A Family of Bayesian Estimators for the Two-Parametric Burr Type II Distribution

This study discusses the posterior estimation for the parameters of the Burr type II distribution (BIID). The informative and noninformative priors along with different loss functions have also been assumed for the posterior estimation. The applicability of the proposed distribution has also been discussed. The modeling capability of the proposed model has been compared with seven classes of the lifetime distributions using real data. The generalizations of Weibull, exponential, Rayleigh, gamma, log normal, Pareto, Maxwell, Levy, Laplace, inverse gamma, Gompertz, chi-square, inverse chi-square, half normal, and log-logistic distributions have been considered for the comparison. The comparison has been made based on different goodness-of-fit criteria, such as Akaike information criteria (AIC), Bayesian information criteria (BIC), and Kolmogorov-Smirnov (KS) test. Based on the results from the study, it can be suggested that the BIID can efficiently replace commonly used lifetime distributions and their modifications. The results under this model were comparable with different conventional/modified distributions having up to six parameters.

Baseline Energy Use Modeling and Characterization in Tertiary Buildings Using an Interpretable Bayesian Linear Regression Methodology

Interpretable and scalable data-driven methodologies providing high granularity baseline predictions of energy use in buildings are essential for the accurate measurement and verification of energy renovation projects and have the potential of unlocking considerable investments in energy efficiency worldwide. Bayesian methodologies have been demonstrated to hold great potential for energy baseline modelling, by providing richer and more valuable information using intuitive mathematics. This paper proposes a Bayesian linear regression methodology for hourly baseline energy consumption predictions in commercial buildings. The methodology also enables a detailed characterization of the analyzed buildings through the detection of typical electricity usage profiles and the estimation of the weather dependence. The effects of different Bayesian model specifications were tested, including the use of different prior distributions, predictor variables, posterior estimation techniques, and the implementation of multilevel regression. The approach was tested on an open dataset containing two years of electricity meter readings at an hourly frequency for 1578 non-residential buildings. The best performing model specifications were identified, among the ones tested. The results show that the methodology developed is able to provide accurate high granularity baseline predictions, while also being intuitive and explainable. The building consumption characterization provides actionable information that can be used by energy managers to improve the performance of the analyzed facilities.

Parameter Optimization of the 3PG Model Based on Sensitivity Analysis and a Bayesian Method

Sensitivity analysis and parameter optimization of stand models can improve their efficiency and accuracy, and increase their applicability. In this study, the sensitivity analysis, screening, and optimization of 63 model parameters of the Physiological Principles in Predicting Growth (3PG) model were performed by combining a sensitivity analysis method and the Markov chain Monte Carlo (MCMC) method of Bayesian posterior estimation theory. Additionally, a nine-year observational dataset of Chinese fir trees felled in the Shunchang Forest Farm, Nanping, was used to analyze, screen, and optimize the 63 model parameters of the 3PG model. The results showed the following: (1) The parameters that are most sensitive to stand stocking and diameter at breast height (DBH) are nWs(power in stem mass vs. diameter relationship), aWs(constant in stem mass vs. diameter relationship), alphaCx(maximum canopy quantum efficiency), k(extinction coefficient for PAR absorption by canopy), pRx(maximum fraction of NPP to roots), pRn(minimum fraction of NPP to roots), and CoeffCond(defines stomatal response to VPD); (2) MCMC can be used to optimize the parameters of the 3PG model, in which the posterior probability distributions of nWs, aWs, alphaCx, pRx, pRn, and CoeffCond conform to approximately normal or skewed distributions, and the peak value is prominent; and (3) compared with the accuracy before sensitivity analysis and a Bayesian method, the biomass simulation accuracy of the stand model was increased by 13.92%, and all indicators show that the accuracy of the improved model is superior. This method can be used to calibrate the parameters and analyze the uncertainty of multi-parameter complex stand growth models, which are important for the improvement of parameter estimation and simulation accuracy.

Fast effect size shrinkage software for beta-binomial models of allelic imbalance

Allelic imbalance occurs when the two alleles of a gene are differentially expressed within a diploid organism and can indicate important differences in cis-regulation and epigenetic state across the two chromosomes. Because of this, the ability to accurately quantify the proportion at which each allele of a gene is expressed is of great interest to researchers. This becomes challenging in the presence of small read counts and/or sample sizes, which can cause estimators for allelic expression proportions to have high variance. Investigators have traditionally dealt with this problem by filtering out genes with small counts and samples. However, this may inadvertently remove important genes that have truly large allelic imbalances. Another option is to use pseudocounts or Bayesian estimators to reduce the variance. To this end, we evaluated the accuracy of four different estimators, the latter two of which are Bayesian shrinkage estimators: maximum likelihood, adding a pseudocount to each allele, approximate posterior estimation of GLM coefficients (apeglm) and adaptive shrinkage (ash). We also wrote C++ code to quickly calculate ML and apeglm estimates and integrated it into the apeglm package. The four methods were evaluated on two simulations and one real data set. Apeglm consistently performed better than ML according to a variety of criteria, and generally outperformed use of pseudocounts as well. Ash also performed better than ML in one of the simulations, but in the other performance was more mixed. Finally, when compared to five other packages that also fit beta-binomial models, the apeglm package was substantially faster and more numerically reliable, making our package useful for quick and reliable analyses of allelic imbalance. Apeglm is available as an R/Bioconductor package at http://bioconductor.org/packages/apeglm.

Energy-efficient capture of stochastic events based on on-line scheduling scheme

We improve the off-line scheduling scheme of existing wireless sensor network. Firstly, we introduce Bayesian statistical method in synchronous wireless sensor network. Then, we let duration and interval, the reflection of characteristics of stochastic events, obey exponential distribution. Next, we make Bayes posterior estimation on parameter. Based on Bayesian estimate, we obtain the analytical solution of the capture probability of stochastic events and sensor energy efficiency of capture events. Finally, we propose an on-line scheduling scheme for synchronous wireless sensor networks. This paper compares and analyzes the simulation experiments in on-line scheduling scheme and off-line scheduling scheme, and the results show that compared with off-line scheduling scheme with constant distribution parameter values, on-line scheduling scheme can effectively reduce the probability of missing stochastic events and increase the probability of capturing events, further save energy consumption of wireless sensor network, and extend network lifetime.

Energy-Efficient Capture of Stochastic Events based on On-line Scheduling Scheme

We improve the off-line scheduling scheme of existing wireless sensor network. Firstly, we introduce Bayesian statistical method in synchronous wireless sensor network. Then we let duration and interval, the reflection of characteristics of stochastic events, obey exponential distribution. Next we make Bayes posterior estimation on parameter. Based on Bayesian estimate, we obtain the analytical solution of the capture probability of stochastic events and sensor energy efficiency of capture events. Finally, we propose an on-line scheduling scheme for synchronous wireless sensor networks. This paper compares and analyzes the simulation experiments in on-line scheduling scheme and off-line scheduling scheme and the results show that compared with off-line scheduling scheme with constant distribution parameter values, on-line scheduling scheme can effectively reduce the probability of missing stochastic events and increase the probability of capturing events, further save energy consumption of wireless sensor network and extend network lifetime.