Random Coefficients Research Articles

Maximum-likelihood estimation of the Po-MDDRCINAR(p) model with analysis of a COVID-19 data

Integer-valued data are frequently encountered in time series studies. A pth-order mixed dependence-driven random coefficient integer-valued autoregressive time series model (Po-MDDRCINAR(p)) in view of binomial and negative binomial operators, where the innovation sequence follows a Poisson distribution, is investigated to provide meaningful theoretical explanations. Strict stationary and ergodicity of the model are demonstrated. Furthermore, the conditional least-squares and conditional maximum-likelihood methods are adopted to estimate the parameters, where the asymptotic characterization of the estimators is derived. Finite-sample properties of the conditional maximum-likelihood estimator are examined in relation to the widely used conditional least-squares estimator. The conclusion is that, if the Poisson assumption of the innovation sequence can be justified, conditional maximum-likelihood method performs better in terms of MADE and MSE. Finally, the practical performance of the model is illustrated by a set of COVID-19 data of suspected cases in China with a comparison with relevant models that exist so far in the literature.

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

Extending the Scope of Instrumental Variable Methods

Abstract Since Philip Wright’s (1928) proposal of the linear instrumental variables (IV) estimator the scope of application of IV models has greatly expanded. There are now nonlinear IV models in use with both additive and nonadditive latent variables, employing both semiparametric and nonparametric specifications. A notable feature of Wright’s linear IV estimator is that it is applicable to incomplete models that leave the genesis of endogenous explanatory variables unspecified. On the other hand, inversion of the linear model enables the value of unobservable heterogeneity to be expressed as a function of observable variables. Only recently has the application of incomplete IV models been extended to cases in which this inversion produces a non-singleton set of values of unobservable variables. This situation arises in many models such as those featuring discrete choice, counts, or censored outcomes, or when there are multiple sources of heterogeneity as in random coefficient models, or when economic considerations result in inequality restrictions on values taken by observed and unobserved variables. This paper provides an introduction to the methods set out for analyzing such generalized instrumental variable (GIV) models in Chesher and Rosen (2017). An illustrative example is provided in which an outcome is determined by a random coefficients linear model with an endogenous explanatory variable and instrumental variable exclusion and independence restrictions.

Stability, uniqueness and existence of solutions to McKean–Vlasov SDEs: a multidimensional Yamada–Watanabe approach

We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean–Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic case, we also obtain the existence of unique strong solutions. By using our approach, which is based on an extension of the Yamada–Watanabe ansatz to the multidimensional setting and which does not rely on the construction of Lyapunov functions, we prove first moment and pathwise exponential stability. Furthermore, Lyapunov exponents are computed explicitly.

Deep Learning and Handcrafted Features for Thyroid Nodule Classification

ABSTRACTIn this research, we present a refined image‐based computer‐aided diagnosis (CAD) system for thyroid cancer detection using ultrasound imagery. This system integrates a specialized convolutional neural network (CNN) architecture designed to address the unique aspects of thyroid image datasets. Additionally, it incorporates a novel statistical model that utilizes a two‐dimensional random coefficient autoregressive (2D‐RCA) method to precisely analyze the textural characteristics of thyroid images, thereby capturing essential texture‐related information. The classification framework relies on a composite feature vector that combines deep learning features from the CNN and handcrafted features from the 2D‐RCA model, processed through a support vector machine (SVM) algorithm. Our evaluation methodology is structured in three phases: initial assessment of the 2D‐RCA features, analysis of the CNN‐derived features, and a final evaluation of their combined effect on classification performance. Comparative analyses with well‐known networks such as VGG16, VGG19, ResNet50, and AlexNet highlight the superior performance of our approach. The outcomes indicate a significant enhancement in diagnostic accuracy, achieving a classification accuracy of 97.2%, a sensitivity of 84.42%, and a specificity of 95.23%. These results not only demonstrate a notable advancement in the classification of thyroid nodules but also establish a new standard in the efficiency of CAD systems.

Strict monotonicity of stochastic process extreme distributions

Strict monotonicity is proved for the distributions of extremes of processes consisting of series of bounded function with independent random coefficients, in particular for zero mean continuous Gaussian processes over compact metric space. These results have wide applications to global inference problems on unknown functions.

An extension of ℤ-valued time series with Poisson difference innovation via logistic regression

ℤ-valued time series are a type of models that are extremely significant and widely utilized. The Poisson difference distribution is a crucial element in this kind of time series. This paper considers an extension of ℤ-valued autoregressive models with Poisson difference innovation by introducing the random coefficient composed of logistic regression. The estimation process is examined using conditional maximum likelihood and conditional least squares methods. A two-step approach is suggested to further optimize the estimation results. The likelihood ratio test is utilized to ascertain the presence of the random coefficient. Both simulation studies and analysis of real data demonstrate that the suggested model and method demonstrate outstanding performance.

Regularized maximum likelihood estimation for the random coefficients model

. The random coefficients model Y i = β 0 i + β 1 i X 1 i + β 2 i X 2 i + … + β d i X d i , with 𝐗 i , Y i , 𝜷 i i.i.d, and 𝜷 i independent of 𝐗 i is often used to capture unobserved heterogeneity in a population. We propose a quasi-maximum likelihood method to estimate the joint density distribution of the random coefficient model. This method implicitly involves the inversion of the Radon transformation in order to reconstruct the joint distribution, and hence is an inverse problem. To add stability to the solution, we apply Tikhonov-type regularization methods. Nonparametric estimation for the joint density of β i = ( β 0 i , … , β d i ) based on kernel methods or Fourier inversion have been proposed in recent years. Most of these methods assume a heavy tailed design density f 𝐗 . We analyze the convergence of the quasi maximum likelihood method without assuming heavy tails for f 𝐗 and illustrate performance by applying the method on simulated and real data.

Normalizing Basis Functions: Approximate Stationary Models for Large Spatial Data

ABSTRACTIn geostatistics, traditional spatial models often rely on the Gaussian process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes, necessitating the use of approximate methods. A powerful class of methods approximate the GP as a sum of basis functions with random coefficients. Although this technique offers computational efficiency, it does not inherently guarantee a stationary covariance. To mitigate this issue, the basis functions can be ‘normalized’ to maintain a constant marginal variance, avoiding unwanted artefacts and edge effects. This allows for the fitting of nearly stationary models to large, potentially non‐stationary datasets, providing a rigorous base to extend to more complex problems. Unfortunately, the process of normalizing these basis functions is computationally demanding. To address this, we introduce two fast and accurate algorithms to the normalization step, allowing for efficient prediction on fine grids. The practical value of these algorithms is showcased in the context of a spatial analysis on a large dataset, where significant computational speedups are achieved. While implementation and testing are done specifically within the LatticeKrig framework, these algorithms can be adapted to other basis function methods operating on regular grids.

The relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients

The relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients

Bounds for Exponential Sums With Random Multiplicative Coefficient

Abstract For $f$ a Rademacher or Steinhaus random multiplicative function, we prove that $ \max _{\theta \in [0,1]} \frac{1}{\sqrt{N}} \bigl | \sum _{n \leq N} f(n) \mathrm{e} (n \theta ) \bigr | \gg \sqrt{\log N}$, asymptotically almost surely as $N \rightarrow \infty $. Furthermore, for $f$ a Steinhaus random multiplicative function, and any $\varepsilon> 0$, we prove the partial upper bound result $ \max _{\theta \in [0,1]} \frac{1}{\sqrt{N}} \bigl | \sum _{\substack{n \leq N \\ P(n) \geq N^{0.8}}} f(n) \mathrm{e} (n \theta ) \bigr | \ll{(\log N)}^{7/4 + \varepsilon }$, asymptotically almost surely as $N \rightarrow \infty $, where $P(n)$ denotes the largest prime factor of $n$.

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution.Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlogn) instead of the typical O(n3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

Estimating heterogeneous effects: Applications to labor economics

A growing number of applications involve settings where, in order to infer heterogeneous effects, a researcher compares various units. Examples of research designs include children moving between different neighborhoods, workers moving between firms, patients migrating from one city to another, and banks offering loans to different firms. We present a unified framework for these settings, based on a linear model with normal random coefficients and normal errors. Using the model, we discuss how to recover the mean and dispersion of effects, other features of their distribution, and to construct predictors of the effects. We provide moment conditions on the model’s parameters, and outline various estimation strategies. A main objective of the paper is to clarify some of the underlying assumptions by highlighting their economic content, and to discuss and inform some of the key practical choices.

Variability in Causal Effects and Noncompliance in a Multisite Trial: A Bivariate Hierarchical Generalized Random Coefficients Model for a Binary Outcome.

Within each of 170 physicians, patients were randomized to access e-assist, an online program that aimed to increase colorectal cancer screening (CRCS), or control. Compliance was partial: of the experimental patients accessed e-assist while no controls were provided the access. Of interest are the average causal effect of assignment to treatment and the complier average causal effect as well as the variation of these causal effects across physicians. Each physician generates probabilities of screening for experimental compliers (experimental patients who accessed e-assist), control compliers (controls who would have accessed e-assist had they been assigned to e-assist), and never takers (patients who would have avoided e-assist no matter what). Estimating physician-specific probabilities jointly over physicians poses novel challenges. We address these challenges by maximum likelihood, factoring a "complete-data likelihood" uniquely into the conditional distribution of screening and partially observed compliance given random effects and the distribution of random effects. We marginalize this likelihood using adaptive Gauss-Hermite quadrature. The approach is doubly iterative in that the conditional distribution defies analytic evaluation. Because the small sample size per physician constrains estimability of multiple random effects, we reduce their dimensionality using a shared random effects model having a factor analytic structure. We assess estimators and recommend sample sizes to produce reasonably accurate and precise estimates by simulation, and analyze data from a trial of a CRCS intervention.

Simulation of a temporally dynamic atmospheric wavefront using the modified von-Kármán spectrum and Zernike-based method

In the simulation of the atmospheric wavefront, the Kolmogorov spectrum facilitates the mathematical treatments, but this model gives inaccurate predictions in cases where the effects of outer- and inner-scale can not be neglected. Therefore, we derive the covariance formula of Zernike coefficients based on the modified von-Kármán turbulence spectrum to improve the Zernike-based method. Further, using the frozen flow hypothesis, the temporal power spectra of Zernike coefficients are derived, and the effects of wind velocity and direction, as well as the outer and inner scales, are also taken into account. Then, we introduce a method for generating the temporally dynamic atmospheric wavefront using the inverse Fourier transform to draw random time-evolving coefficients from the temporal spectra. We evaluate the performance on simulated atmospheric wavefront, and the results confirm that accurate spatial and temporal statistics are obtained.

Information Theoretic Evaluation of Raccoon's Side-Channel Leakage

Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model.

B-027 CLSI-Based Result Precision on the cobas ISE neo and cobas c 703 Analytical Units Across Two Sites in Europe

Abstract Background Novel cobas® pro integrated solutions analytical units, the cobas® ISE neo and cobas c 703 analytical units (all Roche Diagnostics International Ltd, Rotkreuz, Switzerland), were assessed at two sites in Europe (Aalst, Belgium and Heidelberg, Germany). During the system design validation, precision was evaluated under intended use conditions in a routine simulation setting. Methods Quality control (QC) materials at two analyte concentrations were measured per site for selected assays (ion selective electrodes [ISEs], general chemistries and specific proteins, and immunochemistry assays); analyte recovery per QC was closely monitored. Precision was evaluated at both study sites based on Clinical and Laboratory Standards Institute EP05-A3 guidelines over 21 days for 53 applications representing the entire assay menu: six ISE serum/plasma and urine applications; 40 clinical chemistry serum/plasma and urine applications (four were measured using cobas c 503 at one site only); and seven immunochemistry serum/plasma applications. Reproducibility under various stressed routine-like conditions, including provocations, was tested using routine simulation imprecision experiments. To test the interaction of new and existing analytical units under routine conditions, two test configurations were used: the first configuration comprised one cobas ISE neo, two cobas c 703, and one cobas e 801 analytical units; and the second configuration comprised one cobas ISE neo, one cobas c 703, one cobas c 503, and one cobas e 801 analytical units. The precision of batch type measurements was compared with the precision under routine simulated random access conditions. Random access coefficients of variance (CVs) that exceeded 1.5× reference batch CVs, or single measurements deviating by >10% from the batch mean, triggered in-depth analysis of the system components that contributed to the result. CVs for intermediate precision comprised measurements from ≤4 cobas c 703 reagent disks, dependent on the system set-up and application assignment. CVs for reproducibility were calculated across four ISE measuring units, ≤3 cobas c 703 reagent disks, or ≤4 cobas e 801 measuring cells. Results Using four analytical units, n=511 CVs for repeatability, intermediate precision, and reproducibility were calculated. For repeatability, the median CV for ISE (n=24) was 0.8%, for clinical chemistry (cobas c 703: n=146; cobas c 503: n=8) was 0.9%, and for immunochemistry (n=28) was 1.0%. For intermediate precision, the median CV for ISE (n=24) was 1.1%, for clinical chemistry (cobas c 703: n=146; cobas c 503: n=8) was 1.2%, and for immunochemistry (n=28) was 1.5%. For reproducibility, the median CV for ISE (n=12) was 0.9%, for clinical chemistry (cobas c 703: n=73) was 1.6%, and for immunochemistry (n=14) was 1.7%. Conclusions The novel cobas ISE neo and cobas c 703 analytical units demonstrated robust precision, comparable to the existing cobas pro integrated solutions analytical units, over a prolonged period.

B-028 Result Precision on the New cobas pro integrated solutions cobas ISE neo and cobas c 703 Analytical Units Under Routine-Like Conditions Across Two Sites in Europe

Abstract Background The precision of the new cobas® pro integrated solutions cobas® ISE neo and cobas c 703 analytical units (Roche Diagnostics International Ltd, Rotkreuz, Switzerland) was measured under intended use conditions in a routine simulation setting. Methods The interaction of hardware, software, assays, and samples was tested at two sites (Aalst, Belgium and Heidelberg, Germany) between October and December 2023. Reproducibility under various stressed routine-like conditions, including provocations, was tested using routine simulation imprecision experiments. To test the interaction of new and existing analytical units under routine conditions, test configurations including commercially available cobas c 503 and cobas e 801 analytical units were used. The first configuration comprised one cobas ISE neo analytical unit, two cobas c 703 analytical units, and one cobas e 801 analytical unit. The second configuration comprised one cobas ISE neo analytical unit, one cobas c 703 analytical unit, one cobas c 503 analytical unit, and one cobas e 801 analytical unit. The precision of batch type measurements was compared with the precision under routine simulated random access conditions. Random access coefficients of variance (CVs) that exceeded 1.5× reference batch CVs, or single measurements deviating by >10% from the batch mean, triggered in-depth analysis of the system components that contributed to the result. Results Overall, 56 applications were measured during the reference and random parts of seven routine simulation imprecision runs: six ion selective electrodes (ISE; three serum, three urine), 35 clinical chemistry applications on cobas c 703 (27 serum, eight urine), seven clinical chemistry applications on cobas c 503 (five serum, one urine, one whole blood) and eight immunochemistry (serum) applications. Of six ISE (serum and urine) applications, the mean reference and random CVs were 0.8% and 0.9%, respectively. Of 42 clinical chemistry (serum, urine, and whole blood) applications, the mean reference CV was 0.9% and the mean random CV was 1.0%. Of eight immunochemistry (serum only) applications, mean reference and random CVs were 1.1% and 1.4%, respectively. Conclusions The findings from this study demonstrate that the new cobas ISE neo and cobas c 703 analytical units show consistent results over a prolonged time period, with most CVs in this setting below 0.9%. These results also show the successful integration of the new analytical units into the cobas pro integrated solutions, with seamless interaction of existing and analytical units under stressed conditions.

Coping with intensive training demands: a longitudinal investigation of the relationships between appraisal, emotion, coping effectiveness and engagement among elite fencers

ABSTRACT Training is, by essence, very challenging, both physically and mentally. The way athletes stay fully engaged in their intensive training programme and achieve their performance goals may depend on their capacity to deal effectively with such daily training demands. This study therefore aimed to further the understanding of the relationships between appraisal, emotion, coping effectiveness and engagement among elite fencers in relation to the demands of intensive training over the course of a competitive season. Twenty-three elite fencers (15 women, 8 men; age: 23.04 ± 3.54 years; fencing experience: 15.04 ± 3.74 years) completed an online questionnaire once a week, measuring perceived effort, perceived difficulty, pleasant and unpleasant emotions, athlete engagement, and coping effectiveness (i.e., 36 time-points). The results of the random coefficient regression models revealed the mediating role played by emotions in the dynamic relationships (a) between perceived difficulty and coping effectiveness (pleasant emotions: Sobel Test = −2.39, p < .05; unpleasant emotions: Sobel Test = −2.47, p < .05), and (b) between perceived effort and coping effectiveness (pleasant emotions: Sobel Test = 2.15, p < .05). Results also highlighted the partial mediating role played by coping effectiveness in the dynamic relationships (a) between perceived effort and engagement (Sobel Test = 2.27, p < .05), and (b) between perceived difficulty and engagement (Sobel Test = −2.16, p < .05). This study underlines the need to consider subjective appraisal during training over the course of a competitive season and its influence on psychological adaptation and engagement in intensive training settings.

School-level variation in children's moderate to vigorous intensity physical activity before and after COVID-19: a multilevel model analysis.

Schools play a crucial role in facilitating physical activity among children, but the COVID-19 pandemic has affected both children's physical activity and the school environment. It is essential to understand between-school differences in children's physical activity post lockdown, to determine if and how the role of schools has changed. Active-6 is a natural experiment comparing postlockdown accelerometer-estimated physical activity to a pre-COVID-19 comparator group. Accelerometer and individual data were collected on 1296 children aged 10-11 pre-COVID-19 (2017-8), with school characteristics collected from the 50 schools they attended. Post lockdown, we collected accelerometer, individual and school data from 393 children in 23 of the same schools and 436 children in 27 of the same schools in 2021 (Wave 1) and 2022 (Wave 2), respectively. Sources of variation (between-school, between-pupil and within-pupil) in child weekday moderate to vigorous physical activity at each wave were modelled using linear mixed-effects models with school-level wave random coefficients. We extended the model to estimate the proportion of between-school variation explained by school policy, curriculum and physical environment factors and school-aggregated pupil characteristics. We also explored the extent to which postlockdown differences in moderate to vigorous physical activity were mediated by individual or school factors. Between-school variation comprised 13% of the total variation pre-COVID-19, 7% in Wave 1 and 13% in Wave 2. School factors associated with moderate to vigorous physical activity were the following: whether physical education was compromised due to space (often: 9 minutes lower moderate to vigorous physical activity; sometimes: 5.4 minutes lower); high after-school club attendance (7 minutes higher moderate to vigorous physical activity for each additional club attended on average in the school); cycle training policy (4 minutes higher moderate to vigorous physical activity); and higher prevalence of active travel (1 minute higher moderate to vigorous physical activity for each 10% point increase in prevalence). These factors explained 22% of the between-school variation pre-COVID-19, and 72% at Wave 2. The relative importance changed, with cycle training policy and active travel being the most important pre-COVID-19 and cycle training policy, active after-school clubs and compromised physical education space most important in Wave 2. No factors were found to mediate the postlockdown differences in moderate to vigorous physical activity, except compromised physical education space, which had a suppressor effect in Wave 2. Only 27 of the initial 50 schools participated post lockdown, limiting our ability to make comparisons across waves. Sample sizes were additionally affected by missing data for some variables. While schools continue to play an important role in facilitating children's physical activity, the factors that contribute to this have changed post-COVID-19, with cycle training, active after-school clubs and ensuring physical education is prioritised even when space is limited now explaining nearly three-quarters of the between-school variation in children's moderate to vigorous physical activity. School-level interventions that focus on these areas, and policies that support them, may offer the potential to increase children's physical activity. This article presents independent research funded by the National Institute for Health and Care Research (NIHR) Public Health Research programme as award number NIHR131847.