Class Of Probabilistic Models Research Articles

Properties and Applications of Neutrosophic Burr XII Distribution

Primarily, when the hazards function has intricate structures, the BrXII distribution is an established framework for lifetime data analysis. However, classical probability models are limited in the sense that they cannot measure or record the data in exactness fueling the notion of indeterminacy in data collection process. This study addresses this issue by proposing the idea of neutrosophic BrXII (NeS-BrXII) distribution. The primary objective is to study the statistical properties of the proposed model by providing explicit expressions of reliability properties, the expression of moments and generating function, expression of order statistics, mean residual life, mean inactivity time, stochastic ordering, income inequality measures, and entropy in neutrosophic realm. In addition, the neutrosophic model parameters are estimated using the principle of maximum-likelihood estimation. Further, the precision of these model estimates is verified via a simulation study of the proposed model. Applying the model on two real-world material sciences data sets reinforces its efficacy with the NeS-BrXII distribution proving to be more suitable for managing anomalies in neutrosophic surface analysis among other models.

Estimating Extreme Drought Risk Through Classical and Bayesian Paradigms

ABSTRACTDrought poses significant challenges to both the environment and the economy, necessitating proactive mitigation strategies. This study introduces both classical and Bayesian Markov Chain Monte Carlo (MCMC) extreme value probabilistic models for quantifying drought risk. The models utilise the generalised extreme value (GEV) distribution to characterise the distribution of standardised precipitation index (SPI) and non‐stationary standardised precipitation index (NSSPI) variables. Drought risk is probabilistically assessed across five regions in Baluchistan (a drought‐prone area of Pakistan) over two 20‐year periods per region. The study presents a novel approach in probabilistic quantification models, demonstrating slight performance improvement with the Bayesian MCMC paradigm, as evaluated by the continuously ranked probability scoring. Moreover, the application of the presented methodology can be extended to other climatic zones using Bayesian MCMC with informative priors constructed from historical records of the neighbouring regions.

A Teaching Design on "Classical Probability Model"

This article presents a teaching design scheme for classical probability models. It conducts targeted analysis and training on several aspects where students are prone to make mistakes when learning classical probability models. It is hoped that through comparative analysis of different solutions to typical examples, students can greatly improve in terms of calculation accuracy and simplicity. The mistakes made by students mainly include misjudging the equal possibility of sample points, inaccurate reduction of the sample space, and being unable to choose the simplest method when choosing permutation or combination for calculation.

On ZLindley distribution: statistical properties and applications

The modeling and analysis of lifetime data is critical in many areas, including actuarial science, management, engineering, medicin, physics, biology, hydrology, and computer science. Classical probability distributions have been used to manage data sets of varied sizes. However, considerable issues occur when real-world data does not fit into any of the classical or conventional probability models. Consequently, there arises a crucial requirement to enhance the flexibility of existing probability models by including the blending of two distributions or introducing additional parameters. This work introduces a ZLindley distribution with a single parameter. Both symmetric and left-skewed data can utilize the proposed model. We generate statistical features such as the mode, moments, quantile function, and moment-generating function to accurately represent the usefulness of the suggested distribution. We compute the parameter using the maximum likelihood estimation approach. A thorough simulation exercise evaluates the goodness-of-fit performance. We demonstrate the applicability and flexibility of the new recommended distribution by using a real dataset.

Adulteration detection of edible oil by one‐class classification and outlier detection

AbstractEdible oil adulteration is a mostly practiced phenomenon. However, the traditional discriminant methods fail to detect oil adulteration involving more than one adulterant. Recently, one‐class classifiers were built for food or oil authentication. Unfortunately, as it is hard to determine the application domain of the one‐class classifier, high prediction error was obtained for real samples in market surveillance. In this study, a new method was developed based on one‐class classification and outlier detection for edible oil adulteration detection in market surveillance. The model population was constructed using Monte Carlo sampling of unidentified inspected samples to select the plateau region exhibiting the highest accumulated absolute centered residual (ACR) values. Subsequently, the number of models in the plateau region was validated by the theoretical ones calculated by the classical probability model. The models in the plateau region with the highest cumulative accumulated ACR values were used to identify adulterated oils. Furthermore, the cross‐validation was conducted by comparing identification results from two different Monte Carlo sampling ratios to ensure the accuracy of our method. Both single adulteration and multiple adulteration of peanut oils were prepared to validate our method. Moreover, this method was used to detect adulteration of sesame oils, which have already been identified by the markers in our previous study. The validation results of three datasets indicated that this method could effectively identify adulterated samples and therefore provide a novel solution for inspecting potential adulteration in practice.

A combinatorial problem related to the classical probability

In the classical probability model, let f(n) be the maximum number of pairwise independent events for the sample space with n sample points. The determination of f(n) is equivalent to the problem of determining the maximum cardinality of specific intersecting families on the set {1,2,…,n}. We show that f(n)≤n+1, and f(n)=n+1 if there exists a Hadamard matrix of order n.

Вероятностное прогнозирование «иррациональных» решений на основе смысловой композиции контекстов

Difficulties in prognosis of human behavior are due to the complexity of our cognition, routinely breaking the boundaries of classical rationality. The paper solves this problem for the simplest kind of such “irrational” behavior in which a single binary decision is made in three related contexts. Subjective meanings of these contexts relative to the basis decision alternative are represented by three qubit states, borrowed from quantum theory. These states are bound together by linear superpositions, which encode semantic composition of the contexts in the subject’s mind. The resulting theory supplements classical probabilistic model with nonlinear interference factor, accounting for the “irrational”, emotionally-semantic side of intelligence. This model is built for different realizations of two classic experiments used to study behavioral irrationality: the prisoner’s dilemma and the two-stage gambling task. In 24 such realizations, the interference phase is shown to fall in a narrow range of values, encoding regularities of semantic composition of contexts. Extrapolation of this regularity to novel experiments allows using the model in prognostic mode. This possibility is tested on the task of probabilistic prediction of target decision based on the same probability in two other contexts. For the prisoner’s dilemma and the two-stage gambling task the such prognosis has relative errors of 9 and 11% respectively. The proposed approach allows for putting other quantum models of cognition and decision to predictive and interpretable use, whereas its principles also apply to modeling of decisions with larger sets of contexts and behavioral options. By formalizing a novel type of semantic regularities behind “irrational” thinking, models of the present type open prospects for empowering the existing means for socio-economical analytics and prediction.

A Tutorial on the Spectral Theory of Markov Chains.

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically. This tutorial provides an in-depth introduction to Markov chains and explores their connection to graphs and random walks. We use tools from linear algebra and graph theory to describe the transition matrices of different types of Markov chains, with a particular focus on exploring properties of the eigenvalues and eigenvectors corresponding to these matrices. The results presented are relevant to a number of methods in machine learning and data mining, which we describe at various stages. Rather than being a novel academic study in its own right, this text presents a collection of known results, together with some new concepts. Moreover, the tutorial focuses on offering intuition to readers rather than formal understanding and only assumes basic exposure to concepts from linear algebra and probability theory. It is therefore accessible to students and researchers from a wide variety of disciplines.

Deep Generators on Commodity Markets Application to Deep Hedging

Four deep generative methods for time series are studied on commodity markets and compared with classical probabilistic models. The lack of data in the case of deep hedgers is a common flaw, which deep generative methods seek to address. In the specific case of commodities, it turns out that these generators can also be used to refine the price models by tackling the high-dimensional challenges. In this work, the synthetic time series of commodity prices produced by such generators are studied and then used to train deep hedgers on various options. A fully data-driven approach to commodity risk management is thus proposed, from synthetic price generation to learning risk hedging policies.

Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems, which is generally challenging for classical computers due to high computational complexities. Here, we report experimental preparations of Gibbs states and excited states of Heisenberg XX and XXZ models by using a 5-qubit programmable superconducting processor. In the experiments, we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits. We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits, which enable us to prepare excited states at arbitrary energy density. We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error. Based on numerical results, we further show that the time complexity of our approach scales polynomially in the number of qubits, revealing its potential in solving large-scale problems.

Credible Bayesian reliability model for structures with interval uncertain parameters

If a non-probabilistic interval model is adopted to describe the uncertainty, the determination of the interval bounds is challenging, which degrades the accuracy and credibility of the reliability analysis. In this study, based on Bayesian theory, a non-probabilistic credible Bayesian reliability model, which can be updated by introducing new sample points, is proposed for three failure modes and developed to model the credibility of non-probabilistic reliability. The relations between the classical probabilistic confidence reliability model and the proposed non-probabilistic credible Bayesian reliability model are investigated and discussed. Two relevant numerical examples are selected for the investigation to demonstrate the effectiveness of the proposed model and the limitations of the classical confidence reliability in the evaluation of structural safety.

Assessment of fuzzy global seismic vulnerability for RC structures

This paper proposed a fuzzy global seismic vulnerability analysis framework to investigate the effect of stochastic uncertainty and epistemic uncertainty for RC structures simulated by Monte Carlo simulation (MCS) and OpenSeesPy. The classical probability model was used to describe the stochastic uncertainty in fuzzy-random variables (model design parameters). The epistemic uncertainties in the probability model parameters and performance level threshold values were portrayed by incorporating triangle fuzzy numbers. Meanwhile, the vine copula-based global vulnerability curves were obtained by R-Packages to reflect that the dependence configuration between each component-level seismic response. The results showed that the global vulnerability can be accurately simulated by the selected d-vine structure and situated between the upper and lower bounds. The third floor can be regarded as the least fragile component under all performance levels in the case of perfectly independence, and the pair-copula model C34 consisted of the third and fourth floors showed a sensitive seismic response. Moreover, epistemic uncertainties showed different effects on the global vulnerability for RC structures under four limit states. The vulnerability curves considering fuzzy performance level and distribution parameters included a wider interval. The framework provided a practical approach for engineers and researchers to be informed of how stochastic, epistemic uncertainties, and dependence configuration affect global seismic vulnerability, facilitating the structure design, decision-making, and post-earthquake rehabilitation.

Quantum decision making in automatic driving

The behavior intention estimation and interaction between Autonomous Vehicles (AV) and human traffic participants are the key problems in Automatic Driving System (ADS). When the classical decision theory studies implicitly assume that the behavior of human traffic participants is completely rational. However, according to the booming quantum decision theory in recent years and actual traffic cases, traffic behaviors and other human behaviors are often irrational and violate the assumptions of classical cognitive and decision theory. This paper explores the decision-making problem in the two-car game scene based on quantum decision theory and compares it with the current mainstream method of studying irrational behavior-Cumulative Prospect Theory (CPT) model. The comparative analysis proved that the Quantum Game Theory (QGT) model can explain the separation effect which the classical probability model can’t reveal, and it has more advantages than CPT model in dealing with game scene decision-making. When two cars interact with each other, the QGT model can consider the interests of both sides from the perspective of the other car. Compared with the classical probability model and CPT model, the QGT is more realistic in the behavior decision-making of ADS.

Marine Target Extraction Based on Adjoint Covariance Correction Model

AbstractConstant False‐Alarm Rate (CFAR) algorithm is a mature method in marine target detection at present, the key of which is the choice of probability model. The most classical probability model is Gaussian distribution, which is suitable for modeling the calm ocean surface. Complex ocean conditions generally do not obey to Gaussian distribution, which limits the performance of CFAR algorithm. Therefore, we propose Adjoint Covariance Correction Model (ACCM) to improve the performance of CFAR marine target detection. Analyzing the distribution characteristic of ocean clutter under complex ocean conditions based on experiments, we find that it has long‐tail characteristic. Aiming at this characteristic, we have conducted fitting experiment on 23 kinds of probability density functions (PDFs) and find Loglogistic distribution has a better fitting effect on long‐tail characteristic, therefore, we use it to model ocean clutter under complex ocean conditions for the first time. In order to further improve the fitting goodness, we add a variance correction term to the Loglogistic model to construct ACCM for marine target extraction. The experiment result shows that ACCM effectively fits the long‐tail characteristic caused by Synthetic Aperture Radar backscatter under complex ocean conditions. The goodness of fit improves by 50% compared with Loglogistic model, and the amount of false alarms is 81.42% of that of Loglogistic model. The extraction accuracy of marine target characteristic parameter based on ACCM is 11.58% higher than that of Loglogistic model, and 12.18% higher than that of two‐parameter CFAR model based on standard error function (named SEF‐CFAR).

Research on quantum cognition in autonomous driving

Autonomous vehicles for the intention of human behavior of the estimated traffic participants and their interaction is the main problem in automatic driving system. Classical cognitive theory assumes that the behavior of human traffic participants is completely reasonable when studying estimation of intention and interaction. However, according to the quantum cognition and decision theory as well as practical traffic cases, human behavior including traffic behavior is often unreasonable, which violates classical cognition and decision theory. Based on the quantum cognitive theory, this paper studies the cognitive problem of pedestrian crossing. Through the case analysis, it is proved that the Quantum-like Bayesian (QLB) model can consider the reasonability of pedestrians when crossing the street compared with the classical probability model, being more consistent with the actual situation. The experiment of trajectory prediction proves that the QLB model can cover the edge events in interactive scenes compared with the data-driven Social-LSTM model, being more consistent with the real trajectory. This paper provides a new reference for the research on the cognitive problem of intention on bounded rational behavior of human traffic participants in autonomous driving.

Predicting quantum dynamical cost landscapes with deep learning

State-of-the-art quantum algorithms routinely tune dynamically parametrized cost functionals for combinatorics, machine learning, equation solving, and energy minimization. However, large search complexity often demands many (noisy) quantum measurements, leading to the increasing use of classical probability models to estimate which areas in the cost functional landscape are of highest interest. Introducing deep learning based modeling of the landscape, we demonstrate order-of-magnitude increases in accuracy and speed over state-of-the-art Bayesian methods with respect to control of a many-body spin chain. Moreover, once trained, the deep neural network enables the extraction of information at a much faster rate than conventional numerical simulation. This allows for on-the-fly experimental optimizations of circuits with large depth and moderate width and detailed classification of problem complexity and navigability throughout the phase diagram of the landscape.

LEARNING HIGH-DIMENSIONAL PROBABILITY DISTRIBUTIONS USING TREE TENSOR NETWORKS

We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density with respect to a product measure, possibly discrete for handling the case of discrete random variables. After discussing the representation of classical model classes in tree-based tensor formats, we present learning algorithms based on empirical risk minimization using a $L^2$ contrast. These algorithms exploit the multilinear parametrization of the formats to recast the nonlinear minimization problem into a sequence of empirical risk minimization problems with linear models. A suitable parametrization of the tensor in tree-based tensor format allows to obtain a linear model with orthogonal bases, so that each problem admits an explicit expression of the solution and cross-validation risk estimates. These estimations of the risk enable the model selection, for instance when exploiting sparsity in the coefficients of the representation. A strategy for the adaptation of the tensor format (dimension tree and tree-based ranks) is provided, which allows to discover and exploit some specific structures of high-dimensional probability distributions such as independence or conditional independence. We illustrate the performances of the proposed algorithms for the approximation of classical probabilistic models (such as Gaussian distribution, graphical models, Markov chain).

An efficient approach for multiple probabilistic inferences with Deepwalk based Bayesian network embedding

As a classical probabilistic graphic model, Bayesian network (BN) is widely used for representing and inferring dependence relationships with uncertainties. However, multiple probabilistic inferences on BN are quite inefficient, since each probabilistic inference on BN is extremely time-consuming and meanwhile the intermediate results cannot be reused. It is necessary to improve the overall efficiency of multiple probabilistic inferences on the same BN by incorporating an easy-to-calculate inference method and an easy-to-reuse technique for common calculations in multiple inference tasks. In this paper, we first propose a Deepwalk based method for BN embedding, as a specification of general graph embedding, which preserves both the graphical structure and conditional probabilities in BN. We then provide the algorithm to approximate probabilistic inferences via the distance among embeddings. We finally present an efficient approach to multiple probabilistic inferences. Extensive experiments illustrate that our proposed method is effective for BN embedding, and outperforms other state-of-the-art competitors by improving the inference efficiency with several orders of magnitude.

Fuzzy Logic in Aircraft Onboard Systems Reliability Evaluation-A New Approach.

This paper is a continuation of research into the possibility of using fuzzy logic to assess the reliability of a selected airborne system. The research objectives include an analysis of statistical data, a reliability analysis in the classical approach, a reliability analysis in the fuzzy set theory approach, and a comparison of the obtained results. The system selected for the investigation was the aircraft gun system. In the first step, after analysing the statistical (operational) data, reliability was assessed using a classical probabilistic model in which, on the basis of the Weibull distribution fitted to the operational data, the basic reliability characteristics were determined, including the reliability function for the selected aircraft system. The second reliability analysis, in a fuzzy set theory approach, was conducted using a Mamdani Type Fuzzy Logic Controller developed in the Matlab software with the Fuzzy Logic Toolbox package. The controller was designed on the basis of expert knowledge obtained by a survey. Based on the input signals in the form of equipment operation time (number of flying hours), number of shots performed (shots), and the state of equipment corrosion (corrosion), the controller determines the reliability of air armament. The final step was to compare the results obtained from two methods: classical probabilistic model and fuzzy logic. The authors have proved that the reliability model using fuzzy logic can be used to assess the reliability of aircraft airborne systems.

What Is Rational and Irrational in Human Decision Making

There has been a growing trend to develop cognitive models based on the mathematics of quantum theory. A common theme in the motivation of such models has been findings which apparently challenge the applicability of classical formalisms, specifically ones based on classical probability theory. Classical probability theory has had a singularly important place in cognitive theory, because of its (in general) descriptive success but, more importantly, because in decision situations with low, equivalent stakes it offers a multiply justified normative standard. Quantum cognitive models have had a degree of descriptive success and proponents of such models have argued that they reveal new intuitions or insights regarding decisions in uncertain situations. However, can quantum cognitive models further benefit from normative justifications analogous to those for classical probability models? If the answer is yes, how can we determine the rational status of a decision, which may be consistent with quantum theory, but inconsistent with classical probability theory? In this paper, we review the proposal from Pothos, Busemeyer, Shiffrin, and Yearsley (2017), that quantum decision models benefit from normative justification based on the Dutch Book Theorem, in exactly the same way as models based on classical probability theory.