Conditional Expectation Research Articles

Additive models with p-order autoregressive skew-normal errors for modeling trend and seasonality in time series

. In this article, we propose an additive model in which the random error follows a skew-normal p-order autoregressive (AR) process where the systematic component is approximated by cubic and cyclic cubic regression splines. The maximum likelihood estimators are calculated through the expectation-maximization (EM) algorithm with analytic expressions for the E and M-steps. The effective degrees of freedom concerning the non parametric component are estimated based on a linear smoother. The smoothing parameters are estimated by minimizing the Bayesian information criterion. The conditional quantile residuals are used to construct simulated confidence bands for assessing departures from the error assumptions. Also, we use the same residuals to construct graphs of the autocorrelation and partial autocorrelation functions to verify the AR structure’s adequacy for the errors. We then perform local influence analysis based on the conditional expectation of the complete-data log-likelihood function. A simulation study is carried out to evaluate the efficiency of the EM algorithm. Finally, the method is illustrated by using a real dataset of the average weekly cardiovascular mortality in Los Angeles.

Linear–quadratic mean-field game for stochastic systems with partial observation

This paper is concerned with a class of linear–quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by the individual noise, and all agents are coupled together via the control average term. By studying the associated mean-field game and using the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward–backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. Thanks to the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related ɛ-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

On characterization of a continuous distribution through lower record values

The characterization results via conditional expectation of lower record and truncation moments are considered for a new family of probability distribution. Several probability distributions can be characterized by the proposed method.

Utilizing contemporary machine learning techniques for determining soilcrete properties

Soilcrete is an innovative construction material made by combining naturally occurring earth materials with cement. It can be effectively used in areas where other construction materials are not readily available due to financial or environmental reasons since soilcrete is made from readily available natural clay. It can also help to cut down the greenhouse gas emissions from the construction industry by encouraging the use of resources that are locally available. Thus, it is imperative to reliably predict different properties of soilcrete since the accurate determination of these properties is crucial for the widespread use of soilcrete materials. However, the laboratory determination of these properties is subjected to significant time and resource constraints. As a result, this research was undertaken to provide empirical prediction models for the density, shrinkage, and strain of soilcrete mixes using two machine learning algorithms: Gene Expression Programming (GEP) and Extreme Gradient Boosting (XGB). The analysis revealed that XGB-based predictions correlated more with real-life values than GEP having training R2=0.999 for both density and shrinkage prediction and R2=0.944 for strain prediction. Moreover, several explanatory analyses including individual conditional expectation (ICE) analysis and shapely analysis were done on the XGB model which showed that water-to-binder ratio, metakaolin content, and modulus of elasticity are some of the most important variables for forecasting soilcrete materials properties. Furthermore, an interactive graphical user interface (GUI) has been developed for effective utilization in civil engineering industry to forecast these properties of soilcrete materials.

Combined interdisciplinary treatment of metastatic bone lesions using 3D robot-assisted image-guided navigation : Embolization, biopsy, ablation, and surgery in one operative session.

To maximize local tumor control, stabilize affected bones, and preserve or replace joints with minimal interventional burden, thereby enhancing quality of life for empowered living. Suitable for patients with bone metastases, particularly those with severe pain and/or fractures and appropriate life expectancy. In primary bone tumors, refer to the sarcoma surgery team for evaluation of wide resection. For patients with poor general condition and/or limited life expectancy (< 6weeks), consider best supportive care. Radiological interventions involve angiography and embolization for hypervascularized metastases, followed by precise biopsy and local tumor control through radiofrequency ablation or cryoablation using navigated imaging. The surgical treatment aims to create adurable, minimally invasive construct for stability, considering various options from percutaneous screws with cement augmentation to joint replacement. Intraoperative imaging and 3D scans guide the procedure, ensuring accurate placement of implants and confirming optimal results. Postoperative care involves immediate mobilization with pain-adapted full weightbearing and daily physiotherapy. The goal is to regain preoperative mobility. Follow-up with regular clinical and radiographic assessments and CT in the case of tumor progression and complications. Since introducing the combined surgical and interventional therapy in October 2021, 16patients have undergone successful procedures. Complications included material failure, component loosening, and surgical site infection. Five patients (31%) died during observation, while surviving patients surpassed their estimated survival, emphasizing the advantages of minimally invasive treatment with durable constructs.

A Snow-Based Hydroclimatic Aggregate Drought Index for Snow Drought Identification

Climate change has increased the risk of snow drought, which is associated with a deficit in snowfall and snowpack. The objectives of this research are to improve drought identification in a warming climate by developing a new snow-based hydroclimatic aggregate drought index (SHADI) and to assess the impacts of snowpack and snowmelt in drought analyses. To derive the SHADI, an R-mode principal component analysis is performed on precipitation, snowpack, surface runoff, and soil water storage. Then, a joint probability distribution function of drought frequencies and drought classes, conditional expectation, and k-means clustering are used to categorize droughts. The SHADI was applied to the Red River of the North Basin (RRB), a typical cold climate region, to characterize droughts in a mostly dry period from 2003 to 2007. The SHADI was compared with the hydroclimatic aggregate drought index (HADI) and U.S. drought monitor (USDM) data. Cluster analysis was also utilized as a benchmark to compare the results of the HADI and SHADI. The SHADI showed better alignment with cluster analysis results than the HADI, closely matching the identified dry/wet conditions in the RRB. The major differences between the SHADI and HADI were observed in cold seasons and in transition periods (dry to wet or wet to dry). The derived variable threshold levels for different categories of drought based on the SHADI were close to, but different from, those of the HADI. The SHADI can be used for short-term lead prediction of droughts in cold climate regions and, in particular, can provide an early warning for drought in the warming climate.

Enhanced iodinated disinfection byproducts formation in iodide/iodate-containing water undergoing UV-chloramine sequential disinfection: Machine learning-aided identification of reaction mechanisms.

Restricted to the complex nature of dissolved organic matter (DOM) in various aquatic environments, the mechanisms of enhanced iodinated disinfection byproducts (I-DBPs) formation in water containing both I- and IO3- (designated as I-/IO3- in this study) during the ultraviolet (UV)-chloramine sequential disinfection process remains unclear. In this study, four machine learning (ML) models were established to predict I-DBP formation by using DOM and disinfection features as input variables. Extreme gradient boosting (XGB) algorithm outperformed the others in model development using synthetic waters and in cross-dataset generalization of surface waters. Shapley additive explanation (SHAP) analysis, partial dependence plots (PDPs), and individual conditional expectation (ICE) analysis were then employed to explain the models' workings and feature interactions, aiding in identification and quantification of underlying mechanisms. A type of DOM component (namely DC_b) was found as the greatest contributor and identified as reduced quinones associated with broken-down lignin within higher plant-derived fulvic substance, serving as precursors and electron shuttles for I-DBP formation. Based on the interactional effects acquired from explanation results, the ejection of e-aq from excited DOM and pre-existing I- in the I-/IO3- system were identified responsible for the enhanced generation of I-DBPs compared to that in the I- or IO3- alone systems; extra DOM scavenged reactive iodine species (RIS), contributing to a limited enhancement. These findings and the methodology developed here together enhance our understanding of the mechanisms how DOM limitedly promotes I-DBP formation during UV-chloramine sequential disinfection of I-/IO3--containing water and facilitate effective online monitoring in the future.

Modeling actuarial data using iterated trigonometric distributions

. A new class of trigonometric distribution (TD) is developed iteratively by replacing the random variable of the TD function (or its survival function) with another TD function (or its survival function). The resulting families of distributions produce various density and hazard shapes and a wide variety of tail shapes for the parametric modeling of complex data arising in actuarial science. The basic properties of these distributions are studied and presented. The new TDs successfully model the AON Re Belgian and Danish fire insurance data sets. Risk measures such as value at risk (VaR) and conditional tail expectation (CTE) are computed and compared with their empirical values and other distributions presented in actuarial literature. Also, limited expected values (LEV) for various policy limits are computed to compare with empirical counterparts to emphasize the new TDs’ validity for actuarial predictions.

Characterizations of Certain (2023-2024) Introduced Univariate Continuous Distributions

This paper deals with various characterizations of certain univariate continuous distributions proposed in (2023-2024). These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) the hazard function; (iii) reverse hazard function and (iv) conditional expectation of a single function of the random variable. It should be mentioned that for the characterization (i) the cumulative distribution function need not have a closed form and depends on the solution of a first order differential equation, which provides a bridge betweenprobability and differential equation.

Diffusion processes and a random ODE arising in macroeconomics

Given a filtration ( F t , t ≥ 0 ) , our article proves there exists a unique stochastic process ( x t , t ≥ 0 ) such that for each t≥0 there is a conditional expectation process ( E ( x s | F t ) , s ≥ t ) that solves a random ODE (RODE) defined on [t, ∞). The RODE arises in macroeconomics, where conditional expectation is a forecasting device, and links exchange rate forecasts to forecasts of a diffusion process that represents key economic variables. Our result bridges a long standing gap in economic dynamics.

Biplots for understanding machine learning predictions in digital soil mapping

In digital soil mapping, machine learning is gradually replacing traditional statistical models because of their greater flexibility and better prediction performance. However, unlike traditional models, a notable drawback of machine learning models is that they are “black-box” in nature due to their limited ability to provide comprehensive interpretations for their predictions. Explainable machine learning (XML) methods provide visualisations that can be used to aid in understanding predictions made by machine learning models. Popular model-agnostic visualisation methods include partial dependence plots, independent conditional expectation curves, and partial dependence plots produced with Shapley values. These methods require that covariates are uncorrelated which could be restrictive. For cases where covariates are correlated, an alternative approach is the Accumulated Local Effect plot, which however is limited to depicting one or two covariates at a time. Another disadvantage of the above mentioned methods is that no readily available goodness-of-fit metric is available. In this paper we propose the use of a principal component analysis biplot as a model-agnostic method to gain insight into machine learning predictions in digital soil mapping. A biplot is a powerful visualisation tool that is used to seek patterns in multivariate data. A biplot does not require covariates included in the visualisation to be uncorrelated, and furthermore, an analytically derived goodness-of-fit metric is provided which allows the user to evaluate the accuracy of the approximation. We present examples from a case study in South Africa in which soil organic carbon is mapped with a random forest model. Our findings show that biplots can provide meaningful interpretations for predictions, making it a worthy addition to the XML toolkit.

Uniform in Number of Neighbor Consistency and Weak Convergence of k-Nearest Neighbor Single Index Conditional Processes and k-Nearest Neighbor Single Index Conditional U-Processes Involving Functional Mixing Data

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation r(m)(φ,t), defined as E[φ(Y1,…,Ym)|(X1,…,Xm)=t] for t∈Xm. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems.

Stochastic modelling for the effects of micromixing on soot in turbulent non-premixed flames

The impact of micromixing and scalar dissipation rate (SDR) fluctuations on the evolution of soot particle size distribution (PSD) dynamics in non-premixed turbulent flames is investigated within the context of Large Eddy Simulation (LES). To accomplish this, a stochastic approach based on a physicochemical sectional soot model, spatially homogeneous Conditional Moment Closure (CMC) with first-order moment closure, and a stochastic differential equation for the SDR are employed, mimicking the function of an LES sub-grid scale (SGS) combustion model. After linking the magnitude of SDR fluctuations to the LES filter size, it was found that the standard deviation of observables, such as the soot volume fraction and soot number density, decreases rapidly with increasing LES filter size, which can significantly influence the intermittency of soot reproduced by models. Mean conditional expectations are also affected, indicating a closure problem, with the mean soot volume fraction, in particular, showing a decrease of up to 20% in the case considered compared to a direct numerical simulation resolution even when the Pope criterion is satisfied. The influence of SDR fluctuations on the dynamic behaviour of the soot PSD is further discussed under different working assumptions for particle transport, and the role of differential diffusion in soot oxidation- and formation-dominant regions is particularly highlighted. The findings underline the shortcomings of LES-CMC and similar mixture-fraction-based combustion models in capturing the dynamic evolution of soot at the SGS, which has significant implications for modelling the emissions of practical combustion devices. However, this study also offers a framework for better evaluating the effectiveness of these models using numerical experimentation and a stochastic model for the turbulent fluctuations of the micromixing rate.

Experimental and interpretable machine learning-based analysis of pedestrian evacuation behavior in attack situations

Previous studies have extensively examined pedestrian evacuation behavior during emergencies such as fires. However, few studies have focused on evacuation behavior during violent attacks. In this paper, we design an experiment to simulate a violent attack and study the evacuation behavior of pedestrians during such an event. A random forest model is used to predict evacuation outcomes based on experimental data. Additionally, we employ interpretable machine learning methods, specifically Partial Dependence Plots (PDPs) and Individual Conditional Expectation (ICE), to investigate the variables influencing evacuation outcomes. The results indicate that the distance variable is the key variable influencing evacuation outcomes, followed by preparation time. Generally, shorter preparation time is beneficial to a higher probability of successful evacuation. However, immediate action after identification of the attacker is instead associated with a lower probability of successful evacuation. Moreover, shorter preparation time is also related to lower probabilities of successful evacuation when approaching the attacker. The number of attackers and exits has exerted a relatively limited monotonic influence. This study contributes to the development of safety guidelines and contingency plans in the event of a violent attack.

Quantum spheres as graph C*-algebras: A review

In this survey, we discuss the description of Vaksman–Soibelman quantum spheres using graph C*-algebras, following the seminal work of Hong and Szymański. We give a slightly different proof of the isomorphism with a graph C*-algebra, borrowing the idea of Mikkelsen and Kaad of using conditional expectations to prove the desired result.

How Do Short-Form Video Creators Select Media Platforms? Research Based on the Extended UTAUT Model

Since the inception of the short video platform, the interaction details between the social network and creators continue to require further exploration. This study explores the determinants that influence short-form video creators’ platform selection in China, leveraging the extended UTAUT model. Conducting a survey method (N = 468), a comprehensive questionnaire identified facilitating condition (FC) and effort expectancy (EE) as key factors, and the ATU was confirmed as the mediating variable whereas the SSNM was as the moderating variable, challenging the presumed dominance of social networks and their popularity. The study extends the UTAUT model to the context of short video platforms and creators and contributes to the discourse on digital content creation by highlighting the critical interplay between technology, social influence, and user engagement, offering strategic insights for platform innovation and creator engagement. Examining creators’ preferences and behaviors, we aim to pave the way for future research in the rapidly evolving digital content ecosystem.

Bayesian and Non-Bayesian Inference to Bivariate Alpha Power Burr-XII Distribution with Engineering Application

In this research, we present a new distribution, which is the bivariate alpha power Burr-XII distribution, based on the alpha power Burr-XII distribution. We thoroughly examine the key features of our newly developed bivariate model. We introduce a new class of bivariate models, which are built with the copula function. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, and product moments were studied. This was accomplished with two datasets of real data that came from two distinct devices. We employed Bayesian, maximum likelihood estimation, and least squares estimation strategies to obtain estimated points and intervals. Additionally, we generated bootstrap confidence intervals and conducted numerical analyses using the Markov chain Monte Carlo method. Lastly, we compared this novel bivariate distribution’s performance to earlier bivariate models, to determine how well it fit the real data.

A novel bounded ℤ-valued autoregressive model with its application on crime data

This paper tackles the challenge of autoregressive modelling for bounded Z -valued count time series, a topic that has been largely overlooked in the existing literature. To bridge this gap, we introduce the trinomial difference bounded Z -valued autoregressive (TDBZAR) model utilizing the trinomial difference thinning operator, and we explore its stochastic properties in detail. Two notable advantages of the TDBZAR model are that the incorporated trinomial difference thinning operator ensures the conditional expectation takes a linear form and allows its 1-step transition probability to be expressed as the convolution of two independent trinomial difference distributions. This significantly simplifies the computation of both the conditional least squares (CLS) and conditional maximum likelihood (CML) estimates, making them more practical and straightforward. Second, we examine the two-step CLS and CML estimates, establishing their asymptotic properties. Third, we compare the performance of these estimators through simulation studies. Finally, we apply the proposed model to a real dataset to investigate which type of crime (rape or sex offense) was more prevalent in police reports from January 1990 to December 1998.

Detecting interactions with random forests: a comment on Gries’ words of caution and suggestions for improvement

Abstract Tree-based methods are being both successfully applied and critically discussed in corpus linguistics. In this article, we would like to contribute a few aspects to this discussion from a methodological point of view. These aspects include the interpretation of interaction effects in single trees and random forests, as well as more general aspects like stability and overfitting. In particular, we have conducted a simulation study to investigate an approach suggested by Gries for computing the importance of interactions in random forests more systematically than the previous literature. The evidence of this simulation study shows that, even when interaction predictors are explicitly added, the permutation variable importance is not suited for distinguishing between main effects and interaction effects or between interaction effects of different orders. We also discuss the use of partial dependence (PD) and individual conditional expectation (ICE) plots for illustrating the functional form and potential interaction effects, and other means of interpretable machine learning.

Tracial states on groupoid $C^{*}$-algebras and essential freeness

Let \mathcal{G} be a locally compact Hausdorff étale groupoid. We call a tracial state \tau on a general groupoid C^{*} -algebra C_{\nu}^{*}(\mathcal{G}) canonical if \tau=\tau|_{C_0(\mathcal{G}^{(0)})}\circ E , where E:C^{*}_{\nu}(\mathcal{G}) \to C_{0}(\mathcal{G}^{(0)}) is the canonical conditional expectation. In this paper, we consider so-called fixed point traces on C_{c}(\mathcal{G}) , and prove that \mathcal{G} is essentially free if and only if any tracial state on C_{\nu}^{*}(\mathcal{G}) is canonical and any fixed point trace is extendable to C_{\nu}^{*}(\mathcal{G}) .As applications, we obtain the following: (1) a group action is essentially free if every tracial state on the reduced crossed product is canonical and every isotropy group is amenable; (2) if the groupoid \mathcal{G} is second-countable, amenable and essentially free then every (not necessarily faithful) tracial state on the reduced groupoid C^{*} -algebra is quasidiagonal.