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This paper focuses mainly on the problem of computing the γ th , γ > 0 , moment of a random variable Y n : = ∑ i = 1 n α i X i in which the α i 's are positive real numbers and the X i 's are independent and distributed according to noncentral chi-square distributions. Finding an analytical approach for solving such a problem has remained a challenge due to the lack of understanding of the probability distribution of Y n , especially when not all α i 's are equal. We analytically solve this problem by showing that the γ th moment of Y n can be expressed in terms of generalized hypergeometric functions. Additionally, we extend our result to computing the γ th moment of Y n when X i is a combination of statistically independent Z i 2 and G i in which the Z i 's are distributed according to normal or Maxwell–Boltzmann distributions and the G i 's are distributed according to gamma, Erlang, or exponential distributions. Our paper has an immediate application in interest rate modeling, where we can explicitly provide the exact transition probability density function of the extended Cox–Ingersoll–Ross (ECIR) process with time-varying dimension as well as the corresponding γ th conditional moment. Finally, we conduct Monte Carlo simulations to demonstrate the accuracy and efficiency of our explicit formulas through several numerical tests. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the program started in [W. Gangbo, S. Mayorga, and A. Święch, SIAM J. Math. Anal., 53 (2021), pp. 1320–1356]. We consider stochastic optimal control problems for systems of n particles with common noise, interacting through their empirical measures. We prove that their value functions un, when converted to functions of the empirical measures, converge uniformly on bounded sets in the Wasserstein space of probability measures to a limiting function V which is the unique so-called L-viscosity solution of the limiting Hamilton–Jacobi–Bellman (HJB) equation in the Wasserstein space. This generalizes such a result from the 2021 paper, in the sense that our drift and cost functions are allowed to be unbounded. The L-viscosity solution is defined using the lifting of the function and the HJB equation to a Hilbert space of square integrable random variables. The proof of the convergence of un to V uses PDE viscosity solution techniques. The lifted function V of V is the value function of a stochastic optimal control problem in the Hilbert space and we prove that V is C1,1 and that the problem has an optimal feedback control. Using this we then characterize V as the value function of a stochastic optimal control problem in the Wasserstein space. [ABSTRACT FROM AUTHOR]

Assembly and disassembly are important activities in the manufacturing/remanufacturing process. Although the line balancing problems of them have been extensively discussed in the existing literature, they are rarely integrated into one system. In this paper, a hybrid production line balancing problem is adopted while considering the similarity between the assembly and disassembly tasks. First, to better reflect the uncertainty existing in the actual production environment, a mathematical model of the multi-objective stochastic hybrid production line balancing problem is presented, in which task disassembly times are assumed to be random variables with known normal probability distributions. Then, a hybrid VNS-NSGA II algorithm combining variable neighbourhood search (VNS) and non-dominated sorting genetic algorithm II (NSGA II) is proposed to solve the problem. VNS is embedded into NSGA II as a local search to improve the quality of the solutions found by the NSGA II at each generation. Finally, the effectiveness of the proposed method is verified by a case study, and the superiority of hybrid production line is reflected by comparing the solutions of the independent production line with the hybrid production line. Computational comparisons demonstrate the potential benefits of the hybrid production line and the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers secret-key generation between several agents and a base station that observe independent and identically distributed realizations of correlated random variables. Each agent wishes to generate the longest possible individual key with the base station by means of public communication. All keys must be jointly kept secret from all external entities. In this many-to-one secret-key generation setting, it can be shown that the agents can take advantage of a collective protocol to increase the sum rate of their generated keys. However, when each agent is only interested in maximizing its own secret-key rate, agents may be unwilling to participate in a collective protocol. Furthermore, when such a collective protocol is employed, how to fairly allocate individual key rates arises as a valid issue. This paper studies the tension between cooperation and self-interest with a game-theoretic treatment. This paper establishes that cooperation is in the best interest of all individualistic agents and that there exist individual secret-key rate allocations that incentivize the agents to follow the protocol. In addition, an explicit coding scheme that achieves such allocations is proposed. [ABSTRACT FROM AUTHOR]

In this paper, a new model for arbitrarily varying classical-quantum channels is proposed. In this model, a jammer has side information. The communication scenario in which a jammer can select only classical inputs as a jamming sequence is considered in the first part of the paper. This situation corresponds to the standard model of arbitrarily varying classical-quantum channels. Two scenarios are considered. In the first scenario, the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. The capacity for both average and maximum error criteria for both scenarios is determined in this paper. A strong converse is also proved. It is shown that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity. The communication scenario with a fully quantum jammer is considered in the second part of the paper. A single letter characterization for the capacity with secret random key as assistance for both average and maximum error criteria is derived in the paper. [ABSTRACT FROM AUTHOR]

A generalized framework of spectrum sensing disruption for a power-limited adversary is proposed in this paper. In the literature, a conventional sensing attack typically assumes that the adversary has perfect knowledge of the spectral usage status. The framework in this paper considers a more general case where there are uncertainties in the estimates at the adversary. These uncertainties are modeled utilizing the probability of detection and the probability of false alarm. Then, the sum of the conditional probabilities of false detection at the secondary within the spectral range of interest, conditioned on the adversary’s estimated spectrum usage status, is maximized. It is shown that the optimal sensing attack, given perfect estimation is a special case of the proposed framework. When the adversary has perfect spectrum usage information, this framework reduces to a previously demonstrated optimal sensing disruption. When the adversary has imperfect information on the spectral status, the proposed framework is significantly more robust than conventional sensing attacks. Further, when the adversary’s power budget increases, it asymptotically approaches the sensing disruption performance upper bound. [ABSTRACT FROM AUTHOR]

Physical and probabilistic interpretations of the fractional derivatives and integrals are basic problems to their applications. In this paper, we establish a relation between the Dzhrbashyan fractional integral and the expectation of a corresponding random variable by constructing the cumulative distribution function. As examples, interpretations of the Riemann–Liouville fractional integral and Kober integral operator are given. Furthermore, probabilistic interpretations of the Caputo fractional derivative and the fractional integral of a function with respect to another function are discussed too. With the help of probabilistic interpretations proposed in this paper, models described by fractional derivatives and integrals can be endowed with corresponding statistical meanings, while some statistical physics models can be rewritten in fractional calculus too. [ABSTRACT FROM AUTHOR]

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate deviations result. More precisely we mean a class of large deviation principles that fill the gap between the (trivial) weak convergence of some non-Gaussian identically distributed random variables to their common law, and the convergence of some other related random variables to a constant. Some other minor results concern large deviations for the inverse of the tempered subordinators considered in this paper; actually, in some results, these inverse processes appear as random time-changes of other independent processes. [ABSTRACT FROM AUTHOR]

The increasing penetration rate of electric vehicles, associated with a growing charging demand, could induce a negative impact on the electric grid, such as higher peak power demand. To support the electric grid, and to anticipate those peaks, a growing interest exists for forecasting the day-ahead charging demand of electric vehicles. This paper proposes the enhancement of a state-of-the-art deep neural network to forecast the day-ahead charging demand of electric vehicles with a time resolution of 15 min. In particular, new features have been added on the neural network in order to improve the forecasting. The forecaster is applied on an important use case of a local charging site of a hospital. The results show that the mean-absolute error (MAE) and root-meansquare error (RMSE) are respectively reduced by 28.8% and 19.22% thanks to the use of calendar and weather features. The main achievement of this research is the possibility to forecast a high stochastic aggregated EV charging demand on a day-ahead horizon with a MAE lower than 1 kW. [ABSTRACT FROM AUTHOR]

This paper investigates the relation between three different notions of privacy: identifiability, differential privacy, and mutual-information privacy. Under a unified privacy-distortion framework, where the distortion is defined to be the expected Hamming distance between the input and output databases, we establish some fundamental connections between these three privacy notions. Given a maximum allowable distortion D , we define the privacy-distortion functions \epsilon _{\mathrm{ i}}^{*}(D) , \epsilon _{\mathrm{ d}}^{*}(D) , and \epsilon \mathrm{ m}^{*}(D) to be the smallest (most private/best) identifiability level, differential privacy level, and mutual information between the input and the output, respectively. We characterize \epsilon \mathrm{ i}^{*}(D) and \epsilon \mathrm{ d}^{*}(D) , and prove that \epsilon \mathrm{ i}^{*}(D)-\epsilon X\le \epsilon \mathrm{ d}^{*}(D)\le \epsilon \mathrm{ i}^{*}(D) for D within certain range, where \epsilon _{X} is a constant determined by the prior distribution of the original database X , and diminishes to zero when X is uniformly distributed. Furthermore, we show that \epsilon _{\mathrm{ i}}^{*}(D) and \epsilon _{\mathrm{ m}}^{*}(D)$ can be achieved by the same mechanism for D$ within certain range, i.e., there is a mechanism that simultaneously minimizes the identifiability level and achieves the best mutual-information privacy. Based on these two connections, we prove that this mutual-information optimal mechanism satisfies \epsilon $ -differential privacy with . The results in this paper reveal some consistency between two worst case notions of privacy, namely, identifiability and differential privacy, and an average notion of privacy, mutual-information privacy. [ABSTRACT FROM PUBLISHER]

This paper provides a model-based method for analysis and hypothesis testing for paired data where one source of data has to be validated against another source of data that contains subjective and dynamic errors. This study deals with human-observed flow counts collected from traffic videos of freeway cameras. The available videos are mainly used for the purpose of manual observation by transportation personnel in case of emergency. This amounts to a varying inconsistency of the quality of the videos, which presents an additional challenge when analyzing the data. Video processing cannot be performed due to the mentioned issues with regard to the video quality. The processing has to be manually performed by humans who unfortunately have an inherent bias. If the video data have to be used for validating flow detector sensors, then a technique that performs validation with subjective and dynamic erroneous data as a result of the human bias is needed. This paper presents a methodology to deal with this issue. It is based on statistical testing with heteroscedasticity, which is demonstrated through a case study using data from traffic flow detectors and traffic cameras installed on highways in the Southern Nevada Region. A model for the relationship between the video ratings and the distribution of the human errors is developed taking into consideration the human bias. A method for identification of faulty detectors is also demonstrated based on the developed technique. [ABSTRACT FROM PUBLISHER]

In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply normalized utility-based shortfall risk measures to summarize the transportation cost random variables. In this paper, we demonstrate that the multi-dimensional shortfall–Wasserstein ball can be affinely projected onto a one-dimensional one. A noteworthy result of this reformulation is that our program benefits from finite sample guarantee without a dependence on the dimension of the nominal distribution. This distributionally robust optimization problem also has computational tractability, and we provide a dual formulation and verify the strong duality that enables a direct and concise reformulation of this problem. Our results offer a new DRO framework that can be applied in numerous contexts such as regression and portfolio optimization. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the possible impact of foreign direct investment inflows (FDI) on environmental pollution and to test the validity of the pollution haven hypothesis (PHH) in the case of Turkey over the period 1970–2020. For this purpose, we apply the Fourier approximation to determine stochastic properties of the variables that are FDI, economic growth, energy consumption, and CO2 emissions used in empirical analysis and the relationship between them. The advantage of the Fourier approximation is capable of capturing possible structural breaks in unknown forms and numbers in the series. According to Fourier KPSS and Fourier FADF tests, all series are stationary at order one, I (1). Fourier Shin and Fourier ADL cointegration tests put forth evidence of the existence of a long-term relationship between CO2, GDP, EC, and FDI. FMOLS expanded with Fourier terms suggesting that FDI has relatively little but a positive impact on CO2 emissions, so we conclude that PHH is valid for Turkey. The other finding reveals that there exists an inverted U-shape relationship between economic growth and CO2 emissions. According to this result, the environmental Kuznets curve (EKC) hypothesis for Turkey is also supported. Another remark of this paper is that energy consumption significantly increases environmental degradation in Turkey. These findings also are supported by Fourier Toda and Yamamoto causality test. There is a causality relationship from GDP, EC, and FDI to CO2 emissions. These findings offer useful recommendations for policymakers: the FDI, which uses new and clean technology, should be encouraged and implemented energy policies should be energy intensity reducer and efficiency increaser for reducing environmental pollution in Turkey. [ABSTRACT FROM AUTHOR]

When analyzing the stability of a slope reinforced by frame-anchors, this paper establishes a calculation model of slope stability by using the vertical slice method, and derives the stability performance function. In order to make up the shortcomings of the traditional deterministic calculation method, regarding the physical parameters of the soil as random variables, the slope stability is calculated based on the reliability theory. Applying the method to an engineering example, the reliability index of the overall stability of the slope under the failure of a single anchor is calculated. Finally, by applying the finite element software, GeoStudio, the reliability of the stability in the engineering example is analyzed, and the two methods are compared and evaluated. The results show that the failure of the anchor near the foot of the slope has the greatest impact on the stability of the slope. The theoretical calculations are in good agreement with the numerical simulation results. The proposed method is effective for the stability calculation of slopes reinforced by frame-anchors. The impact of the failure of a single anchor cannot be ignored, especially the anchors at the foot of the slope, whose design should follow the principle of "strengthening foot and waist" to avoid the hidden danger to the overall stability brought about by the failure of the anchor. [ABSTRACT FROM AUTHOR]

In this paper, we establish a chance constrained model for the priority of hesitant fuzzy preference relation based on the idea of statistical distribution for preference information as stochastic variables with unknown distribution. Inspired by the idea of conditional value-at-risk (CVaR) robust optimization, a deterministic convex reformulation is proposed for tackling the chance constrained problem. The existing state-of-the-art methods usually assume that the probability density function of preference information is known a priori, such as Gaussian distribution. However, it is generally over-conservatism. On the contrary, our proposed method provides a tractable second-order cone (SOC) reformulation for the chance constrained problem with the first and second moments, which is easy to handle and calculate. We also analyze the weight acquisition problem of hesitant fuzzy preference relation with unknown distribution preference using the SOC programming method, and obtain the priority weight with its approximately equivalent computationally tractable conic optimization model. A case study is conducted which shows that the proposed method achieves a good general conclusion by comparing it with the optimization method under Gaussian distribution. In addition, this method can also get better decision support for incomplete preference information. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a method for approximating the distribution function and density of a random variable that depends in a nontrivial way on a possibly high number of independent random variables, each with support on the whole real line. Starting with the integral formulations of the distribution and density, the method involves smoothing the original integrand by preintegration with respect to one suitably chosen variable, and then applying a suitable quasi--Monte Carlo method to compute the integral of the resulting smoother function. Interpolation is then used to reconstruct the distribution or density on an interval. The preintegration technique is a special case of conditional sampling, a method that has previously been applied to a wide range of problems in statistics and computational finance. In particular, the pointwise approximation studied in this work is a specific case of the conditional density estimator previously considered by L'Ecuyer, Puchhammer, and Ben Abdellah INFORMS J. Comput., 34 (2022), pp. 1729-1748]. Our theory provides a rigorous regularity analysis of the preintegrated function, which is then used to show that the errors of the pointwise and interpolated estimators can both achieve nearly first-order convergence. Numerical results support the theory. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a Kesten-type inequality for randomly weighted sums, in which the primary random variables are assumed to be real-valued and subexponential following a general dependence structure proposed by J. Geluk and Q. Tang [Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theor. Probab., 22(4):871–882, 2009], and the random weights are assumed to be nonnegative and arbitrarily dependent but independent of the primary random variables. The obtained result extends the work of Y. Chen [A Kesten-type bound for sums of randomly weighted subexponential random variables, Stat. Probab. Lett., 158:108661, 2020]. Then, as an application, we derive an asymptotic formula for finite-time ruin probability of a renewal risk model with constant force of interest and dependent by-claims. [ABSTRACT FROM AUTHOR]

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies by finding maximally correlated embeddings of pairs of random variables. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods for CA do not scale to large, high-dimensional datasets. In this paper, we provide a novel interpretation of CA in terms of an information-theoretic quantity called the principal inertia components. We show that estimating the principal inertia components, which consists in solving a functional optimization problem over the space of finite variance functions of two random variable, is equivalent to performing CA. We then leverage this insight to design algorithms to perform CA at scale. Specifically, we demonstrate how the principal inertia components can be reliably approximated from data using deep neural networks. Finally, we show how the maximally correlated embeddings of pairs of random variables in CA further play a central role in several learning problems including multi-view and multi-modal learning methods and visualization of classification boundaries. [ABSTRACT FROM AUTHOR]

By definition, original Besag-conceived spatial auto-random variables incorporate an autoregressive spatial lag term (i.e., the sum/average of nearby attribute values) to characterize geospatial data. Very common variates include the auto-normal, auto-logistic, and auto-binomial; less common ones include the auto-beta and auto-multinomial. Some of these specifications can capture the full range of spatial autocorrelation, and others cannot. These latter variates are unorthodox in their nonconformist restrictions to either only positive or only negative spatial autocorrelation domains. The literature already offers successful modifications of the auto-Poisson and auto-negative binomial, two popular random variables for describing counts, but neither of which can encapsulate positive spatial autocorrelation. The literature dismissively mentions the auto-exponential variate, which cannot accommodate negative spatial autocorrelation situations. Meanwhile, the literature lacks any discussion about auto-uniform random variables, with implications especially from point pattern analysis publications that they solely refer to complete spatial randomness. The purpose of this paper is to postulate a productive and viable spatialized continuous uniform distribution specification that easily extends to its corresponding discrete version. A standard benchmark location-allocation simulation experiment for a simple p = 1 median problem, a spatial optimization circumstance that illuminates bivariate spatial median properties, illustrates its practical applicability. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Finally, a simulation study is carried out to evaluate the performance of this estimate. [ABSTRACT FROM AUTHOR]

In many situations, it is common to have more than one observation per experimental unit, thus generating the experiments with repeated measures. In the modeling of such experiments, it is necessary to consider and model the intra-unit dependency structure. In the literature, there are several proposals to model positive continuous data with repeated measures. In this paper, we propose one more with the generalization of the beta prime regression model. We consider the possibility of dependence between observations of the same unit. Residuals and diagnostic tools also are discussed. To evaluate the finite-sample performance of the estimators, using different correlation matrices and distributions, we conducted a Monte Carlo simulation study. The methodology proposed is illustrated with an analysis of a real data set. Finally, we create an R package for easy access to publicly available the methodology described in this paper. [ABSTRACT FROM AUTHOR]

This paper considers the problem of Phase Identification in power distribution systems. In particular, it focuses on improving supervised learning accuracies by focusing on exploiting some of the problem’s information theoretic properties. This focus, along with recent advances in Information Theoretic Machine Learning (ITML), helps us to create two new techniques. The first transforms a bound on information losses into a data selection technique. This is important because phase identification data labels are difficult to obtain in practice. The second interprets the properties of distribution systems in the terms of ITML. This allows us to obtain an improvement in the representation learned by any classifier applied to the problem. We tested these two techniques experimentally on real datasets and have found that they yield phenomenal performance in every case. In the most extreme case, they improve phase identification accuracy from 51.7% to 97.3%. Furthermore, since many problems share the physical properties of phase identification exploited in this paper, the techniques can be applied to a wide range of similar problems. [ABSTRACT FROM AUTHOR]

The paper formulates a stochastic model by introducing the present value of a continuous uniform cash flow, with rate of payment and duration being random and force of interest being constant, in the maximum of a random number of positive random variables. The paper also provides an interpretation and practical applications of the stochastic model. Moreover, the paper establishes sufficient conditions for the representation of the stochastic model as the maximum of a random number of random contractions. In addition, the paper makes clear that the structural elements, the principal components, and the mathematical form of the stochastic model facilitate the development of synergies between the concepts of extremity, proactivity, and information for supporting intelligent systems. [ABSTRACT FROM AUTHOR]

Non-negative limited normal or gamma distributed random variables are commonly used to model physical phenomenon such as the concentration of compounds within gaseous clouds. This paper demonstrates that when a collection of random variables with limited normal or gamma distributions represents a stationary process for which the underlying variables have exponentially decreasing correlations, then a central limit theorem applies to the correlated random variables. [ABSTRACT FROM AUTHOR]

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the full nonlinear ac power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model the effects of arbitrary uncertainties of finite variance, which enables to predict and optimize the system state for a range of operating conditions. We apply chance constraints to limit the probability of violations of inequality constraints. Our method incorporates a more detailed and a more flexible description of both the controllable variables and the resulting system state than previous methods. Two case studies highlight the efficacy of the method, with a focus on satisfaction of the ac power flow equations and on the accurate computation of moments of all random variables. [ABSTRACT FROM AUTHOR]

An additive white Gaussian noise energy-harvesting channel with an infinite-sized battery is considered. The energy arrival process is modeled as a sequence of independent and identically distributed random variables. The channel capacity $\frac {1}{2}\log (1+P)$ is achievable by the so-called best-effort and save-and-transmit schemes where $P$ denotes the battery recharge rate. This paper analyzes the save-and-transmit scheme whose transmit power is strictly less than $P$ and the best-effort scheme as a special case of save-and-transmit without a saving phase. In the finite blocklength regime, we obtain new non-asymptotic achievable rates for these schemes that approach the capacity with gaps vanishing at rates proportional to $1/\sqrt {n}$ and $({(\log n)/n})^{1/2}$ respectively where $n$ denotes the blocklength. The proof technique involves analyzing the escape probability of a Markov process. When $P$ is sufficiently large, we show that allowing the transmit power to back off from $P$ can improve the performance for save-and-transmit. The results are extended to a block energy arrival model where the length of each energy block $L$ grows sublinearly in $n$. We show that the save-and-transmit and best-effort schemes achieve coding rates that approach the capacity with gaps vanishing at rates proportional to $\sqrt {L/n}$ and $({\max \{\log n, L\}/n})^{1/2}$ , respectively. [ABSTRACT FROM AUTHOR]

When multiple distributed energy resource (DER) aggregators exist in a non-cooperative power market, the calculation of individual aggregator’s bidding strategies could encounter significant uncertainties for considering DERs and competing market participants’ bidding strategies. In this paper, a bi-level bidding strategy optimization model is proposed for a DER aggregator which utilizes wind power, energy storage system (ESS), and curtailable load. At the upper level, the designated aggregator’s bidding strategy is optimized considering the wind power uncertainty. The wind forecast error is modeled by an ambiguity set using the data-driven approach. The information gap decision theory (IGDT) method is employed in this paper to maximize the risk level the designated aggregator can bear for a certain level of expected payoff. By detecting the worst case in wind power generation, the upper-level model is linearized as an MILP. The designated aggregator submits its bids to the market using the linear utility function acquired from linear regression. At the lower level, the market clearing is carried out using competing market participants’ bidding strategy scenarios. The scenarios and the corresponding probability are modeled through a data-driven approach. The market clearing problem is linearized using Taylor series. The price signal is iterated between the two levels as the proposed bi-level model is solved. Numerical results prove the validity and effectiveness of the proposed IGDT-based method. It is shown that the aggregator can adjust either the bidding quantities or coefficients to reach an expected payoff level. The bidding strategies are affected by uncertainties of wind power and competing bidding strategies. For an expected payoff level, when the designated aggregator is posed to consider a higher risk of wind power uncertainty, the aggregator can only bear a lower risk level from competing bidding strategies and vice versa. [ABSTRACT FROM AUTHOR]

This paper presents a new approach, called perturb-max, for high-dimensional statistical inference in graphical models that is based on applying random perturbations followed by optimization. This framework injects randomness into maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation. [ABSTRACT FROM AUTHOR]

We consider a storage process under the generalised order-up-to-level policy, based on a continuous-time Markov chain (CTMC). Specifically, the process starts at level S; whenever it drops to s, an order is sent, which is carried out after an exponential lead time. If during the lead time level S is reached, the order is cancelled, incurring some fee. This paper is written as an extension of Barron [2016. "An Fluid Inventory Model with Exponential Lead Times and Order Cancellations." Stochastic Models 32 (2): 301-332]. While the latter paper considered a fluid inventory model with backlogging and focused on discounted analysis only, the case of lost sales was not solved. The present paper generalises the analysis to incorporate unsatisfied demand for the expected discounted costs and for the average costs per time unit. We consider four costs. There is a fixed nonzero ordering cost or a fee for each order cancellation, a purchase cost for each ordered item, a storage cost for the stock, and a penalty cost due to the unmet demand. Applying renewal theory, multi-dimensional martingales, and stopping time theory, we obtain explicit expressions of the cost components. Numerical study provides several guidelines on the optimal controls. [ABSTRACT FROM AUTHOR]

The present paper is concerned with reliability economics, considering a certain performance-per-cost criterion for coherent and mixed systems, as introduced in [Dugas, M.R. & Samaniego, F.J. (2007). On optimal system designs in reliability-economics frameworks. Naval Research Logistics 54, 568–582]. We first present a new comparison result for performance-per-cost of systems with independent and identically distributed component lifetimes under certain stochastic orderings. We then consider optimization of the performance-per-cost criterion, first reconsidering and refining results from the above cited paper, and then considering mixtures of given subsets of coherent systems. [ABSTRACT FROM AUTHOR]

In this paper, we obtain equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent identically distributed random variables under sublinear expectations space. The results obtained in the paper are extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space. [ABSTRACT FROM AUTHOR]

Summary: Power systems face more uncertainty by increasing photovoltaic system installations on the roof of buildings. To optimally manage energy and available flexibility in a building, stochastic optimization is used to take an optimal decision under uncertainty and minimize the operational cost. In stochastic optimization, a scenario set is used as an input to represent the uncertainty in a random variable, PV energy generation in this case. In this paper, a data‐driven method is proposed to obtain the distribution of the random variable and later generate scenario sets representing the uncertainty on day‐ahead PV energy generation installed on the roof of a building. This method is only based on historical PV generation and it does not require any other external data such as weather forecasts. A machine learning‐based technique is applied to forecast the PV energy production following by generating a scenario set for day‐ahead decision‐making. Later, the day‐ahead PV‐battery system management problem is formulated as a two‐stage stochastic optimization while the generated scenario set is the input of this optimization. The proposed algorithm is tested in the day‐ahead scheduling of a PV‐battery system for a commercial building, informed by real‐life measurement data. The results show that the proposed algorithm is able to capture the uncertainty in PV system while providing a cost‐optimal and reliable solution to the application problem. Without using any weather data, the error of the proposed PV energy forecast method reaches to NRMSE = 11.89, while there is 5% reduction in the operational cost of the proposed two‐stage stochastic optimization. Moreover, the proposed algorithm is easy to implement in the energy management system of a building to manage PV‐battery system. [ABSTRACT FROM AUTHOR]

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Lomax–Rayleigh distribution to increase its kurtosis. The construction of this distribution is based on the idea of the Slash distribution, that is, its representation is based on the quotient of two independent random variables, one being a random variable with a Lomax–Rayleigh distribution and the other a beta (q , 1) . Based on the representation of this family, we study its basic properties, such as moments, coefficients of skewness, and kurtosis. We perform statistical inference using the methods of moments and maximum likelihood. To illustrate this methodology, we apply it to two real data sets. [ABSTRACT FROM AUTHOR]

The author studies the laws of large numbers for weighted sums of negatively superadditivedependent random variables. The obtained results in this paper extend and improve the corresponding theorems of Yang et al. [Commun. Stat. Theor. M., 48 (2019), 3044-3054]. Moreover, the author obtains a new theorem of mean convergence for weighted sums of negatively superadditive-dependent random variables, which was not considered in Yang et al. (2019). [ABSTRACT FROM AUTHOR]

In this paper, we present a new method to construct new classes of distortion functions. A distortion function maps the unit interval to the unit interval and has the characteristics of a cumulative distribution function. The method is based on the transformation of an existing non-negative random variable whose distribution function, named the generating distribution, may contain more than one parameter. The coherency of the resulting risk measures is ensured by restricting the parameter space on which the distortion function is concave. We studied cases when the generating distributions are exponentiated exponential and Gompertz distributions. Closed-form expressions for risk measures were derived for uniform, exponential, and Lomax losses. Numerical and graphical results are presented to examine the effects of the parameter values on the risk measures. We then propose a simple plug-in estimate of risk measures and conduct simulation studies to compare and demonstrate the performance of the proposed estimates. The plug-in estimates appear to perform slightly better than the well-known L-estimates, but also suffer from biases when applied to heavy-tailed losses. [ABSTRACT FROM AUTHOR]

Comfort on railway vehicles has been proven to depend on the number of passengers on the car, on their seating arrangement, as well as on the position in which it is assessed. The number of possible seating arrangement combinations is so large that comfort at a given location becomes a random variable even if passengers are considered deterministic vibration absorbers. In this paper we determine probability density functions (PDF) of comfort using a Monte Carlo scheme in which the number of passengers, their seating locations and their vibration characteristics (derived from passenger mass) are all random parameters with their own PDFs. Two types of distributions are obtained: the expected comfort of a single passenger and the compound comfort of all passengers on a given railway car. The carbody is represented by a beam model in which the first bending mode frequency has been allowed to vary so that the scope of results widens slightly. This variation is within the range of human sensitivity because this is the case in current lightweight construction, making carbody flexibility a key contributor to passenger comfort (or discomfort). Results confirm that comfort is indeed a stochastic variable with sizeable variance, and this prompts questions about the relation between the stochastic distribution and the tests prescribed in standard EN–12299. It will be shown that, surprisingly, comfort PDFs may be inferred with a high degree of accuracy (errors lower than 2%) from the tests in standard EN–12299. This is a most fortunate finding that radically transforms the interpretation of said standard, and allows rolling stock manufacturers and rail transport operators to have a much richer assessment of comfort on their vehicles from the same tests they now conduct, without having to perform Monte Carlo tests or simulations. [ABSTRACT FROM AUTHOR]

In order to detect radionuclides and dangerous substances in a fractured medium with the least amount of time and maximum probability, this paper provides a revolutionary tracking model. It relies on a coordinated tracking strategy using set of programmed nano-sensors. The radionuclide particle has a linear flow from d-directions to spread in a single direction with Random Walk process. We assume that this particle has been spread over a short period of time along phantomic cylindrical path inside the fluid. Two nano-sensors will track or search along each cylinder's route, starting from any location in the fragmented medium (space). A vector of random variables with a known probability distribution makes up the particle's initial position. We add the discounted effort-reward track as a reduction parameter in the distance function. The expected value of the first meeting time between one of the nano-sensors and a Random walk target will be reduced as a result. We extract various supplementary results regarding the optimal tracking strategy in addition to presenting the analytical solution that demonstrates the existence of a finite tracking technique. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-level dynamic factor model to identify common components in output gap estimates. We pool multiple estimates for 157 countries and decompose them into one global, eight regional, and 157 country-specific cycles. Our approach easily deals with mixed frequencies, ragged edges, and discontinuities in the underlying output gap estimates. To restrict the parameter space in the Bayesian state space model, we apply a stochastic search variable selection approach and base the prior inclusion probabilities on spatial information. Our results suggest that the global and the regional cycles explain a substantial proportion of the output gaps. On average, 18% of a country's output gap is attributable to the global cycle, 24% to the regional cycle, and 58% to the local cycle. [ABSTRACT FROM AUTHOR]

Benchmarking different optimization algorithms is tasky, particularly for network-based cellular communication systems. The design and management process of these systems involves many stochastic variables and complex design parameters that demand an unbiased estimation and analysis. Though several optimization algorithms exist for different parametric modeling and tuning, an in-depth evaluation of their functional performance has not been adequately addressed, especially for cellular communication systems. Firstly, in this paper, nine key numerical and global optimization algorithms, comprising Gauss–Newton (GN), gradient descent (GD), Genetic Algorithm (GA), Levenberg–Marguardt (LM), Quasi-Newton (QN), Trust-Region–Dog-Leg (TR), pattern search (PAS), Simulated Annealing (SA), and particle swam (PS), have been benchmarked against measured data. The experimental data were taken from different radio signal propagation terrains around four eNodeB cells. In order to assist the radio frequency (RF) engineer in selecting the most suitable optimization method for the parametric model tuning, three-fold benchmarking criteria comprising the Accuracy Profile Benchmark (APB), Function Evaluation Benchmark (FEB), and Execution Speed Benchmark (ESB) were employed. The APB and FEB were quantitatively compared against the measured data for fair benchmarking. By leveraging the APB performance criteria, the QN achieved the best results with the preferred values of 98.34, 97.31, 97.44, and 96.65% in locations 1–4. The GD attained the worst performance with the lowest APE values of 98.25, 95.45, 96.10, and 95.70 in the tested locations. In terms of objective function values and their evaluation count, the QN algorithm shows the fewest function counts of 44, 44, 56, and 44, and the lowest objective values of 80.85, 37.77, 54.69, and 41.24, thus attaining the best optimization algorithm results across the study locations. The worst performance was attained by the GD with objective values of 86.45, 39.58, 76.66, and 54.27, respectively. Though the objective values achieved with global optimization methods, PAS, GA, PS, and SA, are relatively small compared to the QN, their function evaluation counts are high. The PAS, GA, PS, and SA recorded 1367, 2550, 3450, and 2818 function evaluation counts, which are relatively high. Overall, the QN algorithm achieves the best optimization, and it can serve as a reference for RF engineers in selecting suitable optimization methods for propagation modeling and parametric tuning. [ABSTRACT FROM AUTHOR]

In the recent JAVELIN Bladder 100 phase 3 trial, avelumab plus best supportive care significantly prolonged overall survival relative to best supportive care alone as first-line maintenance therapy following first-line platinum-based chemotherapy in patients with advanced urothelial cancer (aUC). Discovering biomarkers using genomic profiling to understand potential patient heterogeneity is essential to help improve patient care with precision medicine. For the JAVELIN Bladder 100 trial, it is unclear which variable selection methods can most reliably identify biomarkers to inform patient care because the dataset is characterized by high collinearity and low signal. The aim of this paper was to evaluate available selection methods and their ability to discover prognostic and predictive biomarkers in patients with aUC receiving first-line maintenance therapy. A simulation study evaluated the performance of popular variable selection approaches for high-dimensional data, including penalized regression models, random survival forests, and Bayesian variable selection methods. For Bayesian variable selection methods, a modified Bayesian Information Criterion (BIC) thresholding rule was proposed in addition to the traditional BIC thresholding rule. These methods were applied to the JAVELIN Bladder 100 dataset to investigate potential biomarkers associated with survival benefit. Results from the simulations demonstrated the strengths and limitations of the different methods. The variable selection methods demonstrated low false discovery rates under different conditions. However, their performance declined in the presence of high collinearity. Using the JAVELIN Bladder 100 data, we identified some potentially significant biomarkers across multiple models. Several lasso-related methods were able to identify potentially biologically meaningful variables in the trial. Some variable selection methods (such as stochastic search variable selection and random survival forest) may not be well suited to this type of data due to the presence of extreme collinearity and low signal. Future research should explore novel variable selection methods that may be more suitable for identifying prognostic and predictive biomarkers in this population. Trial registration: ClinicalTrials.gov Identifier: NCT02603432. [ABSTRACT FROM AUTHOR]

In this paper, by establishing a Bernstein inequality for m-asymptotically almost negatively associated random variables, some results on consistency for the nearest neighbor estimator of the density function are further established. The results generalize some existing ones in the literature. Some numerical simulations are also provided to support the results. [ABSTRACT FROM AUTHOR]

From the perspective of wireless communication, as communication systems become more complex, order statistics have gained increasing importance, particularly in evaluating the performance of advanced technologies in fading channels. However, existing analytical methods are often too complex for practical use. In this research paper, we introduce innovative statistical findings concerning the sum of ordered gamma-distributed random variables. We examine various channel scenarios where these variables are independent but not-identically distributed. To demonstrate the practical applicability of our results, we provide a comprehensive closed-form expression for the statistics of the signal-to-interference-plus-noise ratio in a multiuser scheduling system. We also present numerical examples to illustrate the effectiveness of our approach. To ensure the accuracy of our analysis, we validate our analytical results through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

• An original centrality metric objective function for the LMRNP is introduced. • A new data-driven adaptive distributionally robust equilibrium programming method. • The DBSCAN algorithm is newly adopted to construct a data-driven ambiguity set. • The proposed model is theoretically derived into a computationally solvable form. • The performance of the deduced model is validated by two real data sets. This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residual supplies centrality metric. Under the scenario-based design, the demand in each scenario is described as a random fuzzy variable whose probability distribution is ambiguous. In order to characterize its ambiguousness, this paper designs a Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm based on sample data to construct a data-driven ambiguity set containing the support and mean, which not only realizes the visualization of the ambiguous probability distribution, but also provides a finite set of scenarios for the uncertain demand. Given the constructed data-driven ambiguity set, this paper proposes a data-driven adaptive distributionally robust equilibrium programming (DDADREP) method for the last mile relief network problem (LMRNP). In view of its computational difficulty, the safe approximation, duality technique and credibility measure theory are used to approximate it as a mixed integer second-order cone programming with significant computational advantages. Finally, the proposed model is validated with two real-world cases, and its effectiveness as well as advantages is demonstrated by comparison with the classical robust optimization and the nominal equilibrium optimization, respectively. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating a continuous random variable, characterized by a cumulative distribution function (cdf) F(x), by means of k points, x 1 < x 2 < ⋯ < x k , with probabilities p i , i = 1 , ⋯ , k . For a given k, a criterion for determining the x i and p i of the approximating k-point discrete distribution can be the minimization of some distance to the original distribution. Here we consider the weighted Cramér-von Mises distance between the original cdf F(x) and the step-wise cdf F ^ (x) of the approximating discrete distribution, characterized by a non-negative weighting function w(x). This problem has been already solved analytically when w(x) corresponds to the probability density function of the continuous random variable, w (x) = F ′ (x) , and when w(x) is a piece-wise constant function, through a numerical iterative procedure based on a homotopy continuation approach. In this paper, we propose and implement a solution to the problem for different choices of the weighting function w(x), highlighting how the results are affected by w(x) itself and by the number of approximating points k, in addition to F(x); although an analytic solution is not usually available, yet the problem can be numerically solved through an iterative method, which alternately updates the two sub-sets of k unknowns, the x i 's (or a transformation thereof) and the p i 's, till convergence. The main apparent advantage of these discrete approximations is their universality, since they can be applied to most continuous distributions, whether they possess or not the first moments. In order to shed some light on the proposed approaches, applications to several well-known continuous distributions (among them, the normal and the exponential) and to a practical problem where discretization is a useful tool are also illustrated. [ABSTRACT FROM AUTHOR]

For a sequence of multi-state trials with l possible outcomes denoted by 1 , 2 , ... , l , let E be the event that at least k 1 consecutive 1s followed by at least k 2 consecutive 2s,..., followed by at least k l consecutive ls. Denote by T r the number of trials for the rth occurrence of the event E in a sequence of multi-state trials. This paper studies the distribution of the waiting time random variable T r when the sequence consists of independent and identically distributed multi-state trials. In particular, distributional properties of T r are examined via matrix-geometric distributions. [ABSTRACT FROM AUTHOR]