Much of the recession forecasting literature is focused on producing a model for predicting current and future economic states. Nevertheless, the question of why a model predicts a given class (recession or expansion), that is, which features are mostly responsible for the classification outcome, remains unaddressed. The main goal of our paper is to fill this gap. To address this, we apply Shapley values to provide model transparency. Using high-quality macroeconomic data from multiple U.S. government agencies, we use competing linear and non-linear models. We then compute Shapley values across 154 feature candidates to nowcast US recessions. Our findings offer novel insights into feature importance and model decision-making, which allows rationalizing model predictions. This is useful, for example, in the context of monetary policy, where the central banker needs, not only a good prediction of whether or not we are in a recession, but also a sense of why that prediction was made.
Quality control is essential for ensuring manufacturing processes consistently meet predefined specifications and for minimizing the risks caused by process deviations. The MEWMA control chart is widely used for detecting small shifts in multivariate processes which does not require strict multivariate normality but the performance can be compromised when data contain outliers or high multicollinearity that commonly found in plastic waste processing. This study proposes a robust monitoring approach by integrating PCA to address multicollinearity, Bayesian estimation to improve parameter robustness. The four charts examined in this study are PCA-Bayesian MEWMA (SELF), PCA-Bayesian MEWMA (MSELF), PCA-Bayesian MEWMA (KLF), and PCA-MEWMA using Bootstrap control limit as comparison. These charts are evaluated across 324 simulated scenarios, varying in collinearity levels (0.2, 0.6, 0.95), sample sizes (10, 20, 30), outlier proportions (5%, 10%, 15%), and smoothing parameters (λ = 0.2, 0.5, 0.8). Performance is measured using Average Run Length (ARL), Standard Deviation of Run Length (SDRL), Median Run Length (MRL), and False Alarm Rate (FAR). Results indicate that the PCA-Bayesian MEWMA outperformed PCA-MEWMA using Bootstrap control limit. PCA-Bayesian MEWMA (SELF) excelled under clean data condition, whereas PCA-Bayesian (MSELF) provided stable detection under high correlation, moderate-to-high outlier contamination, and larger smoothing parameters, achieving an average ARL of 3.44, an SDRL of 0.58, an MRL of 3.46, and FAR of 0.03, making it well-suited for monitoring complex industrial plastic waste processes and demonstrating its effectiveness for robust quality monitoring in production.
Most of the scientific literature on causal modeling considers the structural framework of Pearl and the potential-outcome framework of Rubin to be formally equivalent and therefore interchangeably uses do-interventions and the potential-outcome framework to define counterfactual outcomes. In this article, we agnostically superimpose a structural causal model and a Rubin causal model compatible with the same observations to specify the mathematical conditions under which counterfactual outcomes obtained via do-interventions and potential outcomes need to, do not need to, can, or cannot be equal (almost surely or in law). Our comparison builds upon the fact that such causal models do not have to produce the same counterfactual outcomes and highlights real-world problems where they generally cannot correspond under classical causal-inference assumptions. Then, we examine common claims and practices from the causality literature in the light of this comparison. In doing so, we aim at clarifying the links between the two causal frameworks and the interpretation of their respective counterfactuals.
A Strong interval – valued Pythagorean fuzzy soft sets (SIVPFSS) an extending the theory of Interval-valued Pythagorean fuzzy soft set (IVPFSS). Then we Propose Strong interval valued Pythagorean fuzzy soft graphs (SIVPFSGs). We also present several different types of operations on Strong interval- valued Pythagorean fuzzy soft graphs and explore of their analysis.
Umar ishtiaq, Muhammad Saeed, Khaleel Ahmad
et al.
This study demonstrates that, for the non-linear contractive conditions in Neutrosophic metric spaces, a common fixed-point theorem may be proved without requiring the continuity of any mappings. A novel commutativity requirement for mappings weaker than the compatibility of mappings is used to demonstrate the conclusion. We provide several examples to illustrate our major idea. Also, we provide an application to the non-linear fractional differential equation to show the validity of our main result.
The purpose of this paper is to introduce and study the nano binary exterior, nano binary border and nano binary derivedin nano binary topological spaces. Also studied their characterizations
We obtain weak convergence and optimal scaling results for the random walk Metropolis algorithm with a Gaussian proposal distribution. The sampler is applied to hierarchical target distributions, which form the building block of many Bayesian analyses. The global asymptotically optimal proposal variance derived may be computed as a function of the specific target distribution considered. We also introduce the concept of locally optimal tunings, i.e., tunings that depend on the current position of the Markov chain. The theorems are proved by studying the generator of the first and second components of the algorithm and verifying their convergence to the generator of a modified RWM algorithm and a diffusion process, respectively. The rate at which the algorithm explores its state space is optimized by studying the speed measure of the limiting diffusion process. We illustrate the theory with two examples. Applications of these results on simulated and real data are also presented.
Central Java in 2017 was one of the provinces with high life expectancy, ranking second. Life expectancy of Central Java Province in 2017 is 74.08% per year. The fields of education, health and socio-economics, are several factors that are thought to influence the life expectancy in an area. To find out what factors that the regression analysis method can use to find out what factors influence the life expectancy. But in observations found data that have a spatial effect (location) called spatial data, a spatial regression method was developed such as linear regression analysis by adding spatial effects. One form of spatial regression is Spatial Durbin Model (SDM) which has a form like the Spatial Autoregressive Model (SAR). The difference between the two if in the SAR model the effect of spatial lag taken into account in the model is only on the response variable (Y) but in the SDM method, effect of spatial lag on the predictor variable (X) and response (Y) are also taken into account. Selection of the best model using Mean Square Error (MSE), obtained by the MSE value of 1.156411, the number mentioned is relatively small 0, which indicates that the model is quite good.
In this article we present numerical computation of pseudo-spectra and the bounds of Structured Singular Values (SSV) for a family of matrices obtained while considering matrix representation of SturmLiouville (S-L) problems with eigenparameter-dependent boundary conditions. The low rank ODE’s based technique is used for the approximation of the bounds of SSV. The lower bounds of SSV discuss the instability analysis of linear system in system theory. The numerical experimentation show the comparison of bounds of SSV computed by low rank ODE’S technique with the well-known MATLAB routine mussv available in MATLAB Control Toolbox.
Pak Hang Chris Lau, Chen-Te Ma, Jeff Murugan
et al.
The primary goal of this study is to remind, emphasize and revive the ideas of C. Radhakrishna Rao, inscribed in his words “Chance deals with order in disorder while chaos deals with disorder in order”. We will focus upon some concepts such as randomness, probability measure, chaos, fractals, random sequences and complexity. Deterministic phenomena need and use mathematics, stochastic phenomena need and use statistics, at least probability theory, as a modeling device. Analysis of measurements always need statistics. Modeling of some natural phenomena need fractional calculus. Fractional calculus nor stochastic calculus will be used.
The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding joint probability density function of its eigenvalues was identified. Moreover, a relation with the Cauchy two-matrix model was discovered but never thoroughly investigated, leaving open in particular the following question: How are the kernels of the Pfaffian point process of the Bures random matrix ensemble related to the ones of the determinantal point process of the Cauchy two-matrix model, and moreover, how can it be possible that a Pfaffian point process derives from a determinantal point process? We give a very explicit answer to this question. The aim of our work has a quite practical origin since the calculation of the level statistics of the Bures ensemble is highly mathematically involved while we know the statistics of the Cauchy two-matrix ensemble. Therefore, we solve the whole level statistics of a density operator drawn from the Bures prior.
Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), penalized quasi-likelihood, an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision.
M-Группа есть пара (G;*); где G решеточно упорядоченная группа ( l -группа) и * есть убывающий автоморфизм 2 - го порядка G: В статье получено описание m-транзитивных представлений произвольной m-группы. Найдены необходимые и достаточные условия того, что m-группа допускает точное m-транзитивное представление. Изучено строение решетки конгруэнций произвольного m-транзитивного представления, введены понятия m-2-транзитивного и m-примитивного представлений. Получено описание m-транзитивных примитивных представлений в терминах стабилизаторов. Указаны необходимые и достаточные условия m-2-транзитивности и изучены некоторые свойства таких представлений. Кроме того, введено понятие сплетения m-групп подстановок и доказано, что m-транзитивная группа подстановок вложима в сплетение подходящих m-транзитивных m-групп подстановок. Как следствие, установлено, что произвольная m-транзитивная группа из произведения двух многообразий m-групп вложима в сплетение подходящих m-транзитивных групп из этих многообразий.
Abaas Y. BAYATI, EMAN T. HAMED, Hamsa Th. Chilmerane
In this paper, we have derived anew proposed algorithm for conjugate<br /> gradient method based on a projection matrix. This Algorithm satisfies the<br /> sufficient descent condition and the globally converges . Numerical<br /> comparisons with a standard conjugate gradient algorithm show that this<br /> algorithm very effective depending on the number of iterations and the<br /> number of functions evaluation.
This paper provides an accessible methodology for approximating the distribution of a general linear combination of non-central chi-square random variables. Attention is focused on the main application of the results, namely the distribution of positive definite and indefinite quadratic forms in normal random variables. After explaining that the moments of a quadratic form can be determined from its cumulants by means of a recursive formula, we propose a moment-based approximation of the density function of a positive definite quadratic form, which consists of a gamma density function that is adjusted by a linear combination of Laguerre polynomials or, equivalently, by a single polynomial. On expressing an indefinite quadratic form as the difference of two positive definite quadratic forms, explicit representations of approximations to its density and distribution functions are obtained in terms of confluent hypergeometric functions. The proposed closed form expressions converge rapidly and provide accurate approximations over the entire support of the distribution. Additionally, bounds are derived for the integrated squared and absolute truncation errors. An easily implementable algorithm is provided and several illustrative numerical examples are presented. In particular, the methodology is applied to the Durbin–Watson statistic. Finally, relevant computational considerations are discussed. Linear combinations of chi-square random variables and quadratic forms in normal variables being ubiquitous in statistics, the distribution approximation technique introduced herewith should prove widely applicable.