Bayesian Prediction Method Research Articles

A Bayesian Deep Learning-Based Adaptive Wind Farm Power Prediction Method Within the Entire Life Cycle

A Bayesian Deep Learning-Based Adaptive Wind Farm Power Prediction Method Within the Entire Life Cycle

Implementation of Adaptive-Bayesian DStoch technique for obtaining winds from MST radar covering higher altitudes

It is challenging to estimate winds accurately from higher altitudes using VHF-MST radar. The current study introduces the Adaptive-Bayesian Deterministic Stochastics Technique (ADStoch), which implements an Empirical Bayesian 1D prediction method using stochastics to analyze radar signals. A new and robust estimator for empirical wavelet shrinkage with Gaussian prior of the nonzero mean for wavelet coefficients is presented, which makes the current prior different from other priors. The mean parameters and the prior covariance hyperparameters follow a pseudo maximum likelihood method for computation. Details on the implemented algorithm developed from scratch using C# are also presented. This technique outperforms contemporary techniques discussed in this context that can recover signals buried in noise established based on the analysis of moment and quality. The estimated Wind is cross-validated for accuracy with the observed wind from the GPS radiosonde operated simultaneously. This technique can consistently extract 3D wind that can reach the range of 25.5 km–28.2 km, improving the conventional maximum altitude of 21.2 km in real time for the MST radar. It is concluded that the ADStoch analysis technique can effectively obtain VHF-MST radar signals at significantly higher altitudes, which is helpful in various scientific investigations.

BASIC: A Bayesian adaptive synthetic-control design for phase II clinical trials.

Randomized controlled trials are considered the gold standard for evaluating experimental treatments but often require large sample sizes. Single-arm trials require smaller sample sizes but are subject to bias when using historical control data for comparative inferences. This article presents a Bayesian adaptive synthetic-control design that exploits historical control data to create a hybrid of a single-arm trial and a randomized controlled trial. The Bayesian adaptive synthetic control design has two stages. In stage 1, a prespecified number of patients are enrolled in a single arm given the experimental treatment. Based on the stage 1 data, applying propensity score matching and Bayesian posterior prediction methods, the usefulness of the historical control data for identifying a pseudo sample of matched synthetic-control patients for making comparative inferences is evaluated. If a sufficient number of synthetic controls can be identified, the single-arm trial is continued. If not, the trial is switched to a randomized controlled trial. The performance of The Bayesian adaptive synthetic control design is evaluated by computer simulation. The Bayesian adaptive synthetic control design achieves power and unbiasedness similar to a randomized controlled trial but on average requires a much smaller sample size, provided that the historical control data patients are sufficiently comparable to the trial patients so that a good number of matched controls can be identified in the historical control data. Compared to a single-arm trial, The Bayesian adaptive synthetic control design yields much higher power and much smaller bias. The Bayesian adaptive synthetic-control design provides a useful tool for exploiting historical control data to improve the efficiency of single-arm phase II clinical trials, while addressing the problem of bias when comparing trial results to historical control data. The proposed design achieves power similar to a randomized controlled trial but may require a substantially smaller sample size.

Medium Term Streamflow Prediction Based on Bayesian Model Averaging Using Multiple Machine Learning Models

Medium-term hydrological streamflow forecasting can guide water dispatching departments to arrange the discharge and output plan of hydropower stations in advance, which is of great significance for improving the utilization of hydropower energy and has been a research hotspot in the field of hydrology. However, the distribution of water resources is uneven in time and space. It is important to predict streamflow in advance for the rational use of water resources. In this study, a Bayesian model average integrated prediction method is proposed, which combines artificial intelligence algorithms, including long-and short-term memory neural network (LSTM), gate recurrent unit neural network (GRU), recurrent neural network (RNN), back propagation (BP) neural network, multiple linear regression (MLR), random forest regression (RFR), AdaBoost regression (ABR) and support vector regression (SVR). In particular, the simulated annealing (SA) algorithm is used to optimize the hyperparameters of the model. The practical application of the proposed model in the ten-day scale inflow prediction of the Three Gorges Reservoir shows that the proposed model has good prediction performance; the Nash–Sutcliffe efficiency NSE is 0.876, and the correlation coefficient r is 0.936, which proves the accuracy of the model.

Improving building occupant comfort through a digital twin approach: A Bayesian network model and predictive maintenance method

This study introduces a Bayesian network model to evaluate the comfort levels of occupants of two non-residential Norwegian buildings based on data collected from satisfaction surveys and building performance parameters. A Digital Twin approach is proposed to integrate building information modeling (BIM) with real-time sensor data, occupant feedback, and a probabilistic model of occupant comfort to detect and predict HVAC issues that may impact comfort. The study also uses 200000 points as historical data of various sensors to understand the previous building systems’ behavior. The study also presents new methods for using BIM as a visualization platform and for predictive maintenance to identify and address problems in the HVAC system. For predictive maintenance, nine machine learning algorithms were evaluated using metrics such as ROC, accuracy, F1-score, precision, and recall, where Extreme Gradient Boosting (XGB) was the best algorithm for prediction. XGB is on average 2.5% more accurate than Multi-Layer Perceptron (MLP), and up to 5% more accurate than the other models. Random Forest is around 96% faster than XGBoost while being relatively easier to implement. The paper introduces a novel method that utilizes several standards to determine the remaining useful life of HVAC, leading to a potential increase in its lifetime by at least 10% and resulting in significant cost savings. The result shows that the most important factors that affect occupant comfort are poor air quality, lack of natural light, and uncomfortable temperature. To address the challenge of applying these methods to a wide range of buildings, the study proposes a framework using ontology graphs to integrate data from different systems, including FM, CMMS, BMS, and BIM. This study’s results provide insight into the factors that influence occupant comfort, help to expedite identifying equipment malfunctions and point towards potential solutions, leading to more sustainable and energy-efficient buildings.

Estimating parameters from the generalized inverse Lindley distribution under hybrid censoring scheme

Estimation of parameters of the generalized inverse Lindley (GIL) distribution is considered under a hybrid censoring scheme. The point estimators, such as the maximum likelihood estimators using the Expectation-Maximization (E-M) algorithm, have been derived. The two approximate Bayes estimators using Tierney and Kadane’s method and Gibbs sampling procedure, using the gamma prior and the general entropy loss (GEL) function, have been obtained. Several confidence intervals are proposed, such as the asymptotic confidence intervals (ACIs), bootstrap confidence intervals, and the highest posterior density (HPD) credible intervals. The prediction for future observations has been considered under one and two-sample Bayesian prediction methods using the type-i hybrid censoring scheme. An extensive simulation study has been conducted to numerically evaluate all the estimators’ performances. The point estimators are compared through their biases and mean squared errors (MSEs). The performances of confidence intervals are evaluated using coverage probability (CP), average length (AL), and probability coverage density (PCD). Two real-life datasets have been considered for illustrative purposes.

Combining canopy reflectance spectrometry and genome-wide prediction to increase response to selection for powdery mildew resistance in cultivated strawberry.

High-throughput phenotyping is an emerging approach in plant science, but thus far only a few applications have been made in horticultural crop breeding. Remote sensing of leaf or canopy spectral reflectance can help breeders rapidly measure traits, increase selection accuracy, and thereby improve response to selection. In the present study, we evaluated the integration of spectral analysis of canopy reflectance and genomic information for the prediction of strawberry (Fragaria × ananassa) powdery mildew disease. Two multi-parental breeding populations of strawberry comprising a total of 340 and 464 pedigree-connected seedlings were evaluated in two separate seasons. A single-trait Bayesian prediction method using 1001 spectral wavebands in the ultraviolet-visible-near infrared region (350-1350 nm wavelength) combined with 8552 single nucleotide polymorphism markers showed up to 2-fold increase in predictive ability over models using markers alone. The integration of high-throughput phenotyping was further validated independently across years/trials with improved response to selection of up to 90%. We also conducted Bayesian multi-trait analysis using the estimated vegetative indices as secondary traits. Three vegetative indices (Datt3, REP_Li, and Vogelmann2) had high genetic correlations (rA) with powdery mildew visual ratings with average rA values of 0.76, 0.71, and 0.71, respectively. Increasing training population sizes by incorporating individuals with only vegetative index information yielded substantial increases in predictive ability. These results strongly indicate the use of vegetative indices as secondary traits for indirect selection. Overall, combining spectrometry and genome-wide prediction improved selection accuracy and response to selection for powdery mildew resistance, demonstrating the power of an integrated phenomics-genomics approach in strawberry breeding.

Holistic Process Models: A Bayesian Predictive Ensemble Method for Single and Coupled Unit Operation Models

The coupling of individual models in terms of end-to-end calculations for unit operations in manufacturing processes is a challenging task. We present a probability distribution-based approach for the combined outcomes of parametric and non-parametric models. With this so-called Bayesian predictive ensemble, the statistical moments such as mean value and standard deviation can be accurately computed without any further approximation. It is shown that the ensemble of different model predictions leads to an uninformed prior distribution, which can be transformed into a predictive posterior distribution using Bayesian inference and numerical Markov Chain Monte Carlo calculations. We demonstrate the advantages of our method using several numerical examples. Our approach is not restricted to certain unit operations, and can also be used for the more robust interpretation and assessment of model predictions in general.

Using BayesModelS to provide Bayesian- and phylogenetically-informed primate body mass predictions

An accurate prediction of the body mass of an extinct species can greatly inform the reconstruction of that species' ecology. Therefore, paleontologists frequently predict the body mass of extinct taxa from fossilized materials, particularly dental dimensions. Body mass prediction has traditionally been performed in a frequentist statistical framework, and accounting for phylogenetic relationships while calibrating prediction models has only recently become more commonplace. In this article, we apply BayesModelS—a phylogenetically informed Bayesian prediction method—to predict body mass in a sample of 49 euarchontan species (24 strepsirrhines, 20 platyrrhines, 3 tarsiids, 1 dermopteran, and 1 scandentian) and compare this approach's body mass prediction accuracy with other commonly used techniques, namely ordinary least squares, phylogenetic generalized least squares, and phylogenetic independent contrasts (PICs). When predicting the body masses of extant euarchontans from dental and postcranial variables, BayesModelS and PICs have substantially higher predictive accuracy than ordinary least squares and phylogenetic generalized least squares. The improved performances of BayesModelS and PIC are most evident for dentally derived body mass proxies or when body mass proxies have high degrees of phylogenetic covariance. Predicted values generated by BayesModelS and PIC methods also show less variance across body mass proxies when applied to the Eocene adapiform Notharctus tenebrosus. These more explicitly phylogenetically based methods should prove useful for predicting body mass in a paleontological context, and we provide executive scripts for both BayesModelS and PIC to increase ease of application.

Estimation and prediction for a new Pareto-type distribution under progressive type-II censoring

In this paper, we consider the problems of estimating the unknown parameters as well as predicting the failure times of the removed units in multiple stages of the progressively censored sample coming from a new Pareto-type distribution. First, maximum likelihood, least squares and Bayesian methods (Lindley’s approximation and Markov chain Monte Carlo) are applied for estimating the parameters involved in this model. For predicting the failure times of the removed units, different prediction methods including maximum likelihood, best unbiased, conditional median and Bayesian prediction methods are adopted. We also develop prediction intervals of future lifetimes using pivot and highest conditional density methods. Comprehensive Monte Carlo simulations are performed to assess the performance of the estimation methods as well as prediction methods. Finally, analysis of a real data set representing the duration of remission of leukemia patients who were treated by a specific drug is performed for illustration purposes.

Short-term Traffic Flow Prediction Method in Bayesian Networks Based on Quantile Regression

With the popularization of intelligent transportation system and Internet of vehicles, the traffic flow data on the urban road network can be more easily obtained in large quantities. This provides data support for shortterm traffic flow prediction based on real-time data. Of all the challenges and difficulties faced in the research of short-term traffic flow prediction, this paper intends to address two: one is the difficulty of short-term traffic flow prediction caused by spatiotemporal correlation of traffic flow changes between upstream and downstream intersections; the other is the influence of deviation of traffic flow caused by abnormal conditions on short-term traffic flow prediction. This paper proposes a Bayesian network short-term traffic flow prediction method based on quantile regression. By this method the trouble caused by spatiotemporal correlation of traffic flow prediction could be effectively and efficiently solved. At the same time, the prediction of traffic flow change under abnormal conditions has higher accuracy.

A simple, cost-effective high-throughput image analysis pipeline improves genomic prediction accuracy for days to maturity in wheat

BackgroundHigh-throughput phenotyping and genomic selection accelerate genetic gain in breeding programs by advances in phenotyping and genotyping methods. This study developed a simple, cost-effective high-throughput image analysis pipeline to quantify digital images taken in a panel of 286 Iran bread wheat accessions under terminal drought stress and well-watered conditions. The color proportion of green to yellow (tolerance ratio) and the color proportion of yellow to green (stress ratio) was assessed for each canopy using the pipeline. The estimated tolerance and stress ratios were used as covariates in the genomic prediction models to evaluate the effect of change in canopy color on the improvement of the genomic prediction accuracy of different agronomic traits in wheat.ResultsThe reliability of the high-throughput image analysis pipeline was proved by three to four times of improvement in the accuracy of genomic predictions for days to maturity with the use of tolerance and stress ratios as covariates in the univariate genomic selection models. The higher prediction accuracies were attained for days to maturity when both tolerance and stress ratios were used as fixed effects in the univariate models. The results of this study indicated that the Bayesian ridge regression and ridge regression-best linear unbiased prediction methods were superior to other genomic prediction methods which were used in this study under terminal drought stress and well-watered conditions, respectively.ConclusionsThis study provided a robust, quick, and cost-effective machine learning-enabled image-phenotyping pipeline to improve the genomic prediction accuracy for days to maturity in wheat. The results encouraged the integration of phenomics and genomics in breeding programs.

E- Bayesian Estimation of System Reliability (Series, Parallel) and Failure Rate Functions with Kumaraswamy Distribution based on Type II Censoring Data

In this paper, the failure rate function and the shape parameter for the kumaraswamy distribution and reliability function of a system with a number (m) of independent compounds associated with a system (serial, parallel) were estimated, by relying on observational data of the second type, knowing that the survival time of the compounds are independent. Based on the findings the graphical predictor of the failure rate and parameter - and the reliability function of the serial and parallel system is smaller than the Standard Bayesian estimator (MLE) in simulation and real data. Thus, a decreasing in AMPE with an increase in the sample size n and an increase in the size of the failure sample r as the physical prediction capabilities have a high efficiency. The using of the Bayesian prediction method to estimate the reliability of different production systems for other failure distributions such as the Burr family distributions and various other failure distributions. Based on the output he results are reasonably consistent with simulation and real data. The E-Bayesian method was used for estimating with three primary distribution functions for the above parameters and comparing them with the standard Bayesian method with a squared loss function and the maximum likelihood method where simulation experiments were employed to compare the estimation results and the results showed the advantage of the E-Bayesian method in estimating through comparison statistics (MAPE).

How to Estimate Optimal Malaria Readiness Indicators at Health-District Level: Findings from the Burkina Faso Service Availability and Readiness Assessment (SARA) Data.

One of the major contributors of malaria-related deaths in Sub-Saharan African countries is the limited accessibility to quality care. In these countries, malaria control activities are implemented at the health-district level (operational entity of the national health system), while malaria readiness indicators are regionally representative. This study provides an approach for estimating health district-level malaria readiness indicators from survey data designed to provide regionally representative estimates. A binomial-hierarchical Bayesian spatial prediction method was applied to Burkina Faso Service Availability and Readiness Assessment (SARA) survey data to provide estimates of essential equipment availability and readiness for malaria care. Predicted values of each indicator were adjusted by the type of health facility, location, and population density. Then, a health district composite readiness profile was built via hierarchical ascendant classification. All surveyed health-facilities were mandated by the Ministry of Health to manage malaria cases. The spatial distribution of essential equipment and malaria readiness was heterogeneous. Around 62.9% of health districts had a high level of readiness to provide malaria care and prevention during pregnancy. Low-performance scores for managing malaria cases were found in big cities. Health districts with low coverage for both first-line antimalarial drugs and rapid diagnostic tests were Baskuy, Bogodogo, Boulmiougou, Nongr-Massoum, Sig-Nonghin, Dafra, and Do. We provide health district estimates and reveal gaps in basic equipment and malaria management resources in some districts that need to be filled. By providing local-scale estimates, this approach could be replicated for other types of indicators to inform decision makers and health program managers and to identify priority areas.

Bayesian model based on Markov chain Monte Carlo for identifying mine water sources in Submarine Gold Mining

Based on the Bayesian theory, the Bayesian water source discrimination model and model prediction method were established by using the adaptive differential evolution Metropolis algorithm of Markov chain Monte Carlo simulation as the parameter posterior distribution sampling calculation method. Taking the mine water samples of Sanshandao Gold Mine as an example, according to the chemical composition analysis of the water samples from different monitoring points, six indexes of Mg2+, Na+ + K+, Ca2+, SO42−, Cl− and HCO3− were selected as the discrimination factors. According to the water characteristics of each aquifer and the actual needs of discrimination, the water inrush sources in the mining area were divided into four categories: sea water is class I, Quaternary pore water is class II, bedrock fissure water is class III, and fresh water is class IV. Taking 40 typical water inrush samples as training samples, using SPSS statistics and Bayes method based on Markov Chain Monte Carlo to build Bayes discriminant analysis model, the posterior distribution of algorithm estimation based on water sample information was obtained, and the analysis method of mine water damage source was obtained. The results showed that the Bayes discriminant model based on Markov Chain Monte Carlo has high accuracy, good applicability and discriminant ability, and has certain guiding significance for the prevention and control of water damage and the related field work.

Bayesian Inference of Finite Population Quantiles for Skewed Survey Data Using Skew-Normal Penalized Spline Regression.

Skewed data are common in sample surveys. In probability proportional to size sampling, we propose two Bayesian model-based predictive methods for estimating finite population quantiles with skewed sample survey data. We assume the survey outcome to follow a skew-normal distribution given the probability of selection and model the location and scale parameters of the skew-normal distribution as functions of the probability of selection. To allow a flexible association between the survey outcome and the probability of selection, the first method models the location parameter with a penalized spline and the scale parameter with a polynomial function, while the second method models both the location and scale parameters with penalized splines. Using a fully Bayesian approach, we obtain the posterior predictive distributions of the nonsampled units in the population and thus the posterior distributions of the finite population quantiles. We show through simulations that our proposed methods are more efficient and yield shorter credible intervals with better coverage rates than the conventional weighted method in estimating finite population quantiles. We demonstrate the application of our proposed methods using data from the 2013 National Drug Abuse Treatment System Survey.

The Move toward Biopharma 4.0

Genetic Engineering & Biotechnology NewsVol. 39, No. 6 Bioprocessing TutorialThe Move toward Biopharma 4.0Insilico Biotechnology develops “smart” processes that benefit biomanufacturing through Digital TwinsShilpa Nargund, PhD, Kathrin Guenther, PhD, and Klaus MauchShilpa Nargund, PhDShilpa Nargund, PhD, is a Data Scientist & Business Development ManagerSearch for more papers by this author, Kathrin Guenther, PhDKathrin Guenther, PhD, is a Sr. Business Development ManagerSearch for more papers by this author, and Klaus MauchKlaus Mauch E-mail Address: (klaus.mauch@insilico-biotechnology.com) is the CEO & CTO at Insilico Biotechnology. Website: www.insilico-biotechnology.comSearch for more papers by this authorPublished Online:29 May 2019https://doi.org/10.1089/gen.39.06.18AboutSectionsView articleView Full TextPDF/EPUB Permissions & CitationsPermissionsDownload CitationsTrack CitationsAdd to favorites Back To Publication ShareShare onFacebookTwitterLinked InRedditEmail View articleFiguresReferencesRelatedDetailsCited byContinuous integrated manufacturing for biopharmaceuticals: A new paradigm or an empty promise?28 September 2022 | Biotechnology and Bioengineering, Vol. 120, No. 2Exploring the potential of machine learning for more efficient development and production of biopharmaceuticals11 August 2022 | Biotechnology Progress, Vol. 38, No. 6Arduino Soft Sensor for Monitoring Schizochytrium sp. Fermentation, a Proof of Concept for the Industrial Application of Genome-Scale Metabolic Models in the Context of Pharma 4.029 October 2022 | Processes, Vol. 10, No. 11Architectural and Technological Improvements to Integrated Bioprocess Models towards Real-Time Applications9 October 2022 | Bioengineering, Vol. 9, No. 10Artificial intelligence and machine learning applications in biopharmaceutical manufacturingTrends in Biotechnology, Vol. 349AI-ML applications in bioprocessing: ML as an enabler of real time quality prediction in continuous manufacturing of mAbsComputers & Chemical Engineering, Vol. 164Holistic Process Models: A Bayesian Predictive Ensemble Method for Single and Coupled Unit Operation Models29 March 2022 | Processes, Vol. 10, No. 4Modeling and optimization of bioreactor processesReprint of: Basic considerations for a digital twin of biointelligent systems: Applying technical design patterns to biological systemsCIRP Journal of Manufacturing Science and Technology, Vol. 34Computational Efforts for the Development and Scale-up of Antibody-Producing Cell Culture Processes1 January 2022Continuous downstream bioprocessing for intensified manufacture of biopharmaceuticals and antibodiesChemical Engineering ScienceBasic considerations for a digital twin of biointelligent systems: Applying technical design patterns to biological systemsCIRP Journal of Manufacturing Science and Technology, Vol. 31Digitalization in microbiology – Paving the path to sustainable circular bioeconomyNew Biotechnology, Vol. 59ChromaTech: A discontinuous Galerkin spectral element simulator for preparative liquid chromatographyComputers & Chemical Engineering, Vol. 141Digital Twins and Their Role in Model-Assisted Design of Experiments15 August 2020The Kalman Filter for the Supervision of Cultivation Processes11 November 2020History and Evolution of Modeling in Biotechnology: Modeling & Simulation, Application and Hardware PerformanceComputational and Structural Biotechnology Journal, Vol. 18The Rocky Road From Fed-Batch to Continuous Processing With E. coli20 November 2019 | Frontiers in Bioengineering and Biotechnology, Vol. 7 Volume 39Issue 6Jun 2019 InformationCopyright © by GEN PublishingTo cite this article:Shilpa Nargund, PhD, Kathrin Guenther, PhD, and Klaus Mauch.The Move toward Biopharma 4.0.Genetic Engineering & Biotechnology News.Jun 2019.53-55.http://doi.org/10.1089/gen.39.06.18Published in Volume: 39 Issue 6: May 29, 2019PDF download

Bayesian personalized treatment selection strategies that integrate predictive with prognostic determinants.

The evolution of "informatics" technologies has the potential to generate massive databases, but the extent to which personalized medicine may be effectuated depends on the extent to which these rich databases may be utilized to advance understanding of the disease molecular profiles and ultimately integrated for treatment selection, necessitating robust methodology for dimension reduction. Yet, statistical methods proposed to address challenges arising with the high-dimensionality of omics-type data predominately rely on linear models and emphasize associations deriving from prognostic biomarkers. Existing methods are often limited for discovering predictive biomarkers that interact with treatment and fail to elucidate the predictive power of their resultant selection rules. In this article, we present a Bayesian predictive method for personalized treatment selection that is devised to integrate both the treatment predictive and disease prognostic characteristics of a particular patient's disease. The method appropriately characterizes the structural constraints inherent to prognostic and predictive biomarkers, and hence properly utilizes these complementary sources of information for treatment selection. The methodology is illustrated through a case study of lower grade glioma. Theoretical considerations are explored to demonstrate the manner in which treatment selection is impacted by prognostic features. Additionally, simulations based on an actual leukemia study are provided to ascertain the method's performance with respect to selection rules derived from competingmethods.

Simple Approach to Calculate Random Effects Model Tolerance Intervals to Set Release and Shelf-Life Specification Limits of Pharmaceutical Products.

Tolerance intervals are used to statistically derive the acceptance limits to which drugs must conform upon manufacture (release) and throughout shelf-life. The single measurement per lot in release data and repeated measurements per lot longitudinally for stability data have to be considered in the calculation. Methods for the one-way random effects model by Hoffman and Kringle (HK) for two-sided intervals and Hoffman (H) for one-sided limits are extended to a random-intercept, fixed-slope model in this paper. The performance of HK and H was evaluated via simulation by varying the following factors: (a) magnitude of stability trend over time, (b) sample size, (c) percentage of lot-to-lot contribution to total variation, (d) targeted proportion, and (e) data inclusion. The performance metrics are average width (for two-sided) or average limit (for one-sided) and attained confidence level. HK and H maintained nominal confidence levels as originally developed, but H is too conservative (i.e., achieved confidence level exceeds the nominal level) in some situations. The HK method adapted for an attribute that changes over time performed comparably to the more computationally intensive generalized pivotal quantity and Bayesian posterior predictive methods. Mathematical formulas and example calculations as implemented using R statistical software functions are provided to assist practitioners in implementing the methods. The calculations for the proposed approach can also be easily performed in a spreadsheet given basic regression output from a statistical software package. Microsoft Excel spreadsheets are available from the authors upon request.LAY ABSTRACT: Tolerance intervals (a measure of what can be expected from the manufacturing process) calculated from attribute measurements of drug product lots are one of the factors considered when establishing acceptance limits to ensure drug product quality. The methods often used to calculate tolerance intervals when there are multiple measurements per lot and the attribute changes over time are either lacking in statistical rigor or statistically rigorous but computationally intensive to implement. The latter type requires simulations that have to be programmed using specialized statistical software, because closed-form mathematical formulas are not available. As a consequence, some quality practitioners and applied statisticians involved in setting acceptance limits may be hindered in using such computationally intensive methods. This paper aims to address this need by proposing an approach that is statistically rigorous yet simple enough to implement using spreadsheets. The approach builds upon previously published works developed for attributes that do not change over time and adapts the cited works for attributes that change over time. The proposed approach is demonstrated to have good statistical properties and compares favorably against the more computationally intensive alternative methods. The paper provides closed-form mathematical formulas, example data, and illustrative calculations as implemented in programmed R functions to facilitate implementation by practitioners. Alternatively, the calculations can be performed without requiring complex programming/simulation using Microsoft Excel spreadsheets that can be requested from the authors.

Vulnerability Characteristic Analysis of Urban Group Buildings Based on the Learning and Reasoning of Bayesian Network

This paper takes the building in Huizhou district of Guangdong Province as the research object, selecting the building with typical destructive features as samples. First of all, through the comparative analysis of seismic hazard factors of the sample building such as building structure types, building floors and years of construction after structure stress research, Bayesian network of structural vulnerability characteristics analysis of buildings based on Python is constructed and then the fitting prediction is performed. The method solves errors caused by the correlation of the index in the traditional prediction process, combines the prior information and the distribution characteristics of the training samples effectively. Finally, the method is verified via typical characteristic data of Huizhou and it compares with traditional Bayesian earthquake prediction methods, proving the advantages and reliability of the method. Use GIS to image related data.