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Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the sampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same.

This paper aims to address the Bernoulli factory problem of 2 ⁢ p 2\mathtt{p} coins by analysing the relationship between the negative binomial distributions and binomial distributions generated on the same chain of coin flips. The proposed algorithm requires fewer conditions on the constructed sequences compared with the existing algorithms. The feasibility of obtaining such 2 ⁢ p 2\mathtt{p} -coin based on 𝚙-coins will be considered as well.

This study is a follow-up of two our papers (Appl. Math. Lett. 126 (2022) and MCMA 29:4 (2023)), where we developed a vector randomized algorithms with iterative refinement for large system of linear algebraic equations. We focus in this paper on the application of the vector randomized iterative refinement algorithm to boundary integral equations that solve interior Dirichlet and exterior Neumann boundary value problems for 2D Laplace equation.

A method for calculating the characteristics of stochastic differential equations using semiclassical approximation is proposed. For a stochastic differential equation arising in the study of the pure birth process (Yule process) and the Cox Ingersoll Ross (CIR) model, an analysis of the accuracy of the semiclassical approximation was carried out. This analysis is based on a comparison of approximate values with exact values for the mathematical expectation of a solution to the equation.

The aim of the present paper is first to propose a state-of-art of this domain. Second, some convergence results are established in the case of the Dirichlet distribution. This distribution has the advantage to include both the uniform case and the deterministic one. In a first part, the Dirichlet distribution is defined and some properties are supplied. In a second part, new results are established in connexion with former theorems.

In this paper, we introduce a class of periodic integer-valued autoregressive BL-PINAR(1) models with Bell innovations distribution based on the binomial thinning operator. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed forms of these moments are, under the obtained conditions, derived. Furthermore, the periodic autocovariance structure is also considered while providing the closed form of the periodic autocorrelation function. The conditional least squares (CLS), Yule–Walker (YW), weighted conditional least squares (WCLS), and conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters. The asymptotic properties of the CLS and the YW estimators are obtained. The performances of these methods are compared through a simulation study. An application on a real data set is provided.

The dependence of the binding energies of adsorbed In and Al atoms on the (001) surfaces of InAs and AlAs with β 2 {\beta_{2}} (2 × {\times} 4) reconstruction on the biaxial compression and tension strains has been investigated using the density functional theory. The maps of the potential energy surface of the adsorbed In atom on the (001) surface of InAs and AlAs with β 2 {\beta_{2}} (2 × {\times} 4) reconstruction have been calculated. According to the calculation results, a general trend towards an increase in the absolute values of the binding energy of the adsorbed In and Al atoms on the (001) surface of InAs and AlAs with an increase in the biaxial tension strain has been observed. For certain positions of the adsorbed atoms, a change in the sign of the derivative of the binding energy dependence on the biaxial strain has been observed with a change in the symmetry of the adsorbed state of the atom.

Nowadays, Dynamic Contrast Enhanced MRI (DCE-MRI) is becoming the most widely explored technique in clinical practice for tumor assessment. In acquiring DCE-MRI, a contrast agent (CA), also called tracer, is injected into the blood flow before or during the acquisition of a time series of T 1 {T_{1}} -weighted images with fast imaging techniques. When the CA goes through the tissue, MR signal intensity measurements in voxels of the region of interest (ROI) are registered and used to calculate the CA concentration in each voxel. The Tofts models have become standard for the analysis of DCE-MRI and which express tissue CA concentration C ⁢ ( t ) {C(t)} as function of time t . The analysis of quantitative parameters in DCE-MRI provides the quantitative criterion as a reference rather than relying only on the shape of the DCE-curve, as it is used for diagnosis of prostate cancer (PCa). This study aim to provide a new thinking in quantitative analysis which may therefore improve diagnostic accuracy for detection of prostate cancer and could be used in patient baseline prediction and guide management. A hierarchical Bayesian model was built to estimate the values of the four pharmacokinetic parameters ( K trans {K_{\mathrm{trans}}} , k ep {k_{\mathrm{ep}}} , υ p {\upsilon_{\mathrm{p}}} , υ e {\upsilon_{\mathrm{e}}} ) for both prostate healthy and lesion tissues in the peripheral zone. This estimation is important because it help to understand the behavior of the CA in the body and how this latter reacts to the CA in order to emphasize the expectation or the absence of prostate lesion during the diagnosis step.

Analyzing COVID-19 data presents a challenge in Bayesian computations of the Poisson process because the experimental conditions are not under control. This lack of homogeneity can lead to inconsistent model parameters, which violates the assumptions of Bayesian inference. In this paper, we study the multiple change-point detection problem from this viewpoint for a non-homogeneous sample path of the Poisson process as the response variable. The rate parameters are linked to some explanatory using a generalized linear model. The number of change-points is considered to be unknown as well as their locations. We introduce a Bayesian paradigm to estimate the number and location of change-points. We also present an adaptive RJMCMC algorithm to generate pseudo-random samples from the posterior distributions. We apply the proposed model to analyze the COVID-19 infection curves from different countries and identify patterns of cases. We also assess the efficacy of interventions, such as vaccination and public health emergency responses, implemented by different countries. The results of the analysis provide valuable insights into the spread of COVID-19 and the effectiveness of interventions. The proposed model can be used to inform public health decision-making and help to improve the management of the pandemic.