Posterior Distribution Of Parameters Research Articles

Simulation-based inference of developmental EEG maturation with the spectral graph model

The spectral content of macroscopic neural activity evolves throughout development, yet how this maturation relates to underlying brain network formation and dynamics remains unknown. Here, we assess the developmental maturation of electroencephalogram spectra via Bayesian model inversion of the spectral graph model, a parsimonious whole-brain model of spatiospectral neural activity derived from linearized neural field models coupled by the structural connectome. Simulation-based inference was used to estimate age-varying spectral graph model parameter posterior distributions from electroencephalogram spectra spanning the developmental period. This model-fitting approach accurately captures observed developmental electroencephalogram spectral maturation via a neurobiologically consistent progression of key neural parameters: long-range coupling, axonal conduction speed, and excitatory:inhibitory balance. These results suggest that the spectral maturation of macroscopic neural activity observed during typical development is supported by age-dependent functional adaptations in localized neural dynamics and their long-range coupling across the macroscopic structural network.

The role of Markov chain in Monte Carlo simulation

The Markov Chain Monte Carlo method has been applied in several fields and has thrived in academic research over the past few decades. The method is utilized to estimate the interest parameters posterior distribution through random sampling in the probability space. Monte Carlo method alone can accomplish random simulations for some complicated continuous integrals or discrete summations. However, the method requires the sample set corresponding to the distribution, which demands the application of Markov chain. Nevertheless, problems occur when the probability function of the samples remain unknown, under which circumstance the Markov Chain Monte Carlo method is no longer available. Therefore, the article introduced Metropolis-Hastings Algorithm as a resolution. The paper is intended to provide specific insights about Metropolis-Hastings Algorithm for Markov Chain Monte Carlo and the corresponding interdisciplinary applications. Specifically, the paper will discuss about using the theory mentioned above to check the relationships among species in a common ecosystem. The paper will cover several prepositive theories, including the Law of Large Numbers for Markov Chains, binary sequences, and Metropolis-Hastings Algorithm. Overall, specific cases and the way to draw correct conclusions will be most concerned.

Applying Machine Learning Techniques: Uncertainty Quantification in Nonlinear Dynamics Characters Predictions via Gated Recurrent Unit-Based Reduced-Order Models

The development of reduced-order models has been a pivotal advancement in the computational analysis of fluid dynamics, substantially simplifying the complexity and boosting the efficiency of simulations. The accuracy and practicality of these models largely depend on the reduction techniques applied and the inherent characteristics of the fluid dynamics systems they represent. In this paper, we introduce an innovative machine-learning framework for assessing model uncertainty in computationally intensive reduced-order models. By combining subspace construction methods with advanced Bayesian inference techniques, our approach effectively captures the posterior distribution of model parameters, thereby providing an accurate representation of uncertainty in aerodynamic performance predictions. We employ the NACA0012 airfoil as a case study to validate our method’s ability to enhance the efficiency of reduced-order models and precisely measure the uncertainty inherent in predictions made by recurrent neural networks. It is important to note that our approach is influenced by specific constraints and variables that significantly impact the mean and variability of the predicted final lift coefficient distribution. Our findings indicate that setting the goodness of fit (R2) threshold above 0.985 markedly improves the correlation between Computational Fluid Dynamics (CFD) outcomes and model predictions, increasing from 72.2% to 97.9% as the interval amplification factor adjusts from 1.5 to 3. However, this adjustment causes a considerable expansion of the confidence interval, from 0.0737 to 0.1282, an increase of over 70%. Despite these challenges, our machine learning-based methodology provides essential insights into the further development of reduced-order modeling and uncertainty quantification in fluid dynamics. This highlights the need for ongoing research into the model parameters, especially in applications concerning aircraft control systems, to meet design specifications and ensure system reliability.

Covariance-based MCMC for high-dimensional Bayesian updating with Sequential Monte Carlo

Sequential Monte Carlo (SMC) is a reliable method to generate samples from the posterior parameter distribution in a Bayesian updating context. The method samples a series of distributions sequentially, which start from the prior distribution and gradually approach the posterior distribution. Sampling from the distribution sequence is performed through application of a resample-move scheme, whereby the move step is performed using a Markov Chain Monte Carlo (MCMC) algorithm. The preconditioned Crank-Nicholson (pCN) is a popular choice for the MCMC step in high dimensional Bayesian updating problems, since its performance is invariant to the dimension of the prior distribution. This paper proposes two other SMC variants that use covariance information to inform the MCMC distribution proposals and compares their performance to the one of pCN-based SMC. Particularly, a variation of the pCN algorithm that employs covariance information, and the principle component Metropolis Hastings algorithm are considered. These algorithms are combined with an intermittent and recursive updating scheme of the target distribution covariance matrix based on the current MCMC progress. We test the performance of the algorithms in three numerical examples; a two dimensional algebraic example, the estimation of the flexibility of a cantilever beam and the estimation of the hydraulic conductivity field of an aquifer. The results show that covariance-based MCMC algorithms are capable of producing smaller errors in parameter mean and variance and better estimates of the model evidence compared to the pCN approach.

Toward Robust Corrections for Stellar Contamination in JWST Exoplanet Transmission Spectra

Transmission spectroscopy is still the preferred characterization technique for exoplanet atmospheres, although it presents unique challenges that translate into characterization bottlenecks when robust mitigation strategies are missing. Stellar contamination is one such challenge that can overpower the planetary signal by up to an order of magnitude, and thus not accounting for it can lead to significant biases in the derived atmospheric properties. Yet this accounting may not be straightforward, as important discrepancies exist between state-of-the-art stellar models and measured spectra and between models themselves. Here we explore the extent to which stellar models can be used to reliably correct for stellar contamination and yield a planet’s uncontaminated transmission spectrum. We find that discrepancies between stellar models can significantly contribute to the noise budget of JWST transmission spectra of planets around stars with heterogeneous photospheres, the true number of unique photospheric spectral components and their properties can only be accurately retrieved when the stellar models have sufficient fidelity, and under such optimistic circumstances the contribution of stellar contamination to the noise budget of a transmission spectrum is considerably below that of the photon noise for the standard transit observation setup. Therefore, we advocate for further development of model spectra of stars and their active regions in a data-driven manner, empirical approaches for deriving spectra of photospheric components using the observatories with which the atmospheric explorations are carried out, and analysis techniques accounting for multimodal posterior distributions for photospheric parameters of interest, which will be increasingly revealed by precise JWST measurements.

A Diffusion‐Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration

AbstractCalibrating land surface models and accurately quantifying their uncertainty are crucial for improving the reliability of simulations of complex environmental processes. This, in turn, advances our predictive understanding of ecosystems and supports climate‐resilient decision‐making. Traditional calibration methods, however, face challenges of high computational costs and difficulties in accurately quantifying parameter uncertainties. To address these issues, we develop a diffusion‐based uncertainty quantification (DBUQ) method. Unlike conventional generative diffusion methods, which are computationally expensive and memory‐intensive, DBUQ innovates by formulating a parameterized generative model and approximates this model through supervised learning, which enables quick generation of parameter posterior samples to quantify its uncertainty. DBUQ is effective, efficient, and general‐purpose, making it suitable for site‐specific ecosystem model calibration and broadly applicable for parameter uncertainty quantification across various earth system models. In this study, we applied DBUQ to calibrate the Energy Exascale Earth System Model land model at the Missouri Ozark AmeriFlux forest site. Results indicated that DBUQ produced accurate parameter posterior distributions similar to those from Markov Chain Monte Carlo sampling but with 30 times less computing time. This significant improvement in efficiency suggests that DBUQ can enable rapid, site‐level model calibration at a global scale, enhancing our predictive understanding of climate impacts on terrestrial ecosystems.

Bayesian Model Updating of Multiscale Simulations Informing Corrosion Prognostics Using Conditional Invertible Neural Networks

Abstract Physics-based multi-scale corrosion simulation plays a vital role in predicting the evolution of pitting corrosion on large civil infrastructure such as miter gates, contributing to a model-informed structural health monitoring (SHM) strategy for risk-based asset health management. The physics-based analysis, however, may not accurately reflect the underlying true physics due to various uncertainty sources and needs to be updated using Bayesian inference methods based on observations to make the prediction closer to field observations. However, traditional Bayesian inference requires the evaluation of a likelihood function, which is often unavailable due to the complex model architecture and various surrogate models used in the analysis. Therefore, likelihood-free inference approaches are required for the updating of the multi-scale corrosion simulation models. This paper meets this need by proposing a conditional invertible neural network (cINN)-based Bayesian model updating method for an existing corrosion simulation model. We first train an cINN model based on simulated observations generated from a high-fidelity forward corrosion analysis model. A convolutional neural network (CNN)-based feature extraction algorithm is then employed to extract key features from corrosion images. After that, the extracted corrosion features from CNN is used as inputs of the cINN model to directly obtain posterior distributions of uncertain corrosion model parameters without evaluating the likelihood function. The results show that the proposed cINN-based model updating approach can provide more accurate inference results with a reduced computational cost in comparison to the classical approximate Bayesian computation (ABC) approach.

Bayesian peak identification method for low count rate gamma spectrum under short-time measurement based on physical priors

A Bayesian peak identification method based on physical model had been proposed in this study to perform qualitative analysis for the low count rate gamma spectrum under short-time measurement. Based on the prior knowledge about gamma detection, the distribution of energy deposited in the detector near the region of interest of a target peak through photoelectric effect, Compton scattering and multiple scattering had been analyzed and approximated using three elementary components, then, the distribution of each component after convolution had been studied, and at last, a probabilistic mixture model had been proposed to directly describe the distribution of measured energy within region of interest. When the data measurement has been completed, a Gibbs sampler was used to estimate the posterior distribution of model parameters to discriminate the existence of target peaks. The numerical and physical experiments were performed to verify the effectiveness of the parameter estimation algorithm and the performance of the proposed identification method. The numerical experiments showed the identification precision is proportional to counts and peak-to-total ratio, when the peak-to-total ratio is greater than 0.5, the proposed method could identify the peak with a probability greater than 50% given 50 observations. The physical experiment used a NaI(Tl) detector to measure 137Cs, 60Co and 152Eu sources in a laboratory environment at different equivalent distances, the peak identification precision had been tested for the proposed method, and the experiments proved that the probabilistic model is a good approximation to the physical process, and the proposed identification method outperformed the conventional method under short-time measurement conditions.

Unsupervised gas pipeline network leakage detection method based on improved graph deviation network

Historical data has shown that the natural gas pipeline network, as a critical urban lifeline system, is susceptible to disasters such as earthquakes resulting in leakage. Graph neural network modeling provides frontier rapid detection solutions for pipeline leakage; however, the challenges of collecting gas network anomaly data for training limit the precision and robustness of current model. This research proposes an unsupervised gas leakage detection and localization method based on a contained preprocessing process, with a graph deviation model that combines a structural learning approach with a graph neural network to model the spatial dependence of the sensors based on an attention mechanism, and variational inference models the posterior distributions of the hyper-parameters to optimize the model and improve the model precision. Meanwhile, in the preprocessing stage, the automatic optimization strategy of Northern Goshawk Optimization (NGO) for the best parameters K and ɑ in the Variable Mode Decomposition (VMD) efficiently extracts the valid signals and ensures that the model gives full play to the detection and localization effectiveness. The gas pipeline network dataset constructed by Pipeline Studio was used for comparing the performance of the model in this study with other frontier models. The results demonstrate that the model in this research has competitive detection Precision (93.31%), Recall (70.82%), and F1-score (0.81), and the posterior distribution of the model parameters strengthens the gas leakage localization precision, which provides a comprehensive solution for subsequent decision-making and reduces the hidden hazard of leakage effectively.

Practical guidelines for Bayesian phylogenetic inference using Markov Chain Monte Carlo (MCMC)

Phylogenetic estimation is, and has always been, a complex endeavor. Estimating a phylogenetic tree involves evaluating many possible solutions and possible evolutionary histories that could explain a set of observed data, typically by using a model of evolution. Modern statistical methods involve not just the estimation of a tree, but also solutions to more complex models involving fossil record information and other data sources. Markov Chain Monte Carlo (MCMC) is a leading method for approximating the posterior distribution of parameters in a mathematical model. It is deployed in all Bayesian phylogenetic tree estimation software. While many researchers use MCMC in phylogenetic analyses, interpreting results and diagnosing problems with MCMC remain vexing issues to many biologists. In this manuscript, we will offer an overview of how MCMC is used in Bayesian phylogenetic inference, with a particular emphasis on complex hierarchical models, such as the fossilized birth-death (FBD) model. We will discuss strategies to diagnose common MCMC problems and troubleshoot difficult analyses, in particular convergence issues. We will show how the study design, the choice of models and priors, but also technical features of the inference tools themselves can all be adjusted to obtain the best results. Finally, we will also discuss the unique challenges created by the incorporation of fossil information in phylogenetic inference, and present tips to address them.

A Bayesian Spatiotemporal Modeling Approach to the Inverse Heat Conduction Problem

Abstract This study introduces a Bayesian spatiotemporal modeling approach to solve inverse heat conduction problems (IHCPs), employing penalized splines within a spatiotemporal forward model. The complexity and ill-posed nature of IHCPs, characterized by potential nonexistence, nonuniqueness, or instability of solutions, pose significant challenges for traditional methods. Addressing this, our study presents a spatiotemporal forward model that incorporates spatial, temporal, and interaction terms, accurately capturing the intricate dynamics inherent in IHCPs and using this information as a leverage to solve the inverse problem. We adopted a Bayesian inference framework for the subsequent parameter estimation problem and developed a Gibbs sampling algorithm to sample from the posterior distribution of the model's parameters, enhancing the estimation process. Through case studies on a one-dimensional (1D) heat simulation and a pool boiling experiment using multisensor thermocouple data for heat flux reconstruction, we demonstrate the model's superiority over traditional methods. The inclusion of the spatiotemporal interaction term significantly enhances model performance, indicating its potential for broader application in solving IHCPs. The application of this method in both simulated and real-world scenarios highlights its effectiveness in capturing the spatiotemporal complexities of IHCPs. This work contributes to the field by offering a robust methodology for addressing the spatial and temporal complexities inherent in IHCPs, supported by a comprehensive Bayesian inference framework and the use of a Gibbs sampling algorithm for parameter estimation.

Bayesian analysis of physiologically based toxicokinetic (PBTK) modeling for pentachlorophenol exposure in pregnant women

Pentachlorophenol (PCP) is a persistent organic compound that is widely present in the environment. The estimation of internal exposure levels for a given external exposure using toxicokinetic models is key to the human health risk assessment of PCP. The present study developed a physiologically based multicompartmental pharmacokinetic (PBTK) model to describe and predict the behavior of pentachlorophenol (PCP) in an organism. The model consists of stomach, intestines, adipose tissue, kidneys and fast- and poorly perfused tissues that are interconnected via blood circulation. We constructed a PBTK model of PCP in rats and extrapolated it to human dietary PCP exposure. The toxicokinetic data of PCP in human tissues and excreta were obtained from the published literature. Based on the collected PCP dietary survey and internal exposure data of pregnant women in Shanghai, Bayesian statistical analysis was performed for the model using Markov chain Monte Carlo (MCMC) simulation. The posterior distributions of the sensitive parameters were estimated, and the model was parameter optimized and validated using the pregnant women's test dataset. The results showed that the root mean square error (RMSE) improved 37.3% compared to the original model, and a systematic literature search revealed that the optimized model achieved acceptable prediction results for other datasets in China. A PCP metabolism model based on the exposure characteristics of pregnant women in China was constructed in the present study. The model provides a theoretical basis for the study of PCP toxicity and risk assessment.

Combining prior and post‐release data while accounting for dispersal to improve predictions for reintroduction populations

AbstractAttempts to reintroduce species to managed areas may be compromised by dispersal into the surrounding landscape. Therefore, decisions regarding the selection and ongoing management of reintroduction areas require predicting dispersal as well as the survival and reproduction rates of the species to be reintroduced. Dispersal can potentially be measured directly by tracking animals, but this is often impractical. However, dispersal can also be inferred from re‐sighting surveys done within reintroduction areas if such data are available from multiple areas with varying connectivity to the surrounding landscape, allowing apparent survival and recruitment to be modelled as a function of connectivity metrics. Here, we show how data from 10 previous reintroductions of a New Zealand passerine, the toutouwai (Petroica longipes), were used to predict population dynamics at a predator‐controlled reintroduction area with high connectivity, and predictions then updated using post‐release data. Bayesian hierarchical modelling of the previous data produced prior distributions for productivity, adult survival and apparent juvenile survival rates that accounted for random variation among areas as well as rat density and connectivity. The modelling of apparent juvenile survival as a function of connectivity allowed it to be partitioned into estimates of survival and fidelity. Bayesian updating based on post‐release data produced posterior distributions for parameters that were consistent with the priors but much more precise. The prior data also allowed the recruitment rate estimated in the new area to be partitioned into separate estimates for productivity, juvenile survival and juvenile fidelity. Consequently, it was possible to not only estimate population growth under current management, but also predict the consequences of reducing the scale or intensity of predator control, facilitating adaptive management. The updated model could then be used to predict population growth as a function of the connectivity and predator control regime at proposed reintroduction areas while accounting for random variation among areas.

Using machine learning techniques in inverse problems of acoustical oceanography

AbstractThe goal of the work presented here is to study a novel approach for inverting acoustic signals recorded in the marine environment for the estimation of environmental parameters of the water column and/or the seabed. The proposed approach is based on signal feature extraction using a discrete wavelet packet transform, applied to the measured signal, and hidden Markov models that exploit the sequential patterns of the signals. The signal feature is thereafter used in the framework of a mixture density network, which, after training with sets of simulated signals calculated within a predefined search space, provides conditional posterior distributions of the recoverable parameters. The technique is tested with two test cases corresponding to different types of inverse problems. The first case corresponds to a simple problem of geoacoustic inversion, while the second is referred to a, rather unusual, still interesting problem of recovering the shape of a seamount using long‐range acoustic data. Both test cases are based on simulated experiments. The inversion results obtained using the proposed scheme are compared with inversion results using statistical features of the acoustic signal, which is another inversion approach well documented in the literature and is also based on the wavelet packet transform of the measured signal.

Bayesian Inference for Multiple Datasets

Estimating parameters for multiple datasets can be time consuming, especially when the number of datasets is large. One solution is to sample from multiple datasets simultaneously using Bayesian methods such as adaptive multiple importance sampling (AMIS). Here, we use the AMIS approach to fit a von Mises distribution to multiple datasets for wind trajectories derived from a Lagrangian Particle Dispersion Model driven from 3D meteorological data. A posterior distribution of parameters can help to characterise the uncertainties in wind trajectories in a form that can be used as inputs for predictive models of wind-dispersed insect pests and the pathogens of agricultural crops for use in evaluating risk and in planning mitigation actions. The novelty of our study is in testing the performance of the method on a very large number of datasets (>11,000). Our results show that AMIS can significantly improve the efficiency of parameter inference for multiple datasets.

Estimating causal effects from panel data with dynamic multivariate panel models

Panel data are ubiquitous in scientific fields such as social sciences. Various modeling approaches have been presented for observational causal inference based on such data. Existing approaches typically impose restrictive assumptions on the data-generating process such as Gaussian responses or time-invariant effects, or they can only consider short-term causal effects. To surmount these restrictions, we present the dynamic multivariate panel model (DMPM) that supports time-varying, time-invariant, and individual-specific effects, multiple responses across a wide variety of distributions, and arbitrary dependency structures of lagged responses of any order. We formally demonstrate how DMPM facilitates causal inference within the structural causal modeling framework and we take a Bayesian approach for the estimation of the posterior distributions of the model parameters and causal effects of interest. We demonstrate the use of DMPM by applying the approach to both real and synthetic data.

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

Cyclic behavior of laminated bio-based connections with slotted-in steel plates: Genetic algorithm, deterministic neural network-based model parameter identification, and uncertainty quantification

To support more sustainable construction, this paper experimentally investigates the cyclic behavior of laminated timber (Laminated Veneer Lumber (LVL)) and glubam (Glue Laminated Bamboo) connections with slotted-in steel plates in terms of experimental test, numerical simulations and parameter identification. Experimental tests included eight different configurations: two materials (LVL and glubam), two bolt diameters (8 and 10 mm), and one or two bolts. Two different cyclic-loading protocols were applied for each type of connection: only tension and tension/compression. The observed behavior is then compared to a finite element model developed in OpenSeesPy, which takes into account factors such as sliding, contact, pinching, cyclic stiffness, and strength degradation. To identify the best set of parameters for the model, three different approaches are considered: genetic algorithm, fast deterministic neural network, and probabilistic Bayesian method. First, the model identification is carried out by means of a genetic algorithm-based optimization. The parameter-identification results are evaluated in terms of elastic stiffness, yielding point, and ductility. Next, a sensitivity analysis is performed to determine the significance of the parameters, and an innovative approach combining neural network and sensitivity analysis is proposed for fast and preliminary parameter identification. Then, probabilistic Bayesian identification is employed to calculate the posterior distribution of the model parameters identified and the confidence bounds of the estimated response. Finally, different model identification parameters are compared and suggestions for algorithm selection are provided.

A Bayesian Change Point Model for Dynamic Alternative Transcription Start Site Usage During Cellular Differentiation.

ABSTRACT An alternative transcription start site (ATSS) is a major driving force for increasing the complexity of transcripts in human tissues. As a transcriptional regulatory mechanism, ATSS has biological significance. Many studies have confirmed that ATSS plays an important role in diseases and cell development and differentiation. However, exploration of its dynamic mechanisms remains insufficient. Identifying ATSS change points during cell differentiation is critical for elucidating potential dynamic mechanisms. For relative ATSS usage as percentage data, the existing methods lack sensitivity to detect the change point for ATSS longitudinal data. In addition, some methods have strict requirements for data distribution and cannot be applied to deal with this problem. In this study, the Bayesian change point detection model was first constructed using reparameterization techniques for two parameters of a beta distribution for the percentage data type, and the posterior distributions of parameters and change points were obtained using Markov Chain Monte Carlo (MCMC) sampling. With comprehensive simulation studies, the performance of the Bayesian change point detection model is found to be consistently powerful and robust across most scenarios with different sample sizes and beta distributions. Second, differential ATSS events in the real data, whose change points were identified using our method, were clustered according to their change points. Last, for each change point, pathway and transcription factor motif analyses were performed on its differential ATSS events. The results of our analyses demonstrated the effectiveness of the Bayesian change point detection model and provided biological insights into cell differentiation.

GammaBayes: a Bayesian pipeline for dark matter detection with CTA

We present GammaBayes, a Bayesian Python package for dark matter detection with the Cherenkov Telescope Array (CTA).GammaBayes takes as input the CTA measurements of gamma rays and a user-specified dark-matter particle model.It outputs the posterior distribution for parameters of the dark-matter model including the velocity-averaged cross section for dark-matter self interactions 〈σv〉 and the dark-matter mass mχ .It also outputs the Bayesian evidence, which can be used for model selection.We demonstrate GammaBayes using 525 hours of simulated data, corresponding to 108 observed gamma-ray events.The vast majority of this simulated data consists of noise, but 100000 events arise from the annihilation of scalar singlet dark matter with mχ = 1 TeV.We recover the dark matter mass within a 95% credible interval of mχ ∼ 0.96–1.07 TeV.Meanwhile, the velocity averaged cross section is constrained to 〈σv〉 ∼ 1.4–2.1 × 10-25 cm3 s-1 (95% credibility).This is equivalent to measuring the number of dark-matter annihilation events to be NS ∼ 1.1-0.2 +0.2 × 105.The no-signal hypothesis 〈σv〉 = 0 is ruled out with about 5σ credibility.We discuss how GammaBayes can be extended to include more sophisticated signal and background models and the computational challenges that must be addressed to facilitate these upgrades.The source code is publicly available here.