A novel parametric predictive bootstrap method

It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval’s performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based bootstrap has approximately $50\%$ probability to yield conditional under-coverage. We then develop a new bootstrap algorithm that generates a prediction interval that asymptotically controls both the conditional coverage probability as well as the possibility of conditional under-coverage. We complement the asymptotic results with several finite-sample simulations.

Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.

In reliability theory, risk analysis, renewal processes and actuarial studies, the residual lifetimes data play an important essential role in studying the conditional tail of the lifetime data. In this paper, based on some observed ordered residual Weibull data, we introduce different prediction methods for obtaining prediction intervals (PIs) of future residual lifetimes including likelihood, Wald, moments, parametric bootstrap, and highest conditional methods. Monte Carlo simulations are performed to compare the performances of the so obtained PIs and one data analysis is performed for illustration purposes.

The breaking strength information of structure components is highly correlated with the safety manufacturing and much concerned by engineers. Components with deficient safety quality will be rejected to rework or discard due to an unsatisfactory level of the lower critical breaking strength percentile. When the breaking strength of components is assumed to have a Burr type-XII distribution, five parametric bootstrap methods are suggested to adjust the bias of the lower confidence limit estimate of the lower percentile with progressive type-II censored samples. The performance of the proposed bootstrap methods is evaluated through an intensive simulation study. Numerical results show that the hybrid bootstrap method and the bias-corrected and accelerated bias-corrected methods perform better with coverage probabilities near the nominal confidence level for almost all the cases considered. An example of the breaking strength data set of aluminum sheets is used for illustration.

We critically review the work that has been done in applying basic, smoothed and parametric bootstrap methods to simulation experiments. We develop a framework to classify bootstrap methods in this context and use it to compare various bootstrap schemes. Most bootstrap methods are hard to analyse theoretically. An exception is the parametric case for which a detailed analysis can be carried out. An interesting result in this case is that, whereas in standard statistical experiments bootstrap samples give only information about the variance of a statistic and not its mean, this turns out not to be so in simulation experiments. Thus parametric bootstrap samples can be advantageously included in estimates of the responses of interest.

There is growing interest in the field of digital soil mapping (DSM) to quantify the underlying uncertainty of point predictions through different probabilistic prediction models. Uncertainty in DSM is often described in the format of a prediction interval (PI). Yet, PIs or uncertainty estimates in general are only of value for end users if they have good quality, i.e. when they are reliable. Reliability refers to the consistency between predicted conditional probabilities and observed frequencies of independent validation data. Ideally, PIs are also sharp, which refers to the concentration of probabilistic information, i.e. the narrowness of conditional probability distributions. The prediction interval coverage probability (PICP) is currently used in DSM to assess the reliability of PIs but it is ignorant to a potential one-sided bias of its bounding quantiles. Therefore, we propose to complement the current validation procedure with new metrics suggested in the broader probabilistic literature. This includes metrics that do not only evaluate uncertainty estimates in PI format but also quantiles or full conditional probability distributions. The newly proposed metrics are the quantile coverage probability (QCP), the probability integral transform (PIT) and so-called proper scoring rules for relative comparisons. Examples of scoring rules are the continuous ranked probability score (CRPS), which can be decomposed into a reliability part (RELI) and the interval score (IS). Sharpness can be evaluated through the prediction interval width (PIW). We illustrated the use of the various metrics in a case-study using soil pH data from The Land Use and Coverage Area Frame Survey (LUCAS). Thereby, uncertainty estimates of five different models were compared: Kriging with external drift (KED), quantile regression forest (QRF), quantile regression post-processing of a random forest (QRPP RF), quantile regression neural network (QRNN) and a reference null-model (NM).  KED, NM and QRPP RF showed very good reliability according to QCP, PICP, PIT and RELI. QRF was slightly pessimistic in the centre and QRNN very overoptimistic at the edges of the conditional probability distributions. Despite this, QRF performed best according to mean CRPS and mean IS because it produced fewer outliers at the edges. As expected, NM had the lowest sharpness, i.e. the largest PIW values. Sharpness of the other models was overall similar but QRNN had sharper predictions at the edges and QRF was less sharp in the centre of the conditional probability distributions. Lastly, we also generated PIW maps to indicate the spatial uncertainty of the five prediction models. The spatial variability of PIW was larger for QRF, QRNN and QRPP RF in comparison to KED. Whereas with NM, PIW was completely uniform. 

An intelligent deep learning based prediction model for wind power generation

A confidence interval is an interval estimate of a parameter of a population calculated from a sample drawn from the population. Bootstrapping method, which involves producing several new data sets that are resampled from the original data in order to estimate parameter for each newly created data set, allowing an empirical distribution for the parameter to be estimated. Since certain statistics are harder to estimate, confidence intervals are rarely employed. Several statistics might necessitate multi-step formulas assuming that are impractical for calculating confidence intervals. This paper reviews research on the concept of bootstrapping and bootstrap confidence interval. The current narrative analysis was developed to answer the main research question: (1) What is the concept of the bootstrap method and bootstrap confidence interval? (2) What are the methods of bootstrapping to obtain confidence interval? This study has found general bootstrap method idea, various techniques of bootstrap methods, its advantages and disadvantages, and its limitations. There are normal interval method, percentile bootstrap method, basic method, first-order normal approximation method, bias-corrected bootstrap, accelerated bias-corrected bootstrap and bootstrap-t method. This study concludes that the advantages of using bootstrap CI is that it does not require any assumptions about the shape of distribution and universality of the approach. Bootstrapping is a computer-intensive statistical technique that relies significantly on modern high-speed digital computers to do massive computations.

Measurement uncertainty for < 905 > Uniformity of Dosage Units tests using Monte Carlo and bootstrapping methods – Uncertainties arising from sampling and analytical steps

A short-term wind speed interval prediction method based on WRF simulation and multivariate line regression for deep learning algorithms

The high customer requirements for appropriate product quality pose a challenge for manufacturers and suppliers and also cause them many problems related to ensuring a sufficiently high product quality throughout the entire production cycle. For the above reasons, it is so important to assess the capability of monitored processes, and shaping, analyzing and controlling the capability of processes is an important aspect of managing an organization that uses a process approach to management. The use of an appropriate method to analyze the course of production processes is a necessity imposed by quality standards, e.g., ISO 9001: 2015. That is why it is so important to propose a quick and low-cost method of assessing production processes. For this purpose, a method of assessing the capability of the manufacturing process using bootstrap analysis was used. The article presents the analysis of inherent properties of the production process based on the results of measurements of the characteristic features of the process or the characteristics of the manufactured products (process variables) for the shafts with grooves. The main goals of the work are to develop a procedure for determining process capability based on the bootstrap method, including criteria for the classification of production process capability; to develop the criterion values for confidence intervals of production process capability; as well as to demonstrate the practical application of bootstrap analysis in manufacturing. Moreover, comparative analyses of process capabilities using bootstrap and classic methods were carried out. They confirm both the narrowing of the confidence interval when using the bootstrap method and the possibility of determining a better estimator of the lower limit of this range compared to the results obtained using the classic method. The tests carried out for the unit production of shafts with grooves showed that the analysis of the process capability for measuring tests n = 10 is possible. Finally, new criterion values for the assessment of process capability for the bootstrap method were proposed. The model for assessing the capability of production processes presented in the paper was implemented in low-volume production in the defense industry.

PurposeConfidence intervals play a crucial role in economics and finance, providing a credible range of values for an unknown parameter along with a corresponding level of certainty. Their applications encompass economic forecasting, market research, financial forecasting, econometric analysis, policy analysis, financial reporting, investment decision-making, credit risk assessment and consumer confidence surveys. Signal-to-noise ratio (SNR) finds applications in economics and finance across various domains such as economic forecasting, financial modeling, market analysis and risk assessment. A high SNR indicates a robust and dependable signal, simplifying the process of making well-informed decisions. On the other hand, a low SNR indicates a weak signal that could be obscured by noise, so decision-making procedures need to take this into serious consideration. This research focuses on the development of confidence intervals for functions derived from the SNR and explores their application in the fields of economics and finance.Design/methodology/approachThe construction of the confidence intervals involved the application of various methodologies. For the SNR, confidence intervals were formed using the generalized confidence interval (GCI), large sample and Bayesian approaches. The difference between SNRs was estimated through the GCI, large sample, method of variance estimates recovery (MOVER), parametric bootstrap and Bayesian approaches. Additionally, confidence intervals for the common SNR were constructed using the GCI, adjusted MOVER, computational and Bayesian approaches. The performance of these confidence intervals was assessed using coverage probability and average length, evaluated through Monte Carlo simulation.FindingsThe GCI approach demonstrated superior performance over other approaches in terms of both coverage probability and average length for the SNR and the difference between SNRs. Hence, employing the GCI approach is advised for constructing confidence intervals for these parameters. As for the common SNR, the Bayesian approach exhibited the shortest average length. Consequently, the Bayesian approach is recommended for constructing confidence intervals for the common SNR.Originality/valueThis research presents confidence intervals for functions of the SNR to assess SNR estimation in the fields of economics and finance.

Fragility analysis and probabilistic performance evaluation of nuclear containment structure subjected to internal pressure

Recent molecular studies have incorporated the parametric bootstrap method to test a priori hypotheses when the results of molecular based phylogenies are in conflict with these hypotheses. The parametric bootstrap requires the specification of a particular substitutional model, the parameters of which will be used to generate simulated, replicate DNA sequence data sets. It has been both suggested that, (a) the method appears robust to changes in the model of evolution, and alternatively that, (b) as realistic model of DNA substitution as possible should be used to avoid false rejection of a null hypothesis. Here we empirically evaluate the effect of suboptimal substitution models when testing hypotheses of monophyly with the parametric bootstrap using data sets of mtDNA cytochrome oxidase I and II (COI and COII) sequences for Macaronesian Calathus beetles, and mitochondrial 16S rDNA and nuclear ITS2 sequences for European Timarcha beetles. Whether a particular hypothesis of monophyly is rejected or accepted appears to be highly dependent on whether the nucleotide substitution model being used is optimal. It appears that a parameter rich model is either equally or less likely to reject a hypothesis of monophyly where the optimal model is unknown. A comparison of the performance of the Kishino–Hasegawa (KH) test shows it is not as severely affected by the use of suboptimal models, and overall it appears to be a less conservative method with a higher rate of failure to reject null hypotheses.

It is good scientific practice to the report an appropriate estimate of effect size and a confidence interval (CI) to indicate the precision with which a population effect was estimated. For comparisons of 2 independent groups, a probability-based effect size estimator (A) that is equal to the area under a receiver operating characteristic curve and closely related to the popular Wilcoxon-Mann-Whitney nonparametric statistical tests has many appealing properties (e.g., easy to understand, robust to violations of parametric assumptions, insensitive to outliers). We performed a simulation study to compare 9 analytic and 3 empirical (bootstrap) methods for constructing a CI for A that can yield very different CIs for the same data. The experimental design crossed 6 factors to yield a total of 324 cells representing challenging but realistic data conditions. Results were examined using several criteria, with emphasis placed on the extent to which observed CI coverage probabilities approximated nominal levels. Based on the simulation study results, the bias-corrected and accelerated bootstrap method is recommended for constructing a CI for the A statistic; bootstrap methods also provided the least biased and most accurate standard error of A. An empirical illustration examining score differences on a citation-based index of scholarly impact across faculty at low-ranked versus high-ranked research universities underscores the importance of choosing an appropriate CI method.