Parametric Bootstrap Research Articles

Bayesian inference for modified Weibull distribution under simple step‐stress model based on type‐I censoring

AbstractIn this paper, we consider a simple step‐stress accelerated life test (SSALT) model under the tampered random variable (TRV) model for the modified Weibull distribution (MWD) with type‐I censoring. We consider the classical and Bayesian estimation methods for the estimation of unknown parameters of the MWD model. In the classical scenario, we derive the maximum likelihood estimates (MLEs) and approximate confidence intervals (ACIs) for model parameters. Also, a parametric bootstrap resampling technique is used to derive the bootstrap confidence intervals. Under the Bayesian paradigm, the point estimates of the unknown parameters for different symmetric, asymmetric, and balanced loss functions and highest posterior density (HPD) credible intervals (CIs) are derived via Gibbs within metropolis‐hasting sampling procedure. A simulation study is conducted to compare the performance of Bayesian estimates with MLEs. Moreover, we also compare the precision of considered CIs. Finally, a real application is considered for illustration purpose.

MSA: reproducible mutational signature attribution with confidence based on simulations

BackgroundMutational signatures proved to be a useful tool for identifying patterns of mutations in genomes, often providing valuable insights about mutagenic processes or normal DNA damage. De novo extraction of signatures is commonly performed using Non-Negative Matrix Factorisation methods, however, accurate attribution of these signatures to individual samples is a distinct problem requiring uncertainty estimation, particularly in noisy scenarios or when the acting signatures have similar shapes. Whilst many packages for signature attribution exist, a few provide accuracy measures, and most are not easily reproducible nor scalable in high-performance computing environments.ResultsWe present Mutational Signature Attribution (MSA), a reproducible pipeline designed to assign signatures of different mutation types on a single-sample basis, using Non-Negative Least Squares method with optimisation based on configurable simulations. Parametric bootstrap is proposed as a way to measure statistical uncertainties of signature attribution. Supported mutation types include single and doublet base substitutions, indels and structural variants. Results are validated using simulations with reference COSMIC signatures, as well as randomly generated signatures.ConclusionsMSA is a tool for optimised mutational signature attribution based on simulations, providing confidence intervals using parametric bootstrap. It comprises a set of Python scripts unified in a single Nextflow pipeline with containerisation for cross-platform reproducibility and scalability in high-performance computing environments. The tool is publicly available from https://gitlab.com/s.senkin/MSA.

Estimating Exposure Intensity Based on Odor.

The odor detection threshold for a chemical typically varies widely across population members, and the values can be described by a lognormal distribution. Assuming that the parameters of a chemical's odor detection threshold distribution can be estimated, a method is presented to retrospectively estimate exposure intensity based on detecting the chemical's odor. The context is a single exposure period involving a single air contaminant. In brief, where k out of n identically exposed persons detect the chemical's odor, the best estimate of the chemical's concentration in air corresponds to the k ÷ n fractile of the odor detection threshold distribution. Where n is small and/or k ÷ n is close to zero or one, exact 100×(1-α)% confidence bounds for the fractile estimate can be computed without using the normal distribution assumption. In addition, statistical uncertainty in the parameter estimates of the chemical's odor detection threshold distribution can be considered via a parametric bootstrap procedure, such that an overall 100×(1-α)% confidence interval on the chemical's concentration in air is obtained. The method is illustrated for benzene. Analysis of the available benzene odor detection threshold literature provides best estimates of a population geometric mean equal to 37.8 ppm and geometric standard deviation equal to 1.92. In a hypothetical example in which two out of six workers detect the odor of benzene, the point estimate of the benzene exposure level is 28.5 ppm, and the approximate one-sided lower 95% confidence limit is 8.2 ppm. The present analysis also makes clear that odor does not provide an adequate warning of excessive levels of airborne benzene.

The Measures of Accuracy of Claim Frequency Credibility Predictor

Nowadays, the sustainability risks and opportunities start to affect strongly insurance companies in regard to the resulting additional variability of future values of variables taken into account in the decision processes. This is important especially in the era of sustainable non-life insurance promoting, among others, the use of ecological car engines or ecological systems of building heating. The fundamental issue in non-life insurance is to predict future claims (e.g., the aggregate value of claims or the number of claims for a single policy) in a heterogeneous portfolio of policies taking account of claim experience. For this purpose, the so-called credibility theory is used, which was initiated by the fundamental Bühlmann model modified to the Bühlmann–Straub model. Several modifications of the model have been proposed in the literature. One of them is the development of the relationship between the credibility models and statistical mixed models (e.g., linear mixed models) for longitudinal data. The article proposes the use of the parametric bootstrap algorithm to estimate measures of accuracy of the credibility predictor of the number of claims for a single policy taking into account new risk factors resulting from the emergence of green technologies on the considered market. The predictor is obtained for the model which belongs to the class of Generalised Linear Mixed Models (GLMMs) and which is a generalization of the Bülmann–Straub model. Additionally, the possibility of predicting the number of claims and the problem of the assessment of the prediction accuracy are presented based on a policy characterized by new green risk factor (hybrid motorcycle engine) not previously present in the portfolio. The paper presents the proposed methodology in a case study using real insurance data from the Polish market.

Conservative Profitability Evaluation for Newsboy-type Products with Bootstrap Methods

ABSTRACT In the field of inventory management, a profitability evaluation for ordered products is crucial to retailer revenue. Formulating such evaluations requires determining an appropriate order quantity, while ensuring that the product has high profitability potential. The achievable capacity index (ACI) provides a simple breakdown of profitability suitable for newsboy-type products with probabilistic distributed demand under the optimal order quantity. In this study, we investigated the lower confidence bound of ACI (LCBA) to obtain a conservative evaluation of profitability. Obtaining an explicit formula for the LCBA is difficult; therefore, we adopted parametric bootstrap methods to approximate the value for the LCBA. We also created a computational algorithm using R software to simulate the performances of various parametric bootstrap methods. Coverage rates and the corresponding ratios for various sample sizes and expected ACI values were tabulated to facilitate the selection of a suitable method and decide a required sample size with a conservative estimate. An illustrative example was presented to demonstrate the applicability of the proposed method and provide managerial insights.

Thermal Performance Curves Are Shaped by Prior Thermal Environment in Early Life.

Understanding links between thermal performance and environmental variation is necessary to predict organismal responses to climate change, and remains an ongoing challenge for ectotherms with complex life cycles. Distinct life stages can differ in thermal sensitivity, experience different environmental conditions as development unfolds, and, because stages are by nature interdependent, environmental effects can carry over from one stage to affect performance at others. Thermal performance may therefore respond to carryover effects of prior thermal environments, yet detailed insights into the nature, strength, and direction of those responses are still lacking. Here, in an aquatic ectotherm whose early planktonic stages (gametes, embryos, and larvae) govern adult abundances and dynamics, we explore the effects of prior thermal environments at fertilization and embryogenesis on thermal performance curves at the end of planktonic development. We factorially manipulate temperatures at fertilization and embryogenesis, then, for each combination of prior temperatures, measure thermal performance curves for survival of planktonic development (end of the larval stage) throughout the performance range. By combining generalized linear mixed modeling with parametric bootstrapping, we formally estimate and compare curve descriptors (thermal optima, limits, and breadth) among prior environments, and reveal carryover effects of temperature at embryogenesis, but not fertilization, on thermal optima at completion of development. Specifically, thermal optima shifted to track temperature during embryogenesis, while thermal limits and breadth remained unchanged. Our results argue that key aspects of thermal performance are shaped by prior thermal environment in early life, warranting further investigation of the possible mechanisms underpinning that response, and closer consideration of thermal carryover effects when predicting organismal responses to climate change.

Hypothesis Testing for Hierarchical Structures in Cognitive Diagnosis Models

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent attributes are assumed by researchers to characterize their dependence structure. Specifically, a directed acyclic graph is used to specify hierarchical constraints on the allowable configurations of the discrete latent attributes. In this paper, we consider the important yet unaddressed problem of testing the existence of latent hierarchical structures in CDMs. We first introduce the concept of testability of hierarchical structures in CDMs and present sufficient conditions. Then we study the asymptotic behaviors of the likelihood ratio test (LRT) statistic, which is widely used for testing nested models. Due to the irregularity of the problem, the asymptotic distribution of LRT becomes nonstandard and tends to provide unsatisfactory finite sample performance under practical conditions. We provide statistical insights on such failures, and propose to use parametric bootstrap to perform the testing. We also demonstrate the effectiveness and superiority of parametric bootstrap for testing the latent hierarchies over non-parametric bootstrap and the naïve Chi-squared test through comprehensive simulations and an educational assessment dataset.

Wide size dispersion and use of body composition and maturation improves the reliability of allometric exponent estimates.

To evaluate study designs and the influence of dispersion of body size, body composition and maturation of clearance or reliable estimation of allometric exponents. Non-linear mixed effects modeling and parametric bootstrap were employed to assess how the study sample size, number of observations per subject, between subject variability (BSV) and dispersion of size distribution affected estimation bias and uncertainty of allometric exponents. The role of covariate model misspecification was investigated using a large data set ranging from neonates to adults. A decrease in study sample size, number of observations per subject, an increase in BSV and a decrease in dispersion of size distribution, increased the uncertainty of allometric exponent estimates. Studies conducted only in adults with drugs exhibiting normal (30%) BSV in clearance may need to include at least 1000 subjects to be able to distinguish between allometric exponents of 2/3 and 1. Nevertheless, studies including both children and adults can distinguish these exponents with only 100 subjects. A marked bias of 45% (95%CI 41-49%) in the estimate of the allometric exponent of clearance was obtained when maturation and body composition were ignored in infants. A wide dispersion of body size (e.g. infants, children and adults) is required to reliably estimate allometric exponents. Ignoring differences in body composition and maturation of clearance may bias the exponent for clearance. Therefore, pharmacometricians should avoid estimating allometric exponent parameters without suitable designs and covariate models. Instead, they are encouraged to rely on the well-developed theory and evidence that clearance and volume parameters in humans scale with theory-based exponents.

PgHMA: Application of the heteroduplex mobility assay analysis in phylogenetics and population genetics.

The heteroduplex mobility assay (HMA) has proven to be a robust tool for the detection of genetic variation. Here, we describe a simple and rapid application of the HMA by microfluidic capillary electrophoresis, for phylogenetics and population genetic analyses (pgHMA). We show how commonly applied techniques in phylogenetics and population genetics have equivalents with pgHMA: phylogenetic reconstruction with bootstrapping, skyline plots, and mismatch distribution analysis. We assess the performance and accuracy of pgHMA by comparing the results obtained against those obtained using standard methods of analyses applied to sequencing data. The resulting comparisons demonstrate that: (a) there is a significant linear relationship (R2 =.992) between heteroduplex mobility and genetic distance, (b) phylogenetic trees obtained by HMA and nucleotide sequences present nearly identical topologies, (c) clades with high pgHMA parametric bootstrap support also have high bootstrap support on nucleotide phylogenies, (d) skyline plots estimated from the UPGMA trees of HMA and Bayesian trees of nucleotide data reveal similar trends, especially for the median trend estimate of effective population size, and (e) optimized mismatch distributions of HMA are closely fitted to the mismatch distributions of nucleotide sequences. In summary, pgHMA is an easily-applied method for approximating phylogenetic diversity and population trends.

Estimating confidence intervals for cerebral autoregulation: a parametric bootstrap approach

Cerebral autoregulation (CA) refers to the ability of the brain vasculature to control blood flow in the face of changing blood pressure. One of the methods commonly used to assess cerebral autoregulation, especially in participants at rest, is the analysis of phase derived from transfer function analysis (TFA), relating arterial blood pressure (ABP) to cerebral blood flow (CBF). This and other indexes of CA can provide consistent results when comparing groups of subjects (e.g. patients and healthy controls or normocapnia and hypercapnia) but can be quite variable within and between individuals. The objective of this paper is to present a novel parametric bootstrap method, used to estimate the sampling distribution and hence confidence intervals (CIs) of the mean phase estimate in the low-frequency band, in order to optimise estimation of measures of CA function and allow more robust inferences on the status of CA from individual recordings. A set of simulations was used to verify the proposed method under controlled conditions. In 20 healthy adult volunteers (age 25.53.5 years), ABP and CBF velocity (CBFV) were measured at rest, using a Finometer device and Transcranial Doppler (applied to the middle cerebral artery), respectively. For each volunteer, five individual recordings were taken on different days, each approximately 18 min long. Phase was estimated using TFA. Analysis of recorded data showed widely changing CIs over the duration of recordings, which could be reduced when noisy data and frequencies with low coherence were excluded from the analysis (Wilcoxon signed rank test p = 0.0065). The TFA window-lengths of 50s gave smaller CIs than lengths of 100s (p < 0.001) or 20s (p < 0.001), challenging the usual recommendation of 100s. The method adds a much needed flexible statistical tool for CA analysis in individual recordings.

Bivariate small-area estimation for binary and gaussian variables based on a conditionally specified model.

Many large-scale surveys collect both discrete and continuous variables. Small-area estimates may be desired for means of continuous variables, proportions in each level of a categorical variable, or for domain means defined as the mean of the continuous variable for each level of the categorical variable. In this paper, we introduce a conditionally specified bivariate mixed-effects model for small-area estimation, and provide a necessary and sufficient condition under which the conditional distributions render a valid joint distribution. The conditional specification allows better model interpretation. We use the valid joint distribution to calculate empirical Bayes predictors and use the parametric bootstrap to estimate the mean squared error. Simulation studies demonstrate the superior performance of the bivariate mixed-effects model relative to univariate model estimators. We apply the bivariate mixed-effects model to construct estimates for small watersheds using data from the Conservation Effects Assessment Project, a survey developed to quantify the environmental impacts of conservation efforts. We construct predictors of mean sediment loss, the proportion of land where the soil loss tolerance is exceeded, and the average sediment loss on land where the soil loss tolerance is exceeded. In the data analysis, the bivariate mixed-effects model leads to more scientifically interpretable estimates of domain means than those based on two independent univariatemodels.

Estimation and statistical inferences of variance components in the analysis of single-case experimental design using multilevel modeling.

Multilevel models (MLMs) can be used to examine treatment heterogeneity in single-case experimental designs (SCEDs). With small sample sizes, common issues for estimating between-case variance components in MLMs include nonpositive definite matrix, biased estimates, misspecification of covariance structures, and invalid Wald tests for variance components with bounded distributions. To address these issues, unconstrained optimization, model selection procedure based on parametric bootstrap, and restricted likelihood ratio test (RLRT)-based procedure are introduced. Using simulation studies, we compared the performance of two types of optimization methods (constrained vs. unconstrained) when the covariance structures are correctly specified or misspecified. We also examined the performance of a model selection procedure to obtain the optimal covariance structure. The results showed that the unconstrained optimization can avoid nonpositive definite issues to a great extent without a compromise in model convergence. The misspecification of covariance structures would cause biased estimates, especially with small between case variance components. However, the model selection procedure was found to attenuate the magnitude of bias. A practical guideline was generated for empirical researchers in SCEDs, providing conditions under which trustworthy point and interval estimates can be obtained for between-case variance components in MLMs, as well as the conditions under which the RLRT-based procedure can produce acceptable empirical type I error rate and power.

Improved yield estimation with efficient decision power for multi-line processes

Portable devices with multiple functions are commonly used in modern life, and the dies in these products have become much thinner and slimmer over time. Due to the rapid advancements in manufacturing technology in the semi-conductor industry, the process yield requirements grow increasingly strict. In advanced packaging manufacturing, the process is usually with multiple lines and often requires a very low fraction of defective. To assess the manufacturing yield precisely, the process capability index is widely used. is a generalization yield index designated for measuring the yield of multi-line processes. However, the typical existing method for obtaining the lower confidence bound of is conservative and it may mislead managers into making incorrect decisions. In this study, the nonparametric and parametric standard bootstrap methods have been implemented to establish a reliable and improved yield assessment. Three methods are investigated and the power comparison is provided. Then, two effective transformation methods to handle non-normal processes are presented and one example with simulation data is given for algorithm demonstration. Finally, an application of yield assessment for underfill processes with two manufacturing lines is presented. The simulation results demonstrate that based on the proposed method, we can reliably evaluate the true manufacturing yield and make a more powerful decision.

Considering the effect of correlation between the channels in multivariate detectors for evoked responses in the electroencephalogram

Evoked potentials refer to the small responses in the electroencephalogram (EEG), resulting from repeated or continuous auditory, visual or other stimuli. The detection of these responses is most commonly based on visual inspection by experienced professionals. To overcome the inherent subjectivity, automated (usually statistical) methods can be used, which aim to find the statistical significance of some parameter(s) calculated from the recorded signals, based on the null-hypothesis of 'no stimulus response is present'. These tests need to rely on assumptions about the statistical distributions of the signals and their parameters which in many cases allows p-values to be calculated. For some convenient parameters, however, closed form mathematical solutions are intractable and simulations are often required to find p-values (or critical values). The use of multichannel recordings can increase the sensitivity of tests compared to single-channel EEG, permitting the detection of responses in shorter recordings. This can be achieved by simple extensions of originally single channel methods, such as magnitude-squared coherence, component synchrony measure or the spectral F-test. However, the correlation between EEG channels can lead to false-positive rates that are difficult to predict or control. In this paper we present a modified parametric bootstrap method that permits the accurate estimation of false positive rates (p-values and critical values) for multichannel extensions of univariate objective evoked response techniques, with concomitant increases in sensitivity over conventional single channel methods. Illustrative results with evoked potentials from repeated photic stimulation are provided, with multivariate magnitude-squared coherence demonstrating the most robust performance.

On the Use of Aggregate Survey Data for Estimating Regional Major Depressive Disorder Prevalence

Major depression is a severe mental disorder that is associated with strongly increased mortality. The quantification of its prevalence on regional levels represents an important indicator for public health reporting. In addition to that, it marks a crucial basis for further explorative studies regarding environmental determinants of the condition. However, assessing the distribution of major depression in the population is challenging. The topic is highly sensitive, and national statistical institutions rarely have administrative records on this matter. Published prevalence figures as well as available auxiliary data are typically derived from survey estimates. These are often subject to high uncertainty due to large sampling variances and do not allow for sound regional analysis. We propose a new area-level Poisson mixed model that accounts for measurement errors in auxiliary data to close this gap. We derive the empirical best predictor under the model and present a parametric bootstrap estimator for the mean squared error. A method of moments algorithm for consistent model parameter estimation is developed. Simulation experiments are conducted to show the effectiveness of the approach. The methodology is applied to estimate the major depression prevalence in Germany on regional levels crossed by sex and age groups.

A new regression model for rates and proportions data with applications

We propose a new continuous distribution in the interval based on the generalized odd log-logistic-G family, whose density function can be symmetrical, asymmetric, unimodal and bimodal. The new model is implemented using the gamlss packages in R. We propose an extended regression based on this distribution which includes as sub-models some important regressions. We employ a frequentist and Bayesian analysis to estimate the parameters and adopt the non-parametric and parametric bootstrap methods to obtain better efficiency of the estimators. Some simulations are conducted to verify the empirical distribution of the maximum likelihood estimators. We compare the empirical distribution of the quantile residuals with the standard normal distribution. The extended regression can give more realistic fits than other regressions in the analysis of proportional data.

An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture‐based clustering

SummaryWe introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto &amp; Hennig, Journal of the American Statistical Association 111, 1648–1659) of a Gaussian mixture model allowing for observations to be classified as ‘noise’, but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statistic Q that measures how close the within‐cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non‐parametric measure allows for non‐Gaussian clusters as long as they have a good quality according to Q. The simplicity of a model is assessed by a measure S that prefers a smaller number of clusters unless additional clusters can reduce the estimated noise proportion substantially. The simplest model is then chosen that is adequate for the data in the sense that its observed value of Q is not significantly larger than what is expected for data truly generated from the fitted model, as can be assessed by parametric bootstrap. The approach is compared with model‐based clustering using the Bayesian information criterion (BIC) and the integrated complete likelihood (ICL) in a simulation study and on two real data sets.

Testing the Equality of Regression Coefficients of Panel Models in Several Groups

The panel data model is used in many areas, such as economics, social sciences, medicine, and epidemiology. In recent decades, inference on regression coefficients has been developed in panel data models. In this paper, methods are introduced to test the equality models of the panel model among the groups in the data set. First, we present a random quantity that we estimate its distribution by two methods of approximation and parametric bootstrap. We also introduce a pivotal quantity for performing this hypothesis test. In a simulation study, we compare our proposed approaches with an available method based on the type I error and test power. We also apply our method to gasoline panel data as a real data set.

Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data

AbstractMallows's Cp and Akaike information criterion (AIC) are common criteria for selecting the dimensionality of regression models, as an alternative to cross‐validation (CV) and nonparametric bootstrap. A key parameter in the calculation of Cp and AIC is the effective number of degrees of freedom of the model, or model complexity (d). Parameter d is generally easy to calculate for linear smoothers, that is, models for which the prediction of the training response y is given by = S y where S is a projector matrix that does not involve y. Nevertheless, d is more difficult to estimate for nonlinear smoothers, such as partial least squares regression (PLSR). In this article, we present two algorithms for estimating d for PLSR based on Monte Carlo simulation methods (parametric bootstrap and perturbation analysis) and with the particular case of high dimensional data. We compare these Monte Carlo methods to three other algorithms already published. We used the d estimates to compute Cp and AIC and select PLSR model dimensionalities that we then compare to CV. Two real and heterogeneous agronomic near infrared (NIR) datasets were considered as examples.

Ell _2-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

Regional prevalence estimation requires the use of suitable statistical methods on epidemiologic data with substantial local detail. Small area estimation with medical treatment records as covariates marks a promising combination for this purpose. However, medical routine data often has strong internal correlation due to diagnosis-related grouping in the records. Depending on the strength of the correlation, the space spanned by the covariates can become rank-deficient. In this case, prevalence estimates suffer from unacceptable uncertainty as the individual contributions of the covariates to the model cannot be identified properly. We propose an area-level logit mixed model for regional prevalence estimation with a new fitting algorithm to solve this problem. We extend the Laplace approximation to the log-likelihood by an ell _2-penalty in order to stabilize the estimation process in the presence of covariate rank-deficiency. Empirical best predictors under the model and a parametric bootstrap for mean squared error estimation are presented. A Monte Carlo simulation study is conducted to evaluate the properties of our methodology in a controlled environment. We further provide an empirical application where the district-level prevalence of multiple sclerosis in Germany is estimated using health insurance records.