and by applying fuzzy numbers a novel method for the evaluation and profitability analysis of giga-investments is presented. Application of the method is illustrated and issues regarding investment decision-making of large industrial real investments are discussed.Real Options; Fuzzy Real Option Valuation; Giga-Investments; Very Large Industrial Real Investments; Dissertation

A Fuzzy Control Chart Approach for Attributes and Variables

The purpose of this study is to present a new approach for fuzzy control charts. The procedure is based on the fundamentals of Shewhart control charts and the fuzzy theory. The proposed approach is developed in such a way that the approach can be applied in a wide variety of processes. The main characteristics of the proposed approach are: The type of the fuzzy control charts are not restricted for variables or attributes, and the approach can be easily modified for different processes and types of fuzzy numbers with the evaluation or judgment of decision maker(s). With the aim of presenting the approach procedure in details, the approach is designed for fuzzy c quality control chart and an example of the chart is explained. Moreover, the performance of the fuzzy c chart is investigated and compared with the Shewhart c chart. The results of simulations show that the proposed approach ha

Economic and regulatory uncertainty in renewable energy system design: a review

Renewable energy is increasingly mobilizing more investment around the globe. However, there has been little attention to evaluating economic and regulatory (E&R) uncertainties, despite their enormous impact on the project cashflows. Consequently, this review analyzes, classifies, and discusses 130 articles dealing with the design of renewable energy projects under E&R uncertainties. After performing a survey and identifying the selected manuscripts, and the few previous reviews on the matter, the following innovative categorization is designed: sources of uncertainty, uncertainty characterization methods, problem formulations, solution methods, and regulatory frameworks. The classification reveals that electricity price is the most considered source of uncertainty, often alone, despite the existence of six other equally influential groups of E&R uncertainties. In addition, real options and optimization arise as the two main approaches researchers use to solve problems in energy system design. Subsequently, the following aspects of interest are discussed in depth: how modeling can be improved, which are the most influential variables, and potential lines of research. Conclusions show the necessity of modeling E&R uncertainties with currently underrepresented methods, suggest several policy recommendations, and encourage the integration of prevailing approaches.Peer ReviewedObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.2 - Per a 2030, augmentar substancialment el percentatge d’energia renovable en el con­junt de fonts d’energiaObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No ContaminantPostprint (published version

Fuzzy logistic regression for detecting differential DNA methylation regions

“Epigenetics is the study of changes in gene activity or function that are not related to a change in the DNA sequence. DNA methylation is one of the main types of epigenetic modifications, that occur when a methyl chemical group attaches to a cytosine on the DNA sequence. Although the sequence does not change, the addition of a methyl group can change the way genes are expressed and produce different phenotypes. DNA methylation is involved in many biological processes and has important implications in the fields of biomedicine and agriculture. Statistical methods have been developed to compare DNA methylation at cytosine nucleotides between populations of interest (e.g., healthy and diseased) across the entire genome from next generation sequence (NGS) data. Testing for the differences between populations in DNA methylation at specific sites is often followed by an assessment of regional difference using post hoc aggregation procedures to group neighboring sites that are differentially methylated. Although site-level analysis can yield some useful information, there are advantages to testing for differential methylation across entire genomic regions. Examining genomic regions produces less noise, reduces the numbers of statistical tests, and has the potential to provide more informative results to biologists. In this research, several different types of logistic regression models are investigated to test for differentially methylated regions (DMRs). The focus of this work is on developing a fuzzy logistic regression model for DMR detection. Two other logistic regression methods (weighted average logistic regression and ordinal logistic regression) are also introduced as alternative approaches. The performance of these novel approaches are then compared with an existing logistic regression method (MAGIg) for region-level testing, using data simulated based on two (one plant, one human) real NGS methylation data sets”--Abstract, page iii

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

Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments

In this doctoral dissertation characteristics of very large industrial real investments (VLIRI) are investigated and a special group of VLIRI is defined as giga-investments. The investment decision-making regarding to giga-investments is discussed from the points of view of discounted cash-flow based methods and real option valuation. Based on the bacground of establishing giga-investments, state-of-the-art in capital budgeting (including real options) and by applying fuzzy numbers a novel method for the evaluation and profitability analysis of giga-investments is presented. Application of the method is illustrated and issues regarding investment decision-making of large industrial real investments are discussed