Monte Carlo Estimation Research Articles

An R Package for Nonparametric Inference on Dynamic Populations with Infinitely Many Types.

Fleming-Viot diffusions are widely used stochastic models for population dynamics that extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally infinite panmictic population, whose individuals undergo random genetic drift and at birth can mutate to a new allelic type drawn from a possibly infinite potential pool, independently of their parent. Recently, Bayesian nonparametric inference has been considered for this model when a finite sample of individuals is drawn from the population at several discrete time points. Previous works have fully described the relevant estimators for this problem, but current software is available only for the Wright-Fisher finite-dimensional case. Here, we provide software for the general case, overcoming some nontrivial computational challenges posed by this setting. The R package FVDDPpkg efficiently approximates the filtering and smoothing distribution for Fleming-Viot diffusions, given finite samples of individuals collected at different times. A suitable Monte Carlo approximation is also introduced in order to reduce the computational cost.

Double-loop importance sampling for McKean–Vlasov stochastic differential equation

This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with the solution to the d-dimensional McKean–Vlasov stochastic differential equation (MV-SDE). MV-SDEs are usually approximated using a stochastic interacting P-particle system, which is a set of P coupled d-dimensional stochastic differential equations (SDEs). Importance sampling (IS) is a common technique for reducing high relative variance of MC estimators of rare-event probabilities. We first derive a zero-variance IS change of measure for the quantity of interest by using stochastic optimal control theory. However, when this change of measure is applied to stochastic particle systems, it yields a P×d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P \ imes d$$\\end{document}-dimensional partial differential control equation (PDE), which is computationally expensive to solve. To address this issue, we use the decoupling approach introduced in (dos Reis et al. 2023), generating a d-dimensional control PDE for a zero-variance estimator of the decoupled SDE. Based on this approach, we develop a computationally efficient double loop MC (DLMC) estimator. We conduct a comprehensive numerical error and work analysis of the DLMC estimator. As a result, we show optimal complexity of OTOLr-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \ extrm{TOL}_{\ extrm{r}}^{-4}\\right) $$\\end{document} with a significantly reduced constant to achieve a prescribed relative error tolerance TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document}. Subsequently, we propose an adaptive DLMC method combined with IS to numerically estimate rare-event probabilities, substantially reducing relative variance and computational runtimes required to achieve a given TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document} compared with standard MC estimators in the absence of IS. Numerical experiments are performed on the Kuramoto model from statistical physics.

Model Optimization and Application of Straw Mulch Quantity Using Remote Sensing

Straw mulch quantity is an important indicator in the detection of straw returned to the field in conservation tillage, but there is a lack of large-scale automated measurement methods. In this study, we estimated global straw mulch quantity and completed the detection of straw returned to the field. We used an unmanned aerial vehicle (UAV) carrying a multispectral camera to acquire remote sensing images of straw in the field. First, the spectral index was selected using the Elastic-net (ENET) algorithm. Then, we used the Genetic Algorithm Hybrid Particle Swarm Optimization (GA-HPSO) algorithm, which embeds crossover and mutation operators from the Genetic Algorithm (GA) into the improved Particle Swarm Optimization (PSO) algorithm to solve the problem of machine learning model prediction performance being greatly affected by parameters. Finally, we used the Monte Carlo method to achieve a global estimation of straw mulch quantity and complete the rapid detection of field plots. The results indicate that the inversion model optimized using the GA-HPSO algorithm performed the best, with the coefficient of determination (R2) reaching 0.75 and the root mean square error (RMSE) only being 0.044. At the same time, the Monte Carlo estimation method achieved an average accuracy of 88.69% for the estimation of global straw mulch quantity, which was effective and applicable in the detection of global mulch quantity. This study provides a scientific reference for the detection of straw mulch quantity in conservation tillage and also provides a reliable model inversion estimation method for the estimation of straw mulch quantity in other crops.

Development of an EGSnrc multi-leaf collimator component module and treatment head model for a low-field MRI linear accelerator.

Monte Carlo (MC) modeling of MR-guided radiotherapy (MRgRT) treatment machines enables the characterization of photon/electron interactions in the presence of a magnetic field. The EGSnrc MC code system is a well-established system for radiation dose calculations. The multi-leaf collimator (MLC) component modules presently available within the EGSnrc MC code system do not include a model of the double-focused MLC available on a low-field (0.35T) MRI linear accelerator (MR linac). Here we developed and validated a new component module (CM) for the low-field MRgRT MLC using the EGSnrc/BEAMnrc/DOSXYZnrc code system. We performed detailed modeling of the treatment head and validated the model using measurements and calculations from the vendor-specific treatment planning system (TPS). The detailed geometry of the low-field MR linac MLC and other treatment head structures were modeled using BEAMnrc. Comparisons of DOSXYZnrc simulated dose against measurements and the low-field MR linac TPS for a variety of AAPM TG-53 task group report suggested square and shaped fields, as well as a step-and-shoot intensity-modulated radiotherapy (IMRT) plan, are presented. Our model agrees with both measured and TPS calculated data on average within 2%/2mm (dose/DTA) criterion for square field profiles. Output factors agreed within 1% for field sizes down to 2.49×2.49cm2 and within 2% of TPS data for the smallest field size of 0.83×0.83cm2. Shaped field and IMRT MC calculations agreed with measured and TPS data such that the gamma pass rates (3%/2mm) were 99.5% and (3%/3mm) 96.2%, respectively. We developed and validated an MLC CM (SYNCVRMLC) for the low-field MR linac using the EGSnrc MC code systems. This new CM will facilitate MC computation of fluence and dose distributions using BEAMnrc/DOSXYZnrc for patients treated on the low-field MR linac.

Laplace Approximation of J-factors for rigid base and rigid base pair models of DNA cyclization

We apply the Laplace approximation to a mathematical formulation of DNA cyclization J-factors, leading to a formula that involves energies of local minima of the DNA energy, factors coming from the Hessian of the energy near each minimum, and geometric factors arising from the orientational portion of J. The approximation is derived in a quite general setting that encompasses both rigid base and rigid base pair models common in the literature. The approximation is applied to several families of 200-400 bp DNA, some relatively straight (fragments of λ-phage) and others quite bent (constructs that include up to ten A-tracts). The accuracy of the approximation is assessed by comparing to (more time-consuming) Monte Carlo computations: Laplace is within 20% of Monte Carlo for most 200 bp molecules and undershoots Monte Carlo by about 30% for 300 bp and 50% for 400 bp. We explore length and sequence dependence, both for our overall approximation of J and for its energy and entropic components, and make comparisons to a different approximation of J proposed by Zhang and Crothers.

Fokker–Planck equation and Feynman–Kac formula for multidimensional stochastic dynamical systems with Lévy noises and time-dependent coefficients

The aim of this paper is to establish a version of the Feynman–Kac formula for the time-dependent multidimensional nonlocal Fokker–Planck equation corresponding to a class of time-dependent stochastic differential equations driven by multiplicative symmetric (or asymmetric) α-stable Lévy noise. First the forward nonlocal Fokker–Planck equation is derived by the adjoint operator method, overcoming the challenges posed by time-dependent multidimensional nonlinear symmetric α-stable Lévy noise. Subsequently, the Feynman–Kac formula for the forward multidimensional time-dependent nonlocal Fokker–Planck equation is established by applying techniques for the backward nonlocal Fokker–Planck equations, which is associated with the backward stochastic differential equation driven by the multiplicative symmetric α-stable Lévy noise. Notably, in the case of asymmetric α-stable Lévy noise case, the presence of the characteristic function in the nonlocal operator adds complexity to the analysis. Using the Feynman–Kac formula, it is demonstrated that the solution of the forward nonlocal Fokker–Planck equation can be readily simulated through Monte Carlo approximation, especially in scenarios involving long-time simulation settings with large steps. These concepts are illustrated with intriguing examples, and the dynamic evolution of the probability density function corresponding to the stochastic SIS model and the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, ComK and ComS) are investigated over an extended period.

Expected constraints on Phobos interior from the MMX gravity and rotation observations

The origin of the Martian moons is still uncertain, and knowledge about their interior could provide support to some of its leading theories. In preparation for the JAXA Martian Moons eXploration (MMX) mission, we review our current knowledge on the interior of Phobos, and provide synthetic tests showing how the gravity and rotation determination could allow the detection of specific interior-structure properties. The inversion of the geodetic observables for the retrieval of the internal mass distribution of a set of synthetic interior models is performed via non-linear least-squares, where the interior parameterization is based on the level-set method. We additionally provide simple expressions allowing to relate some of these interior models to the geodetic observables of Phobos. The results, based on realistic measurement resolution and noise scenarios, show good retrievals for most of the models at the data resolutions expected from MMX. Specifically, we find the gravity information is realistically sufficient for the detection of mass anomalies below the Stickney crater, as well as large scale heterogeneous regions within plausible rubble-pile structures. Libration helps retrieve the more degenerate models for gravity, such as those with concentric layers or with density varying linearly with depth. The incremental improvement from further adding an hypothetical mean obliquity measurement is marginal. Finally, we apply the level-set inversion and the analytical formulas to estimate possible interior characteristics of the ‘real’ Phobos from the currently-available scarce geodetic observables. The level-set solutions for the real-data inversion generally converge to a higher mass concentration towards the surface in the equatorial region. Markov chain Monte Carlo estimations of parameters relative to a simple 2-layer model or a radial density distribution similarly hint at a lighter region inside of Phobos.

A Weak MLMC Scheme for Lévy-Copula-Driven SDEs with Applications to the Pricing of Credit, Equity and Interest Rate Derivatives

This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for Lévy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain approximation [Mijatović, Aleksandar, Matija Vidmar, and Saul Jacka. 2012. “Markov Chain Approximations for Transition Densities of Lévy Processes.” Electronic Journal of Probability 19]) of the pure-jump component of the driving Lévy process and is particularly suited if the multidimensional driver is given by a Lévy copula. The multilevel version of the algorithm requires a new coupling of the approximate Lévy drivers in the consecutive levels of the scheme, which is defined via a coupling of the corresponding Poisson point processes. The multilevel scheme is weak in the sense that the bound on the level variances is based on the coupling alone without requiring strong convergence. Moreover, the coupling is natural for the proposed discretization of jumps and is easy to simulate. The approximation scheme and its multilevel analogous are applied to examples taken from mathematical finance, including the pricing of credit, equity and interest rate derivatives.

Peer effects affect the adaptation behaviour of rural residents to geohazards in China: a new policy pathway

ABSTRACT Disaster prevention and mitigation (DPM) is one of the responses to extreme climate change impacts and depends on the adoption of risk adaptation behaviour by rural residents. While residents exhibit a high willingness to adapt, they also show low behaviour with reference to DPM. While adaptation behaviour of individuals has been studied extensively, the mutual impact of adaptation behaviour among residents has so far been neglected in the literature. Evaluating this interaction could serve as an important foundation for refining disaster reduction policies. Drawing on social cognitive theory, we propose a novel theoretical framework to analyze peer effects on individual decision-making in DPM. Using data gathered from 536 respondents in Sichuan Province, China, this paper adopts the Bayes Markov chain Monte Carlo estimation method to perform a regression of the spatial probit model. Further, the propensity score matching model was used to explore peer effects on the transformation between residents’ willingness to actual behaviour. Results indicate significant and robust peer effects on DPM behaviour among residents. A heterogeneity test indicated that peer effects are predominantly observed among residents with low and medium social status perception and not in those with high social status perception. Peer effects have a significant and positive influence on the transformation from residents’ willingness to their behaviour. Residents are not completely independent in their decision-making, and complex social mechanisms dictate rational and irrational choices of behaviour. Therefore, it is necessary to fully consider positive peer effects on residents in the formulation of policies. Key policy insights Focusing on the adaptation behaviours and peer effects of rural residents is conducive to improving the public's acceptance of disaster reduction policies. It is difficult for homogenization policies to accurately meet the needs of rural residents in China, and the response to geohazard events requires diversified local policies. Through peer effect, the government can create a kind of environmental soft pressure and promote the transformation of residents’ willingness into behaviour. Due to peer effects, the government can utilize the leading role of a small number of target groups to reduce the cost of implementing disaster reduction policies.

Optical beam spread in seawater

We study the spatial and angular distribution of light in a narrow stationary beam propagating in a medium like seawater. For a power-law parametrization of the seawater phase function, using radiative transfer analysis, we derive analytical expressions that determine the radiance distribution in the medium. Both the case of intermediate source–receiver distances, where absorption only begins to affect spreading of the beam, and the asymptotic regime of beam propagation are examined. For the main characteristics of the radiance distribution (the total power, the variance of the angular and radial distributions), scaling relations involving the inherent optical parameters of seawater are found. To validate the expressions obtained we carry out Monte Carlo simulation for commonly adopted seawater scattering models (of Petzold and Morel et al) and their analytical parameterizations. For optical parameters typical to seawater, the predicted analytical laws are in excellent agreement with the results of the Monte Carlo computations.

Efficient ARL estimation for general control charts using censored run lengths

The average run length (ARL), the average number of in-control signals before an out-of-control signal occurs, is a critical measure of the performance of a control chart. Various methods have been explored for estimating the ARL, including Markov chain-based approximation, integration method, and the Monte Carlo method, especially for time-dependent charting statistics. Although computationally expensive, the Monte Carlo method is generic and applicable to all control charts. Typically, it involves choosing the maximum run length in advance and discarding iterations that fail to produce out-of-control signals to accommodate some unusually lengthy runs. However, these discarded runs provide information for estimating the run length. This paper introduces a new Monte Carlo approximation that retains failed iterations as Type I censored observations for ARL estimation. Our approach relies on the memoryless expectation of the run length distribution to have a simple and efficient ARL estimator. This assumption is necessary for mean estimation in Type I censored data and aligns with existing ARL approximations used in popular control charts like Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts. Numerical simulations demonstrate our method’s computational and statistical efficiency across the mean, median, EWMA, and CUSUM charts.

Cross-domain additive learning of new knowledge rather than replacement.

In medical clinical scenarios for reasons such as patient privacy, information protection and data migration, when domain adaptation is needed for real scenarios, the source-domain data is often inaccessible and only the pre-trained source model on the source-domain is available. Existing solutions for this type of problem tend to forget the rich task experience previously learned on the source domain after adapting, which means that the model simply overfits the target-domain data when adapting and does not learn robust features that facilitate real task decisions. We address this problem by exploring the particular application of source-free domain adaptation in medical image segmentation and propose a two-stage additive source-free adaptation framework. We generalize the domain-invariant features by constraining the core pathological structure and semantic consistency between different perspectives. And we reduce the segmentation generated by locating and filtering elements that may have errors through Monte-Carlo uncertainty estimation. We conduct comparison experiments with some other methods on a cross-device polyp segmentation and a cross-modal brain tumor segmentation dataset, the results in both the target and source domains verify that the proposed method can effectively solve the domain offset problem and the model retains its dominance on the source domain after learning new knowledge of the target domain.This work provides valuable exploration for achieving additive learning on the target and source domains in the absence of source data and offers new ideas and methods for adaptation research in the field of medical image segmentation.

Adaptive formulation for probabilistic storm surge predictions through sharing of numerical simulation results across storm advisories

As a tropical storm/cyclone approaches landfall, real-time probabilistic predictions for the anticipated surge provide valuable information for emergency preparedness/response decisions. These probabilistic predictions are made through an uncertainty quantification process that involves: (i) generating a sufficiently large ensemble of storm scenarios based on the nominal storm advisory and the anticipated forecast errors; (ii) performing high-fidelity numerical simulations to obtain surge predictions for each storm scenario; and (iii) estimating surge statistics of interest by assembling the simulation results. This process is repeated whenever the nominal storm advisory is updated. The number of storm scenarios utilized in the analysis directly impacts the statistical accuracy of the probabilistic predictions; a larger ensemble improves accuracy but requires greater computational resources to provide predictions with the desired expediency to guide real-time decisions. This paper revisits two recently proposed Monte-Carlo (MC) frameworks that aim to improve accuracy without increasing the computational burden: adaptive importance sampling (AIS) and adaptive multi-fidelity Monte Carlo (AMFMC). The foundational concept behind them is similar: share numerical simulation results across the probabilistic predictions performed for different storm advisories to accelerate the MC estimation. This is achieved differently for each approach, through adaptive development of an importance sampling proposal density (for AIS) or a surrogate model (for AMFMC). Here, a direct comparison between these frameworks is established, focusing on the mechanisms for the information sharing and the challenges encountered in tuning the algorithm adaptive characteristics to provide probabilistic estimates across a large number of quantities of interest (QoIs), corresponding to the surge predictions for different locations within the coastal region of interest. As this large number results in conflicting choices for the adaptive characteristics, a compromise solution needs to be promoted. The efficacy of the two frameworks is examined in detail in this setting, comparing the accuracy of idealized implementations (adaptive decisions independently made for each QoI) to the accuracy of practical implementations (single, compromise decision within the MC implementation). The study also showcases the importance of information sharing across storm advisories in real-time probabilistic storm surge predictions and provides guidelines for an efficient adaptive MC formulation in such settings.

An improved method for statistics estimation of out-of-plane load resistance of masonry walls using design-code models and mechanics-based finite element models

The susceptibility of masonry walls to out-of-plane failure under seismic loading presents a significant engineering concern. In adherence to contemporary limit state design philosophy and as mandated by performance-based design guidelines, it is crucial to accurately estimate statistics parameters such as the mean and variance of out-of-plane resistance. To achieve this, two deterministic models are often considered within the Monte Carlo simulation framework: design-code models, known for their computational efficiency but potential for significant model error, and mechanics-based finite element models, noted for their accuracy but computational intensity. Relying solely on either model for statistics estimation presents challenges due to their respective inherent limitations. This study introduces an improved strategy that synergizes the strengths of both models, resulting in enhanced statistics estimators for the out-of-plane resistance of masonry walls. The proposed methodology involves the use of the control variate method by integrating numerous design-code model evaluations to boost computational efficiency while incorporating a limited number of finite element model evaluations to ensure accuracy. The constructions of the proposed estimators follow rigorous optimization procedures to minimize associated errors and variances. Theoretical derivations are provided for essential elements in the estimator constructions, such as model evaluation numbers for finite element and design-code models and control variate coefficients. Moreover, the accuracy of the proposed estimators is compared with that of the crude Monte Carlo estimator. A key benefit of the proposed estimators is their unbiased nature, and their accuracy is not compromised by the discrepancies between the finite element model and the design-code model. To demonstrate the practicality of these estimators, two case studies are illustrated: one focusing on unreinforced masonry walls and the other on reinforced masonry walls. The results indicate that design-code model-based estimators exhibit large bias, and compared to the estimators that solely rely on the finite element model, the proposed estimators achieve higher accuracy given the same computational budget.

Monte Carlo Estimation of CoVaR

CoVaR is an important measure of financial systemic risk due to its ability to capture tail dependence between the losses of different portfolios and its capacity to predict financial crises. Estimating CoVaR is challenging because its definition involves a zero-probability event, which is unobservable in the data. The existing model-based methods address this issue by assuming simplified structural models, which introduce biases that are difficult to eliminate. In “Monte Carlo Estimation of CoVaR,” Huang, Lin, and Hong propose using Monte Carlo methods to estimate CoVaR, leveraging the modeling flexibility of Monte Carlo simulation. Specifically, they introduce a batching estimator applicable to a wide range of financial models and prove that its best rate of convergence is [Formula: see text], where n is the sample size. Under the widely used delta-gamma approximation model, they further introduce an importance sampling–inspired estimator and prove that its best rate of convergence can be improved to [Formula: see text].

Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes.

Deep Gaussian process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce neural operator variational inference (NOVI) for DGPs. NOVI uses a neural generator to obtain a sampler and minimizes the regularized Stein discrepancy (RSD) between the generated distribution and true posterior in L2 space. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques and demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to millions demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming state-of-the-art (SOTA) Gaussian process (GP) methods. We are optimistic that NOVI possesses the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical applications.

The slice sampler and centrally symmetric distributions

Abstract We show that the slice sampler generates Markov chains whose variables are mean independent and thus uncorrelated when the target density is centrally symmetric. Skewness instead boosts correlations. Popular implementation algorithms such as stepping-out and multivariate-sampling-with-hyperrectangles add statistical inefficiency, the first in case of multimodality, the second in all circumstances. A new sampler which exploits these structural and algorithmic characteristics to reduce the variance of Monte Carlo estimates is experimented in several sampling problems. An insight into the properties of the product slice sampler is also provided.

B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics.

Throughout an organism's life, a multitude of complex and interdependent biological systems transition through biophysical processes that serve as indicators of the underlying biological states. Inferring these latent, unobserved states is a goal of modern biology and neuroscience. However, in many experimental setups, we can at best obtain discrete snapshots of the system at different times and for different individuals. This challenge is particularly relevant in the study of Alzheimer's Disease (AD) progression, where we observe the aggregation of pathology in brain donors, but the underlying disease state is unknown. This paper proposes a biophysically motivated Bayesian framework (B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics), where the disease state is modeled and continuously inferred from observed quantifications of multiple AD pathological proteins. Inspired by biophysical models, we describe pathological burden as an exponential process. The progression of AD is modeled by assigning a latent score, termed pseudotime, to each pathological state, creating a pseudotemporal order of donors based on their pathological burden. We study the theoretical properties of the model using linearization to reveal convergence and identifiability properties. We provide Markov chain Monte Carlo estimation algorithms, illustrating the effectiveness of our approach with multiple simulation studies across various data conditions. Applying this methodology to data from the Seattle Alzheimer's Disease Brain Cell Atlas, we infer the pseudotime ordering of donors. Finally, we analyze the information within each pathological feature to refine the model, focusing on the most informative pathologies. This framework lays the groundwork for continuous pseudotime modeling in the analysis of neurodegenerative diseases.

Classical and Bayesian estimation of multicomponent stress–strength reliability with power Lindley distribution under progressive first-failure censored samples

This research article presents a methodology for estimating the multicomponent reliability based on progressively first-failure censored samples, where the underlying distribution of stress and strength is modelled using the power Lindley distribution. The classical and Bayesian estimation methods are utilized for estimating the multicomponent reliability. In the Bayesian estimation, the Markov Chain Monte Carlo approximation method is employed to obtain the posterior mean under a generalized entropy loss function. Various intervals including asymptotic confidence, bootstrap-p confidence, bootstrap-t confidence, Bayesian credible, and highest posterior density credible intervals are computed. A simulation study is conducted to evaluate the performance of the proposed methodology. Also, two different real data applications are presented to illustrate the practicality of the approach.

Is the availability and quality of local early childhood education and care services associated with young children's mental health at school entry?

PurposeThis study investigated the relationship between geographic availability (and quality) of local early childhood education and care services and children's early mental health outcomes for all children entering their first year of full-time school in Melbourne, Australia. MethodsWe capitalise on a unique population linked dataset, the Australian Early Development Census – Built Environment, which combines geospatial measures of children's neighbourhoods with demographic information and child mental health outcomes for all school entrants in Australia's 21 most populous cities and towns. Objective early childhood education and care service location and quality exposures were developed for each study child based on home addresses. Four geographic availability exposures (counts within 3 km) were examined for cross-sectional associations with child mental health outcomes (externalising and internalising difficulties, competence). We estimated associations using multilevel logistic regression (Markov Chain Monte Carlo estimation) adjusting for child demographics and stratifying by urbanicity. ResultsChildren with higher counts of high-quality preschool services within 3 km of home had lower odds of difficulties and higher odds of competence. Overall, exposures were most consistently associated with children's competence. Across all outcomes, the most consistent patterning was observed for children living in the inner city and middle ring. Results varied depending on whether service quality was accounted for in measures of availability. Geographic availability of early childhood services showed patterning by neighbourhood disadvantage and by maternal education. ConclusionWe found some evidence that geographic availability of high-quality preschools was associated with better child mental health outcomes, but results varied by urbanicity. While future research is required to unpack these differences, these findings indicate the importance of accounting for both geographic availability and service quality simultaneously in future research, policy and practice.