Markov Chain Monte Carlo Sampling Research Articles

Bayesian response adaptive randomization design with a composite endpoint of mortality and morbidity.

Allocating patients to treatment arms during a trial based on the observed responses accumulated up to the decision point, and sequential adaptation of this allocation, could minimize the expected number of failures or maximize total benefits to patients. In this study, we developed a Bayesian response-adaptive randomization (RAR) design targeting the endpoint of organ support-free days (OSFD) for patients admitted to the intensive care units. The OSFD is a mixture of mortality and morbidity assessed by the number of days of free of organ support within a predetermined post-randomization time-window. In the past, researchers treated OSFD as an ordinal outcome variable where the lowest category is death. We propose a novel RAR design for a composite endpoint of mortality and morbidity, for example, OSFD, by using a Bayesian mixture model with a Markov chain Monte Carlo sampling to estimate the posterior probability distribution of OSFD and determine treatment allocation ratios at each interim. Simulations were conducted to compare the performance of our proposed design under various randomization rules and different alpha spending functions. The results show that our RAR design using Bayesian inference allocated more patients to the better performing arm(s) compared to other existing adaptive rules while assuring adequate power and type I error rate control across a range of plausible clinical scenarios.

Quantum Definition of Molecular Structure.

Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics, despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of the molecular structure from fundamental quantum principles.

Identifying key sectors of sustainable development: A Bayesian framework estimating policy‐impacts in a general equilibrium

AbstractTransformation of the previous centrally growth‐oriented economic systems to a sustainable bio‐economy is a global political trend, where public policy is a key factor in making this successful. Designing effective and efficient policies requires understanding the linkages between policy choices and outcomes. Most existing studies are missing a direct link to policy choices and ignore fundamental model uncertainty present in policy analysis. We empirically estimate a sector‐specific, nested two‐stage policy impact function to address these shortcomings. We apply a Bayesian estimation approach that combines existing statistical data with a priori information from political experts, thus reducing data and estimation problems. This is linked with a Computable General Equilibrium to model the entire link from policies to outcomes. We derive a theoretical framework that allows the definition of indicators for key sectors of an efficient Pro‐Poor‐Growth strategy. In our generalized framework, we show that indicators based only on growth‐poverty linkages might be misleading. To deal with model uncertainty inherent in the application, we derive a set of metamodels via simulations conducted under different model parameter settings and apply Markov Chain Monte Carlo sampling. Applying Bayesian model selection allows drawing statistical inferences on competing models to generate relatively robust policy‐relevant messages even under model uncertainty. The approach is empirically applied to Ghana, Senegal, and Uganda, analyzing the allocation of public spending on agriculture under the Comprehensive Africa Agriculture Development Programme. [EconLit Citations: C11—Bayesian Analysis: General; C63—Computational Techniques, Simulation Modeling; D58—Computable and Other Applied General Equilibrium Models; O55—Africa; Q01—Sustainable Development; Q18—Agricultural Policy].

Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data

This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.

Bayesian mixed-effect higher-order hidden Markov models with applications to predictive healthcare using electronic health records

The disease progression dynamics in electronic health records often reflect patients’ health condition evolution, holding the promise of enabling the development of clinical predictive models. These dynamics, however, generally exist significant variability among patients due to some critical factors (e.g., gender and age) and patient-level heterogeneity. Moreover, future health state may not only depend on the current state but also more distant history states due to the complicated disease progression. To capture this complex transition behavior and address mixed effects in clinical prediction problems, we propose a novel and flexible Bayesian mixed-effect higher-order hidden Markov model (MHOHMM), and develop a classifier based on MHOHMMs. A range of MHOHMMs are designed to capture different data structures and the optimal one is identified by using the k-fold cross-validation. An effective two-stage Markov chain Monte Carlo (MCMC) sampling algorithm is designed for model inference. A simulation study is conducted to evaluate the performance of the proposed sampling algorithm and the MHOHMM-based classification method. The practical utility of the proposed framework is demonstrated by a case study on the acute hypotensive episode prediction for intensive care unit patients. Our results show that the MHOHMM-based framework provides good prediction performance.

A large deviation principle for the empirical measures of Metropolis–Hastings chains

To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to evaluate its efficiency. One approach is to consider the associated empirical measure and how fast it converges to the stationary distribution of the underlying Markov process. Recently, this question has been considered from the perspective of large deviation theory, for different types of MCMC methods, including, e.g., non-reversible Metropolis–Hastings on a finite state space, non-reversible Langevin samplers, the zig-zag sampler, and parallel tempering. This approach, based on large deviations, has proven successful in analysing existing methods and designing new, efficient ones. However, for the Metropolis–Hastings algorithm on more general state spaces, the workhorse of MCMC sampling, the same techniques have not been available for analysing performance, as the underlying Markov chain dynamics violate the conditions used to prove existing large deviation results for empirical measures of a Markov chain. This also extends to methods built on the same idea as Metropolis–Hastings, such as the Metropolis-Adjusted Langevin Method or ABC-MCMC. In this paper, we take the first steps towards such a large-deviations based analysis of Metropolis–Hastings-like methods, by proving a large deviation principle for the empirical measures of Metropolis–Hastings chains. In addition, we also characterize the rate function and its properties in terms of the acceptance- and rejection-part of the Metropolis–Hastings dynamics.

Bayesian tensor-on-tensor regression with efficient computation.

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression coefficient tensor. Traditional tensor regression methods making use of the Tucker decomposition either assume the dimension of the core tensor to be known or estimate it via cross-validation or some model selection criteria. However, no existing method can simultaneously estimate the model dimension (the dimension of the core tensor) and other model parameters. To fill this gap, we develop an efficient Markov Chain Monte Carlo (MCMC) algorithm to estimate both the model dimension and parameters for posterior inference. Besides the MCMC sampler, we also develop an ultra-fast optimization-based computing algorithm wherein the maximum a posteriori estimators for parameters are computed, and the model dimension is optimized via a simulated annealing algorithm. The proposed Bayesian framework provides a natural way for uncertainty quantification. Through extensive simulation studies, we evaluate the proposed Bayesian tensor-on-tensor regression model and show its superior performance compared to alternative methods. We also demonstrate its practical effectiveness by applying it to two real-world datasets, including facial imaging data and 3D motion data.

Probing Disk Ice Content and Polycyclic Aromatic Hydrocarbon Emission through Multiband MagAO+Clio Images of HD 141569

We present resolved images of the inner disk component around HD 141569A using the Magellan adaptive optics system with the Clio2 1–5 μm camera, offering a glimpse of a complex system thought to be in a short evolutionary phase between protoplanetary and debris disk stages. We use a reference star along with the Karhunen–Loéve image projection (KLIP) algorithm for point-spread function subtraction to detect the disk inward to about 0.″24 (∼25 au assuming a distance of 111 pc) at high signal-to-noise ratios at L′ (3.8 μm), Ls (3.3 μm), and narrowband Ice (3.1 μm). We identify an arc or spiral arm structure at the southeast extremity, consistent with previous studies. We implement forward modeling with a simple disk model within the framework of a Markov Chain Monte Carlo sampler to better constrain the geometrical attributes and photometry using our KLIP-reduced disk images. We then leverage these modeling results to facilitate a comparison of the measured brightness in each passband to find a reduction in scattered light from the disk in the Ice filter, implying significant absorption due to water ice in the dust. Additionally, our best-fit disk models exhibit peak brightness in the southwestern, back-scattering region of the disk, which we suggest to be possible evidence of 3.3 μm polycyclic aromatic hydrocarbon emission. However, we point out the need for additional observations with bluer filters and more complex modeling to confirm these hypotheses.

BICEPS: An improved characterization model for low- and intermediate-mass exoplanets

Context. The number of exoplanets with precise mass and radius measurements is constantly increasing thanks to novel ground- and space-based facilities such as HARPS, ESPRESSO, CHEOPS, and TESS. The accuracy and robustness of the planetary characterization largely depends on the quality of the data, but also requires a planetary structure model, capable of accurately modeling the interior and atmospheres of exoplanets over a large range of boundary conditions. Aims. Our goal is to provide an improved characterization model for planets with masses between 0.5 and 30 Earth masses, equilibrium temperatures below <2000 K, and a wide range of planetary compositions and physical phases. Methods. In this work, we present the Bayesian Interior Characterization of ExoPlanetS (BICEPS) model, which combines an adaptive Markov chain Monte Carlo sampling method with a state-of-the-art planetary structure model. BICEPS incorporates many recently developed equations of state suited for large ranges of pressures and temperatures, a description for solid and molten planetary cores and mantles, a gaseous envelope composed of hydrogen, helium, and water (with compositional gradients), and a non-gray atmospheric model. Results. We find that the usage of updated equations of state has a significant impact on the interior structure prediction. The impact varies, depending on the planetary composition. For dense rocky planets, BICEPS predicts radii a few percent different to prior internal structure models. For volatile rich planets, we find differences of 10% or even larger. When applying BICEPS to a particular exoplanet, TOI-130 b, we inferred a 25% larger water mass fraction and a 15% smaller core than previous models. Conclusions. The presented exoplanet characterization model is a robust method applicable over a large range of planetary masses, compositions, and thermal boundary conditions. We show the importance of implementing state-of-the-art equations of state for the encountered thermodynamic conditions of exoplanets. Hence, using BICEPS improves the predictive strength of the characterization process compared to previous methods.

Using mixture density networks to emulate a stochastic within-host model of Francisella tularensis infection.

For stochastic models with large numbers of states, analytical techniques are often impractical, and simulations time-consuming and computationally demanding. This limitation can hinder the practical implementation of such models. In this study, we demonstrate how neural networks can be used to develop emulators for two outputs of a stochastic within-host model of Francisella tularensis infection: the dose-dependent probability of illness and the incubation period. Once the emulators are constructed, we employ Markov Chain Monte Carlo sampling methods to parameterize the within-host model using records of human infection. This inference is only possible through the use of a mixture density network to emulate the incubation period, providing accurate approximations of the corresponding probability distribution. Notably, these estimates improve upon previous approaches that relied on bacterial counts from the lungs of macaques. Our findings reveal a 50% infectious dose of approximately 10 colony-forming units and we estimate that the incubation period can last for up to 11 days following low dose exposure.

A two-stage stochastic programming approach for dynamic OD estimation using LBSN data

Estimating origin–destination (OD) demand is essential for urban transport management and traffic control systems. With the ubiquity of smartphones, location based social networks (LBSN) data has emerged as a new rich data source with broad urban spatial and temporal coverage highly suitable for OD estimation. Its nature of confirmed trip purpose (activity) and activity chain host makes it more advantageous than other data (e.g., household travel surveys and traffic network detection). On the other hand, LBSN data is a more direct and accurate representation of demand patterns and can remove the significant burden of developing traffic models and estimating simulation-based objective functions. However, thus far, most LBSN-based estimation models only focus on static (day-level) OD estimation, making less use of those characteristics. To this end, this paper establishes a two-stage stochastic programming (TSSP) framework integrating the activity chains to model activity-level dynamic mobility flows using LBSN data. The first-stage model aims to minimize the errors introduced by the inter-zone OD flows alongside the expected errors of the check-in patterns. The second-stage model attempts to minimize the errors produced by the considered check-in pattern scenarios. Markov chain Monte Carlo (MCMC) sampling is used to generate plausible check-in scenarios. A generalized Benders decomposition (GBD) algorithm is presented to solve the two-stage stochastic programming model. We conduct the experiments on the case study of Tokyo, Japan, under the employment of the generalized least squares (GLS) estimator. The results show that algorithm convergence can be guaranteed within several iterations. The approach can provide satisfactory estimations of check-in patterns, zonal production and attraction, and OD flows. Furthermore, multiple objective function states are tested for evaluating the completeness of the proposed framework and exploring its potential for simplification and extension. Incorporating specific penalty terms into the objective function also provides a way to verify the reliability of the two-stage structure and validate the effectiveness of the model. Finally, we discuss the model enhancement from the perspectives of online OD estimation by integrating with LBSN simulations, network-wide OD extrapolation using appropriate scaling methods, and removing the user-side data requirement by leveraging activity chain modeling. The proposed framework provides a novel and effective approach to OD demand estimation using LBSN data.

SEAM: An integrated activation-coupled model of sentence processing and eye movements in reading

Models of eye-movement control during reading, developed largely within psychology, usually focus on visual, attentional, lexical, and motor processes but neglect post-lexical language processing; by contrast, models of sentence comprehension processes, developed largely within psycholinguistics, generally focus only on post-lexical language processes. We present a model that combines these two research threads, by integrating eye-movement control and sentence processing. Developing such an integrated model is extremely challenging and computationally demanding, but such an integration is an important step toward complete mathematical models of natural language comprehension in reading. We combine the SWIFT model of eye-movement control (Seelig et al., 2023) with key components of the Lewis and Vasishth sentence processing model (Lewis and Vasishth, 2005). This integration becomes possible, for the first time, due in part to recent advances in successful parameter identification in dynamical models, which allows us to investigate profile log-likelihoods for individual model parameters. We present a fully implemented proof-of-concept model demonstrating how such an integrated model can be achieved; our approach includes Bayesian model inference with Markov Chain Monte Carlo (MCMC) sampling as a key computational tool. The integrated Sentence-Processing and Eye-Movement Activation-Coupled Model (SEAM) can successfully reproduce eye movement patterns that arise due to similarity-based interference in reading. To our knowledge, this is the first-ever integration of a complete process model of eye-movement control with linguistic dependency completion processes in sentence comprehension. In future work, this proof of concept model will need to be evaluated using a comprehensive set of benchmark data.

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global analysis of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalizing flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

Fast and robust quantification of uncertainty in non-linear diffusion MRI models

Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.

Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering

Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs. For an Erd\H{o}s-Renyi random graph, we identify a threshold probability at which with high probability the symmetric edge polytope shares many facet-supporting hyperplanes with that of a complete graph. We also investigate the relationship between the average local clustering, also known as the Watts-Strogatz clustering coefficient, and the number of facets for graphs with either a fixed number of edges or a fixed degree sequence. We use well-known Markov Chain Monte Carlo sampling methods to generate empirical evidence that for a fixed degree sequence, higher average local clustering in a connected graph corresponds to higher facet numbers in the associated symmetric edge polytope.

Statistical landslide susceptibility assessment using Bayesian logistic regression and Markov Chain Monte Carlo (MCMC) simulation with consideration of model class selection

ABSTRACT Landslide susceptibility mapping (LSM) plays an essential role in landslide management and contributes to decision-makers and planners to formulate landslide prevention policies. It is often carried out by predicting possibility of landslide occurrence first from numerous landslides conditioning factors (LCFs), followed by partitioning areas with different landslide susceptibility levels. Numerous methods have been proposed for such a purpose, saying logistic regression (LR), deep learning methods, etc. Among these methods, LR is the most widely used in literature, which may be attributed to its good performance and easy-to-follow. However, few studies explore uncertainty and reliability of the LR in LSM. Furthermore, not all LCFs contribute significantly to the landslide occurrence, saying elevation, distance to roads, etc. How to objectively determine the most relevant LCFs is another issue that remains unsolved. This study proposes a Bayesian LR method for landslide susceptibility assessment (LSA), together with Markov Chain Monte Carlo (MCMC) simulation for parameter estimation. MCMC samples are used to determine the optimal model, and to quantify the uncertainty associated with the LSM. Real-life data from Shaanxi Province are used for illustration. Results show that the proposed method works reasonably well in determination of the optimal model and in uncertainty quantification in LSM.

Machine-learning-accelerated simulations to enable automatic surface reconstruction.

Understanding material surfaces and interfaces is vital in applications such as catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can, in principle, predict the structure of material surfaces as a function of thermodynamic variables. However, accurate energy simulations are prohibitive when coupled to the vast phase space that must be statistically sampled. Here we present a bi-faceted computational loop to predict surface phase diagrams of multicomponent materials that accelerates both the energy scoring and statistical sampling methods. Fast, scalable and data-efficient machine learning interatomic potentials are trained on high-throughput density-functional-theory calculations through closed-loop active learning. Markov chain Monte Carlo sampling in the semigrand canonical ensemble is enabled by using virtual surface sites. The predicted surfaces for GaN(0001), Si(111) and SrTiO3(001) are in agreement with past work and indicate that the proposed strategy can model complex material surfaces and discover previously unreported surface terminations.

Bayesian Structural Time Series Model for Forecasting the Composite Stock Price Index in Indonesia

One of the models that can be used to predict time series data is the Bayesian Structural Time Series (BSTS) model. The BSTS model is a more modern model and can handle data movement better. In the BSTS model, the Markov Chain Monte Carlo (MCMC) sampling algorithm is used to simulate the posterior distribution, which smoothes the forecasting results over a large number of potential models using Bayesian averaging models. The purpose of this study was to obtain the best BSTS model for Composite Stock Price Index (CSPI) data in Indonesia based on the state component and the number of MCMC iterations, and obtain forecasting results for CSPI value in Indonesia for the next 24 months, namely the period July 2023 to June 2024. The results obtained are based on a comparison of the R-square values in the model, the BSTS model with local linear trend and seasonal state components, and the number of MCMC iterations n = 5 00 is the best BSTS model that can be used for forecasting the CSPI value in Indonesia with an R-square value of 99.96%. The results of forecasting the CSPI value in Indonesia for the period July 2023 to June 2024 range from 6589 to 6760, with the lowest forecasting value in October 2023 and the highest in March 2023.

Estimation of site-specific multivariate probability distribution of soil properties using a mixed sampling technique

Estimation of multivariate probability density function (PDF) of soil properties based on limited site investigation data plays an important role in data driven-based geotechnical engineering analysis and design. However, this estimation is often intractable because the site-specific investigation data generally are multivariate, uncertain and unique, sparse, incomplete, sometimes corrupt and spatially variable. The estimation is more challenging when the uncertainties in model parameters of the distribution (i.e., mean, standard deviations and scale of fluctuation of soil properties) are taken into consideration. To address these difficulties, this study proposed a mixed sampling technique by combing the Gibbs sampler and transitional Markov Chain Monte Carlo sampler to effectively estimate the multivariate probability density function of soil properties. The proposed method is demonstrated through a virtual site example while the effect of statistical uncertainty in the scale of fluctuation on reliability analyses is illustrated in an infinite slope example. It is shown that the proposed method can not only handle the complex features of site investigation data but also effectively quantify the statistical uncertainties of the mean values, standard deviations and scale of fluctuation of the investigated soil properties. Ignoring the statistical uncertainties of scale of fluctuation can affect the estimation of mean and standard deviations of the soil parameters. When considering the statistical uncertainty of scale of fluctuation, the 95% confidence intervals for the profiles of the soil properties can rationally cover the actual soil data at the unobserved points. Ignoring the statistical uncertainty of scale of fluctuation can lead to the underestimation of the probability of failure of the infinite slope.

Rayleigh Wave Dispersion and Inversion for Shallow Surface with a High-velocity Rigid Pavement

We investigate the rigid pavement influence on phase velocity dispersion of the Rayleigh wave by using numerical modeling. An overestimation of Rayleigh wave phase velocity is observed more than 10% deviation caused by high-velocity rigid pavement. Based on the generalized reflection and transmission (R/T) coefficient method, the linear eigenvalue problem is solved for vertically heterogeneous media with a rigid pavement structure. The secular function demonstrates the multi-valuedness which is different phase velocity at the same frequency for the single Rayleigh mode. To address mode misidentification problem, we adopt a new misfit function for multimodal dispersion inversion. A Markov chain Monte Carlo (MCMC) sampling algorithm is used to solve dispersion inversion. The synthetic test shows that Rayleigh wave dispersion inversion incorporating a pavement layer can improve estimation accuracy of shear wave velocity.