Modeling Overdispersion, Autocorrelation, and Zero-Inflated Count Data Via Generalized Additive Models and Bayesian Statistics in an Aphid Population Study.

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

Appropriate models in biostatistics are often quite complicated. Such models are typically most easily fit using Bayesian methods, which can often be implemented using simulation techniques. Markov chain Monte Carlo (MCMC) methods are an important set of tools for such simulations. We give an overview and references of this rapidly emerging technology along with a relatively simple example. MCMC techniques can be viewed as extensions of iterative maximization techniques, but with random jumps rather than maximizations at each step. Special care is needed when implementing iterative maximization procedures rather than closed-form methods, and even more care is needed with iterative simulation procedures: it is substantially more difficult to monitor convergence to a distribution than to a point. The most reliable implementations of MCMC build upon results from simpler models fit using combinations of maximization algorithms and noniterative simulations, so that the user has a rough idea of the location and scale of the posterior distribution of the quantities of interest under the more complicated model. These concerns with implementation, however, should not deter the biostatistician from using MCMC methods, but rather help to ensure wise use of these powerful techniques.

The Ideal Observer (IO) performance has been advocated when optimizing medical imaging systems for signal detection tasks. However, analytical computation of the IO test statistic is generally intractable. To approximate the IO test statistic, sampling-based methods that employ Markov-Chain Monte Carlo (MCMC) techniques have been developed. However, current applications of MCMC techniques have been limited to several object models such as a lumpy object model and a binary texture model, and it remains unclear how MCMC methods can be implemented with other more sophisticated object models. Deep learning methods that employ generative adversarial networks (GANs) hold great promise to learn stochastic object models (SOMs) from image data. In this study, we described a method to approximate the IO by applying MCMC techniques to SOMs learned by use of GANs. The proposed method can be employed with arbitrary object models that can be learned by use of GANs, thereby the domain of applicability of MCMC techniques for approximating the IO performance is extended. In this study, both signal-known-exactly (SKE) and signal-known-statistically (SKS) binary signal detection tasks are considered. The IO performance computed by the proposed method is compared to that computed by the conventional MCMC method. The advantages of the proposed method are discussed.

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).

Using the standard one-zone synchrotron self-Compton model and the Markov chain Monte Carlo (MCMC) technique, we systematically analyse the quasi-simultaneous multiwavelength spectral energy distributions (SEDs) of Mrk 421 and Mrk 501 during states of relatively low activity. With this model in place, a semi-analytical method is developed to examine the uncertainty in jet power estimation caused by degeneracy of the radiative models. The semi-analytical method, in combination with the MCMC technique, allows us to explore the jet properties over a wide range of the variability time-scale. Our results seem to support the following. (i) In both Mrk 421 and Mrk 501, the jets are powered by rapidly rotating black holes. The black hole spin in Mrk 501 could be lower than that in Mrk 421 or possibly they are equal under the assumption of the Blandford–Znajek mechanism. (ii) The energy losses, which could be used to form the large-scale radio structure, are important for reconciling the differences of the kinetic power derived from the observations of the large-scale structure and the SED fitting results. Moreover, the jet energy losses in the propagation are more significant for Mrk 501 than for Mrk 421.

Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge.

The aim of this study is to evaluate the association between maternal factors and birth weight among babies by using and comparing frequentist and Bayesian methods’ results from an epidemiologist or public health point of view. Low birth weight babies, defined by WHO as babies born at term who weigh less than 2.5kg is an important indicator of reproductive health and general health status of any Population. The incidence of low birth weight is quite high in the sub region which has a public health concern.The study used a data set based on Multiple Indicators Cluster Survey conducted by Ghana Statistical Service in 2011 to monitor progress of women and children. A sample of 10,963 women within the reproductive age (15 – 49) years across the country between 2009 and 2011 were selected for the survey. The results from the frequentist and the Bayesian models show that, the two approaches can yield similar results using same data set. However, there are factors that the Bayesian technique can unfold which might not be the case using the frequentist model. We were able to show that the Bayesian approach may have advantages over the frequentist one, particularly with respect to our data. The use of informative priors might however be useful in narrowing credible interval and providing precise choice between the null and alternative hypothesis. In case of borderline frequentist results, the Markov Chain Monte Carlo method may be more conservative, particularly without priors. Comparing the two approaches with respect to our data set, we can infer (from table 4) that using Bayesian model provides better estimates in predicting low birth weight among babies in Ghana. We note however that to better understand the phenomenon under study the two methods should be used together. Our findings further revealed that low birth weight is not only a public health problem but also a socio-cultural issue.

We investigate the estimation of multi-stress strength reliability under progressively first failure censoring for the generalized inverted exponential distribution using classical and Bayesian approaches. Classical estimation employs maximum likelihood estimators with the Expectation-Maximization algorithm to handle incomplete data. Bayesian estimation utilizes Markov Chain Monte Carlo (MCMC) techniques and Tierney-Kadane's approximation to approximate the posterior distribution. Furthermore, A generalized entropy loss function is employed to measure estimation accuracy. Finally, Validation is provided through Monte Carlo simulations and real-world applications. Findings highlight the robustness and accuracy of Bayesian methods, particularly with informative priors, and underscore the strengths of MCMC techniques and Bayesian Credible Intervals in specific aspects of estimation.

In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories.

The recruitment process and its underlying mechanisms are among the most studied phenomena in fisheries ecology. Traditional models estimate fish recruitment assuming a direct relationship with spawning stock size. However, highly variable environmental conditions, feeding conditions, and other factors can influence and complicate the results of a simple linear regression analysis between stock and recruitment. We used generalized additive models (GAMs) to investigate the influence of environmental conditions and stock structure on the recruitment processes of Baltic cod. The interaction between abiotic factors and old spawners (>5+ years) and eggs produced by old spawners were the most significant explanatory variables. Eggs produced by young spawners have a positive impact on cod recruitment only at high levels of reproductive volume, while old spawners' eggs have the highest positive effect at low levels of reproductive volume. Here we show: (i) that the number of Baltic cod recruits is strictly dependent on the age structure of the population; (ii) that interactions between biotic and abiotic factors are crucial in explaining recruitment variability; and (iii) that GAMs are a powerful technique for defining and quantifying the intricate multidimensional relationship between biotic and abiotic variables involved in recruitment processes.

The spatial distribution of Antarctic minke whales in the Ross Sea with relation to spatial distributions of their prey – krill – was investigated in this study using generalized additive models (GAMs). Spatial distributions of two species of krill (ice and Antarctic krill) were estimated by GAMs. Three abiotic factors – distance from the continental shelf break (800 m isobaths), the mean temperature and salinity from the surface to 200 m (MTEM‐200 and MSAL‐200), and latitude and longitude – were used as covariates for models of krill. Estimated spatial distributions of krill were then used with other covariates to model the spatial distribution of Antarctic minke whales. In the selected model of Antarctic minke whales, Antarctic krill were more influential than ice krill. The number of Antarctic minke whales increased as the density of Antarctic krill increased to around 1.5 g m−2. Beyond that, the number of Antarctic minke whales decreased as the density of Antarctic krill increased. High densities of the Antarctic minke whales were estimated along the sea ice edge in the eastern part of the Ross Sea. Specifically, the densities were high in the north of the continental shelf break where low MTEM‐200 and MSAL‐200 and intermediate densities of Antarctic krill were observed. Further data collection is needed to investigate interannual variations and trends in their relationship. The results show that the spatial distribution of Antarctic minke whales is a function of longitude, distance from the shelf break, oceanographic condition (temperature and salinity), and densities of ice and Antarctic krill.

PurposeThe application of statistical inversion theory provides a powerful approach for solving estimation problems including the ability for uncertainty quantification (UQ) by means of Markov chain Monte Carlo (MCMC) methods and Monte Carlo integration. This paper aims to analyze the application of a state reduction technique within different MCMC techniques to improve the computational efficiency and the tuning process of these algorithms.Design/methodology/approachA reduced state representation is constructed from a general prior distribution. For sampling the Metropolis Hastings (MH) Algorithm and the Gibbs sampler are used. Efficient proposal generation techniques and techniques for conditional sampling are proposed and evaluated for an exemplary inverse problem.FindingsFor the MH-algorithm, high acceptance rates can be obtained with a simple proposal kernel. For the Gibbs sampler, an efficient technique for conditional sampling was found. The state reduction scheme stabilizes the ill-posed inverse problem, allowing a solution without a dedicated prior distribution. The state reduction is suitable to represent general material distributions.Practical implicationsThe state reduction scheme and the MCMC techniques can be applied in different imaging problems. The stabilizing nature of the state reduction improves the solution of ill-posed problems. The tuning of the MCMC methods is simplified.Originality/valueThe paper presents a method to improve the solution process of inverse problems within the Bayesian framework. The stabilization of the inverse problem due to the state reduction improves the solution. The approach simplifies the tuning of MCMC methods.

This paper presents an efficient method for estimating capacity-fade uncertainty in lithium-ion batteries (LIBs) in order to integrate them into the battery-management system (BMS) of electric vehicles, which requires simple and inexpensive computation for successful application. The study uses the pseudo-two-dimensional (P2D) electrochemical model, which simulates the battery state by solving a system of coupled nonlinear partial differential equations (PDEs). The model parameters that are responsible for electrode degradation are identified and estimated, based on battery data obtained from the charge cycles. The Bayesian approach, with parameters estimated by probability distributions, is employed to account for uncertainties arising in the model and battery data. The Markov Chain Monte Carlo (MCMC) technique is used to draw samples from the distributions. The complex computations that solve a PDE system for each sample are avoided by employing a polynomial-based metamodel. As a result, the computational cost is reduced from 5.5 h to a few seconds, enabling the integration of the method into the vehicle BMS. Using this approach, the conservative bound of capacity fade can be determined for the vehicle in service, which represents the safety margin reflecting the uncertainty.

Performance modelling of web applications involves the task of estimating service demands of requests at physical resources, such as CPUs. In this paper, we propose a service demand estimation algorithm based on a Markov Chain Monte Carlo (MCMC) technique, Gibbs sampling. Our methodology is widely applicable as it requires only queue length samples at each resource, which are simple to measure. Additionally, since we use a Bayesian approach, our method can use prior information on the distribution of parameters, a feature not always available with existing demand estimation approaches. The main challenge of Gibbs sampling is to efficiently evaluate the conditional expression required to sample from the posterior distribution of the demands. This expression is shown to be the equilibrium solution of a multiclass closed queueing network. We define a novel approximation to efficiently obtain the normalising constant to make the cost of its evaluation acceptable for MCMC applications. Experimental evaluation based on simulation data with different model sizes demonstrates the effectiveness of Gibbs sampling for service demand estimation.

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking