An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

A coherent approach to Bayesian Data Envelopment Analysis

A Markov Chain Monte Carlo technique for parameter estimation and inference in pesticide fate and transport modeling

Bayesian inference and Markov chain Monte Carlo techniques have enjoyed enormous popularity since they were introduced into phylogenetics about a decade ago. We provide an overview of the field, with emphasis on recent developments of importance to empirical systematists. In particular, we describe a number of recent advances in the stochastic modeling of evolution that address major deficiencies in current models in a computationally efficient way. These include models of process heterogeneity across sites and lineages, as well as alignment-free models and model averaging approaches. Many of these methods should find their way into standard analyses in the near future. We also summarize the influence of Bayesian methods on insect systematics, with particular focus on current practices and how they could be improved using existing and emerging techniques.

Various remote sensing sensor observe the Earth's surface from coarse spatial resolution to fine spatial resolution. We may get different results from remote sensing images captured at different resolution due to scale effects. On the other hand, vegetation cover is an important parameter in many environmental models. It often affects the model results greatly. So, it is very important to understand the scaling problem of vegetation in remote sensing. This article presents a method to describe the vegetation cover distributions at different scales based on Bayesian Inference techniques. The histograms of vegetation cover show changing shapes with various spatial resolutions, they are very similar to Beta distributions with different parameters. On the other hand, geography spatial distribution probability can be expressed with binominal distribution or negative binominal distribution. Then, given a binominal or negative binominal distribution as likelihood, Beta distribution as a priori, we can get posterior distribution using conjugate prior theory. Such a posterior distribution can be used to predict the histograms of vegetation cover at different scales. Parameters used by this method can be calculated using mean and variance of vegetation cover at various scales. MODIS, Amtis and TM images are used to validate the method. The result shows that if vegetation is scattered, the binominal distribution may be used as the likelihood, on the contrary, a negative binominal distribution is much better. Because determining the spatial distribution is difficult, we combine the two distributions by adding the weight in this paper, and get better result.

Assessing the reliability of two production lines, whether individually or simultaneously, is of significant importance for improving manufacturing processes and guaranteeing superior product quality. This paper examines the reliability assessment of two production lines utilizing joint progressively Type-II censored samples derived from the XLindley distribution. In addition to estimating the unknown parameters, the reliability functions for each production line, as well as for both production lines simultaneously, are analyzed. Both classical likelihood-based and Bayesian methodologies are employed for estimation purposes. The maximum likelihood method is applied to obtain point estimates for the unknown parameters and reliability functions, while Bayesian analysis is performed under the squared error loss function, employing the Markov Chain Monte Carlo technique to generate samples from the posterior distribution. The approximate confidence intervals, percentile bootstrap confidence intervals, and the highest posterior density credible intervals for the unknown parameters and various reliability functions are discussed. The problem of selecting the optimal censoring plan is also considered. A comprehensive simulation study is conducted to assess the performance of the proposed methods, comparing the accuracy and efficiency of the estimates across different censoring schemes. Furthermore, the applicability of the proposed methodology is demonstrated through the analysis of two real-world data sets, underscoring its practical utility within the field of reliability. Finally, three criteria, namely A-optimality, D-optimality, and F-optimality, are considered to determine the optimal censoring plan.

Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China

This article estimates technical and allocative inefficiencies and increase in costs therefrom of individual firms using a translog cost system consisting of the cost function and the cost share equations. We call it a nonlinear random-effects system because technical and allocative inefficiencies are random (hence the term random effects) and are separated from the random noise terms appearing in each equation of the system, and because the inefficiency terms appear in the system in a highly nonlinear fashion, which helps in separating them from random errors. We use Bayesian inference procedures based on Markov chain Monte Carlo (MCMC) techniques to estimate the proposed system. Inferences on firm-specific technical inefficiency and both input-specific and firm-specific allocative inefficiencies are developed using MCMC techniques. We apply the new methods to a sample of 500 U.S. commercial banks. We focus on input allocation problem based on the assumption that banks minimize cost. Empirical results show that cost for the top (bottom) 10% of banks is increased by at least 3% (11%) due to technical inefficiency. In contrast, very few banks are found to be efficient in allocating all the inputs. Costs are increased by 13% on average due to input misallocation. Increase in costs due to both technical and allocative inefficiencies for the top (bottom) 10% of the banks is at least 11% (29%). When translated into dollar figures, this result indicates that elimination of technical and allocative inefficiencies would save the top (bottom) 10% of the banks more than $$.20 ($$3.56) million. We also find that none of the banks in our sample exceeded the efficient scale size, although most of them were operating near their optimum scale (unitary returns to scale).

We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star's photospheric composition. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4) semi-major axes, (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes), and (6) prior distributions are varied. Our main conclusions are: [...]

Group Importance Sampling for particle filtering and MCMC

This study addresses the challenge of estimating parameters for two logistic populations that share a common scale parameter but have different location parameters in the presence of fuzzy data. To handle these complexities, both Maximum Likelihood Estimation (MLE) and Bayesian methods are employed. Asymptotic confidence intervals are constructed using ML estimates. For Bayesian estimation, a conjugate prior is utilized, and Bayes estimators are approximated using Lindley’s method due to the lack of closed-form solutions. Furthermore, Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) techniques, including Hamiltonian Monte Carlo (HMC) and the Metropolis–Hastings (MH) algorithm, are utilized to sample from the posterior distributions and construct Highest Posterior Density (HPD) intervals. A detailed comparative analysis of MLE, Lindley’s approximation, ABC, HMC, and MH is conducted to assess their performance. The effectiveness of the proposed methodology is demonstrated using a real-world dataset under fuzzy conditions.

A novel variational Bayesian method for variable selection in logistic regression models

This thesis presents a measurement of the neutrino oscillation parameters with the T2K experiment. A simultaneous analysis of ND280 and Super-Kamiokande data is performed to measure sin^2 θ_23, ∆m^2_32, sin^2 θ_13 and δ_CP. The parameters estimations performed in this thesis rely on a Bayesian statistical method sampling the parameters posterior probability distributions with a Markov chain Monte-Carlo technique. The analysed data correspond to an exposure of 7.482·10^20 protons on target (POT) in ν-mode and 7.471·10^20 in antiν-mode, consisting of the T2K runs 1 to 7. The mixing angle θ_13 is precisely measured in reactor experiments; using this external input the neutrino mixing parameters are measured to be sin^2 θ_23=0.51+0.04−0.05, ∆m^2_32=2.54+0.12−0.12·10^3 eV^2·c^−4,sin^2 θ_13=0.0219±0.0011, and δ_CP=−1.79+0.91−0.66 rad. CP-conservation in the neutrino sector is excluded with a 90% credibility (or C.L.). An analysis separating νμ from antiνμ disappearance finds consistent results between neutrino and antineutrino oscillations.

BackgroundBayesian phylogenetic inference holds promise as an alternative to maximum likelihood, particularly for large molecular-sequence data sets. We have investigated the performance of Bayesian inference with empirical and simulated protein-sequence data under conditions of relative branch-length differences and model violation.ResultsWith empirical protein-sequence data, Bayesian posterior probabilities provide more-generous estimates of subtree reliability than does the nonparametric bootstrap combined with maximum likelihood inference, reaching 100% posterior probability at bootstrap proportions around 80%. With simulated 7-taxon protein-sequence datasets, Bayesian posterior probabilities are somewhat more generous than bootstrap proportions, but do not saturate. Compared with likelihood, Bayesian phylogenetic inference can be as or more robust to relative branch-length differences for datasets of this size, particularly when among-sites rate variation is modeled using a gamma distribution. When the (known) correct model was used to infer trees, Bayesian inference recovered the (known) correct tree in 100% of instances in which one or two branches were up to 20-fold longer than the others. At ratios more extreme than 20-fold, topological accuracy of reconstruction degraded only slowly when only one branch was of relatively greater length, but more rapidly when there were two such branches. Under an incorrect model of sequence change, inaccurate trees were sometimes observed at less extreme branch-length ratios, and (particularly for trees with single long branches) such trees tended to be more inaccurate. The effect of model violation on accuracy of reconstruction for trees with two long branches was more variable, but gamma-corrected Bayesian inference nonetheless yielded more-accurate trees than did either maximum likelihood or uncorrected Bayesian inference across the range of conditions we examined. Assuming an exponential Bayesian prior on branch lengths did not improve, and under certain extreme conditions significantly diminished, performance. The two topology-comparison metrics we employed, edit distance and Robinson-Foulds symmetric distance, yielded different but highly complementary measures of performance.ConclusionsOur results demonstrate that Bayesian inference can be relatively robust against biologically reasonable levels of relative branch-length differences and model violation, and thus may provide a promising alternative to maximum likelihood for inference of phylogenetic trees from protein-sequence data.

To evaluate the usefulness of the Bayesian method for hepatic fibrosis staging with magnetic resonance elastography (MRE). The sample of this retrospective study comprised patients with chronic liver disease (n = 309), in whom histopathological fibrosis staging and MRE using either a 1.5T (n = 214) or a 3T magnetic resonance imaging (MRI) system (n = 95) had been performed. The optimal cutoff stiffness value was determined and used to calculate the discrimination ability of fibrosis staging by the cutoff method. The Bayesian method calculated post-MRE probability of each fibrosis stage, yielding MRE-based fibrosis staging without a cutoff value as well as the confidence of staging. We compared the discrimination ability in all patients and in a subgroup of patients with high (≥90%) posterior probability. The discrimination ability for hepatic fibrosis staging was comparable between the Bayesian method and the cutoff method in all patients because the accuracy of staging with the Bayesian method and the cutoff method in all patients was not different (P = 1.0000). However, in patients with high posterior probability by the Bayesian method, the accuracy of staging with the Bayesian method was significantly improved compared with that of the cutoff method in all patients; for discriminating stage ≥F2 from F0-F1 (98.9% vs. 94.8%, P = 0.0069); for ≥F3 (99.6% vs. 92.6%, P < 0.0001); and for F4 (100% vs. 94.2%, P = 0.0002). The Bayesian method has a highly accurate discrimination ability for noninvasive hepatic fibrosis staging using MRE, if the posterior probability is high. 3 Technical Efficacy: Stage 2 J. MAGN. RESON. IMAGING 2017;46:375-382.

Race and ethnicity are significant factors in predicting survival time of breast cancer patients. In this study, we applied advanced statistical methods to predict the survival of White non-Hispanic female breast cancer patients, who were diagnosed between the years 1973 and 2009 in the United States (U.S.). Demographic data from the Surveillance Epidemiology and End RESULTS (SEER) database were used for the purpose of this study. Nine states were randomly selected from 12 U.S. cancer registries. A stratified random sampling method was used to select 2,000 female breast cancer patients from these nine states. We compared four types of advanced statistical probability models to identify the best-fit model for the White non- Hispanic female breast cancer survival data. Three model building criterion were used to measure and compare goodness of fit of the models. These include Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC). In addition, we used a novel Bayesian method and the Markov Chain Monte Carlo technique to determine the posterior density function of the parameters. After evaluating the model parameters, we selected the model having the lowest DIC value. Using this Bayesian method, we derived the predictive survival density for future survival time and its related inferences. The analytical sample of White non-Hispanic women included 2,000 breast cancer cases from the SEER database (1973-2009). The majority of cases were married (55.2%), the mean age of diagnosis was 63.61 years (SD = 14.24) and the mean survival time was 84 months (SD = 35.01). After comparing the four statistical models, results suggested that the exponentiated Weibull model (DIC= 19818.220) was a better fit for White non-Hispanic females' breast cancer survival data. This model predicted the survival times (in months) for White non-Hispanic women after implementation of precise estimates of the model parameters. By using modern model building criteria, we determined that the data best fit the exponentiated Weibull model. We incorporated precise estimates of the parameter into the predictive model and evaluated the survival inference for the White non-Hispanic female population. This method of analysis will assist researchers in making scientific and clinical conclusions when assessing survival time of breast cancer patients.