Monte Carlo Algorithm Research Articles

Quantified difference of the collapsed cone convolution (CCC) and Monte Carlo (MC) algorithms based on DVH and gamma analysis for cervical cancer radiation therapy

Quantified difference of the collapsed cone convolution (CCC) and Monte Carlo (MC) algorithms based on DVH and gamma analysis for cervical cancer radiation therapy

Variance estimation for sequential Monte Carlo algorithms: A backward sampling approach

Variance estimation for sequential Monte Carlo algorithms: A backward sampling approach

Bayesian analysis of joint quantile regression for multi-response longitudinal data with application to primary biliary cirrhosis sequential cohort study.

This article proposes a Bayesian approach for jointly estimating marginal conditional quantiles of multi-response longitudinal data with multivariate mixed effects model. The multivariate asymmetric Laplace distribution is employed to construct the working likelihood of the considered model. Penalization priors on regression parameters are incorporated into the working likelihood to conduct Bayesian high-dimensional inference. Markov chain Monte Carlo algorithm is used to obtain the fully conditional posterior distributions of all parameters and latent variables. Monte Carlo simulations are conducted to evaluate the sample performance of the proposed joint quantile regression approach. Finally, we analyze a longitudinal medical dataset of the primary biliary cirrhosis sequential cohort study to illustrate the real application of the proposed modeling method.

Synchrotron x-ray spectra characterisation for radiation therapy applications at the ESRF - ID17 Biomedical beamline

Abstract Objective: Radiation therapy requires reliable dosimetry protocols to deliver successful treatments with high accuracy and precision. In this context, accurate knowledge of the beam’s energy spectra is mandatory. The goal of this study was to validate the synchrotron X-ray spectrum of the ID17 beamline at the European Synchrotron Radiation Facility (ESRF). The modification of the synchrotron storage ring and beamline in recent years necessitates a new characterisation of the radiation spectra of the ID17 beamline. The validated spectra will be a starting point for possible future clinical applications.
Approach: The half value layer method was used to measure the attenuation of the X-ray spectrum in Al and Cu. Experimental data was validated against theoretical data produced using OASYS; an in-house developed software for calculating beamline spectra. Two different spectral configurations, “conventional” and “clinical”, were investigated. The characterised spectra were used to perform dosimetric validation of depth dose profiles measured in a water-equivalent phantom. The dose profile was measured using two different detectors and compared with calculations generated using two different Monte Carlo algorithms.
Main results: The results showed good agreement between measured and predicted half value layers, with differences of less than 1%. Excellent agreement to within 3% was obtained, an agreement that satisfies the requirements in conventional radiotherapy for approvable treatment planning.
Significance: Accurate spectra have been defined and validated for the ESRF – ID17 Biomedical beamline. The validated spectra can be used as input for future dosimetric studies and treatment planning systems in the context of preclinical studies and possible future clinical trials.

Quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs

Quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs

Bayesian compositional models for ordinal response.

Ordinal response is commonly found in medicine, biology, and other fields. In many situations, the predictors for this ordinal response are compositional, which means that the sum of predictors for each sample is fixed. Examples of compositional data include the relative abundance of species in microbiome data and the relative frequency of nutrition concentrations. Moreover, the predictors that are strongly correlated tend to have similar influence on the response outcome. Conventional cumulative logistic regression models for ordinal responses ignore the fixed-sum constraint on predictors and their associated interrelationships, and thus are not appropriate for analyzing compositional predictors.To solve this problem, we proposed Bayesian Compositional Models for Ordinal Response to analyze the relationship between compositional data and an ordinal response with a structured regularized horseshoe prior for the compositional coefficients and a soft sum-to-zero restriction on coefficients through the prior distribution. The method was implemented with R package rstan using efficient Hamiltonian Monte Carlo algorithm. We performed simulations to compare the proposed approach and existing methods for ordinal responses. Results revealed that our proposed method outperformed the existing methods in terms of parameter estimation and prediction. We also applied the proposed method to a microbiome study HMP2Data, to find microorganisms linked to ordinal inflammatory bowel disease levels. To make this work reproducible, the code and data used in this paper are available at https://github.com/Li-Zhang28/BCO.

A generalized stochastic block model for overlapping community detection

Abstract Over the past two decades, community detection has been extensively explored. Yet, the challenge of identifying overlapping communities remains unresolved. In this letter, we introduces a novel approach called the generalized stochastic block model, which addresses this issue by allowing nodes to belong to multiple communities. This approach extends the traditional representation of nodal community assignment from a single community label to a label vector, with each element indicating the membership of a node in a specific community. To tackle this model, we develop a Markov Chain Monte Carlo algorithm. Through numerical experiments conducted on synthetic and empirical networks, we demonstrate the efficacy of our proposed framework in accurately detecting overlapping communities.

Methodological refinement of the submillimeter galaxy magnification bias. I. Cosmological analysis with a single redshift bin

The main goal of this work is to test the results of a methodological improvement in the measurement of the magnification bias signal on a sample of submillimeter galaxies. In particular, we investigate the constraining power of cosmological parameters within the Lambda CDM model. We also discuss important points that can affect the results. We measured the angular cross-correlation function between a sample of foreground GAMA II galaxies in a single wide spectroscopic redshift bin of $0.2<z<0.8$ and a sample of background submillimeter galaxies from Herschel-ATLAS. We focused on the photometric redshift range of $1.2<z<4.0,$ with an improved methodological framework. Interpreting the weak lensing signal within the halo model formalism and performing a Markov chain Monte Carlo (MCMC) algorithm, we obtained the posterior distribution of both the halo occupation distribution and cosmological parameters within a flat Lambda CDM model. Our analysis was also performed with additional galaxy clustering information via a foreground angular auto-correlation function. We observed an overall remarkable improvement in terms of uncertainties in both the halo occupation distribution and cosmological parameters with respect to previous results. A priori knowledge about beta , the logarithmic slope of the background integral number counts, is found to be paramount to derive constraints on $ when using the cross-correlation data alone. Assuming a physically motivated prior distribution for beta , we obtain mean values of $ $ and $ $ and an unconstrained distribution for the Hubble constant. These results are likely to suffer from sampling variance, since one of the fields, G15, appears to have an anomalous behavior with a systematically higher cross-correlation. We find that removing it from the sample yields mean values of $ $ and $ $ and, for the first time, a (loose) restriction of the Hubble constant is obtained via this observable: $h=0.79^ $. The addition of the angular auto-correlation of the foreground sample in a joint analysis tightens the constraints, but also reveals a discrepancy between both observables that might be an aggravated consequence of sampling variance or due to the presence of unmodeled aspects on small and intermediate scales.

Bayesian joint inversion of seismic and electromagnetic data for reservoir lithofluid facies, including geophysical and petrophysical rock properties

A Bayesian approach is developed to estimate lithofluid facies and other rock properties conditioned on seismic and electromagnetic data for reservoir characterization. Prior distributions are assumed to be facies-related Gaussian modes of geophysical rock properties directly acquired or converted from petrophysical properties by calibrated rock-physics modeling. An original generalization includes two distributions in the same marginalization integral, analytically solved under a linearized Gaussian assumption to provide a facies model likelihood conditioned on geophysical data. Because computing this probability for all possible facies configurations may be impractical, a Markov chain Monte Carlo algorithm efficiently samples models to provide a full posterior distribution. The linearized Gaussian approach allows the computation of the conditional distributions of geophysical and petrophysical rock properties by applying local deterministic inversions over the many sampled facies models. The inversion uses simulated geophysical data from a 1D synthetic model based on the geologic scenario and a well from a selected marine oil field. Two other wells from the same reservoir are used to gather prior distributions. Data from the well, calibration of the rock-physics modeling, and facies matching between the priors and the synthetic model are presented and discussed. Numerical tests validate nonlinear forward-modeling adaptations based on the assumed linearized Gaussian approach. The simulated stand-alone and joint geophysical data sets are then inverted for lithofluid facies models under different prior inputs. Two challenging geoelectric scenarios also are tested, one with lower resistivity contrasts and another with a misguided background model. All results demonstrate a gain in precision and accuracy when associating these geophysical signals to estimate the oil column. Facies-conditioned inversions for the rock properties also indicate potential for quantitative reservoir interpretations.

Order selection for heterogeneous semiparametric hidden Markov models.

Hidden Markov models (HMMs), which can characterize dynamic heterogeneity, are valuable tools for analyzing longitudinal data. The order of HMMs (ie, the number of hidden states) is typically assumed to be known or predetermined by some model selection criterion in conventional analysis. As prior information about the order frequently lacks, pairwise comparisons under criterion-based methods become computationally expensive with the model space growing. A few studies have conducted order selection and parameter estimation simultaneously, but they only considered homogeneous parametric instances. This study proposes a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation of heterogeneous semiparametric HMMs. To overcome the difficulties in updating the order, we create a brand-new Markov chain Monte Carlo algorithm coupled with an effective adjust-bound reversible jump strategy. Simulation results reveal that the proposed BDP procedure performs well in estimation and works noticeably better than the conventional criterion-based approaches. Application of the suggested method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness.

Structure and Ultrafast X-ray Diffraction of the Hydrated Metaphosphate.

We study the pathway of metaphosphate hydration when a metaphosphate anion is dissolved in liquid water with an explicit water model. For this purpose, we propose a sequential Monte Carlo algorithm incorporated with the ab initio quantum mechanics/molecular mechanics (QM/MM) method, which can reduce the amount of ab initio QM/MM sampling while retaining the accuracy of the simulation. We demonstrate the numerical calculation of the standard enthalpy change for the successive addition reaction PO3-·2H2O + H2O ⇌ PO3-·3H2O in the liquid phase, which helps to clarify the hydration pathway of the metaphosphate. With the obtained hydrated structure of the metaphosphate anion, we perform ab initio calculations for its relaxation dynamics upon vibrational excitation and characterize the energy transfer process in solution with simulated ultrafast X-ray diffraction signals, which can be experimentally implemented with X-ray free-electron lasers.

Clinical feasibility of deep learning-based synthetic CT images from T2-weighted MR images for cervical cancer patients compared to MRCAT

This work aims to investigate the clinical feasibility of deep learning-based synthetic CT images for cervix cancer, comparing them to MR for calculating attenuation (MRCAT). Patient cohort with 50 pairs of T2-weighted MR and CT images from cervical cancer patients was split into 40 for training and 10 for testing phases. We conducted deformable image registration and Nyul intensity normalization for MR images to maximize the similarity between MR and CT images as a preprocessing step. The processed images were plugged into a deep learning model, generative adversarial network. To prove clinical feasibility, we assessed the accuracy of synthetic CT images in image similarity using structural similarity (SSIM) and mean-absolute-error (MAE) and dosimetry similarity using gamma passing rate (GPR). Dose calculation was performed on the true and synthetic CT images with a commercial Monte Carlo algorithm. Synthetic CT images generated by deep learning outperformed MRCAT images in image similarity by 1.5% in SSIM, and 18.5 HU in MAE. In dosimetry, the DL-based synthetic CT images achieved 98.71% and 96.39% in the GPR at 1% and 1 mm criterion with 10% and 60% cut-off values of the prescription dose, which were 0.9% and 5.1% greater GPRs over MRCAT images.

Bayesian Mechanistic Inference, Statistical Mechanics, and a New Era for Monte Carlo.

On the one hand, much of computational chemistry is concerned with "bottom-up" calculations which elucidate observable behavior starting from exact or approximated physical laws, a paradigm exemplified by typical quantum mechanical calculations and molecular dynamics simulations. On the other hand, "top down" computations aiming to formulate mathematical models consistent with observed data, e.g., parametrizing force fields, binding or kinetic models, have been of interest for decades but recently have grown in sophistication with the use of Bayesian inference (BI). Standard BI provides an estimation of parameter values, uncertainties, and correlations among parameters. Used for "model selection," BI can also distinguish between model structures such as the presence or absence of individual states and transitions. Fortunately for physical scientists, BI can be formulated within a statistical mechanics framework, and indeed, BI has led to a resurgence of interest in Monte Carlo (MC) algorithms, many of which have been directly adapted from or inspired by physical strategies. Certain MC algorithms─notably procedures using an "infinite temperature" reference state─can be successful in a 5-20 parameter BI context which would be unworkable in molecular spaces of 103 coordinates and more. This Review provides a pedagogical introduction to BI and reviews key aspects of BI through a physical lens, setting the computations in terms of energy landscapes and free energy calculations and describing promising sampling algorithms. Statistical mechanics and basic probability theory also provide a reference for understanding intrinsic limitations of Bayesian inference with regard to model selection and the choice of priors.

A Hybrid Monte Carlo study of argon solidification

Abstract A GPU-based implementation of the Hybrid Monte Carlo (HMC) algorithm is presented to explore its utility in the chemistry of solidification at the example of liquid to solid argon. We validate our implementation by comparing structural characteristics of argon fluid-like phases from HMC and MD simulations. Examining solidification, both MD and HMC show similar trends. Despite observable differences, MD simulations and HMC agree within the errors during the phase transition. Introducing voids decreases the solidification temperature, aiding in the formation of a well-structured solids. Further, our findings highlight the importance of larger system sizes in simulating solidification processes. Simulations with a temperature dependent potential show ambiguous results for the solidification which may be attributed to the small system sizes. Future work aims to expand HMC capabilities for complex chemical phenomena in phase transitions.

Bayesian tensor network structure search and its application to tensor completion

Tensor network (TN) has demonstrated remarkable efficacy in the compact representation of high-order data. In contrast to the TN methods with pre-determined structures, the recently introduced tensor network structure search (TNSS) methods automatically learn a compact TN structure from the data, gaining increasing attention. Nonetheless, TNSS requires time-consuming manual adjustments of the penalty parameters that control the model complexity to achieve better performance, especially in the presence of missing or noisy data. To provide an effective solution to this problem, in this paper, we propose a parameters tuning-free TNSS algorithm based on Bayesian modeling, aiming at conducting TNSS in a fully data-driven manner. Specifically, the uncertainty in the data corruption is well-incorporated in the prior setting of the probabilistic model. For TN structure determination, we reframe it as a rank learning problem of the fully-connected tensor network (FCTN), integrating the generalized inverse Gaussian (GIG) distribution for low-rank promotion. To eliminate the need for hyperparameter tuning, we adopt a fully Bayesian approach and propose an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior distribution sampling. Compared with the previous TNSS method, experiment results demonstrate the proposed algorithm can effectively and efficiently find the latent TN structures of the data under various missing and noise conditions and achieves the best recovery results. Furthermore, our method exhibits superior performance in tensor completion with real-world data compared to other state-of-the-art tensor-decomposition-based completion methods.

Analysis of generalized type-II progressively hybrid Lindley-exponential data and its modeling in physics, engineering, and management

The life test is guaranteed to end at a predetermined time using a novel type-II generalized progressively hybrid censoring method that is investigated when the test participants’ lifetime model has a two-parameter Lindley-exponential (LndE) distribution. The LndE characteristics are estimated using Bayes and maximum likelihood inference techniques when the suggested censored data are present. By employing the normal approximation of each unknown quantity, the estimated confidence intervals are also constructed. Additionally, independent gamma density priors are used to generate the Bayesian estimators under symmetrical (squared error) loss. Since the likelihood function is formulated in a difficult manner, the Bayes estimators and their corresponding greatest posterior density intervals cannot be computed theoretically, but they may be evaluated using Markov-chain Monte Carlo algorithms. The most progressive design is then determined by applying four optimality criteria. Using Monte Carlo comparisons, the efficiency of the proposed estimating processes is evaluated, and some suggestions are made. In the end, the usefulness of the suggested methods that may be applied in practical situations is demonstrated by analyzing three distinct applications: physics, engineering, and management. When the experimenter’s primary concern is the test’s duration, the numerical findings revealed that the sampling strategy is adaptable and incredibly successful in finishing the experiment in a variety of realistic scenarios.

Stochastic inversion of fracture networks using the reversible jump Markov chain Monte Carlo algorithm

Characterization of fracture networks is essential in the production optimization or storage calculation for enhanced geothermal systems or geologic carbon storage. A novel inversion approach is proposed for estimating the fracture networks in this research. The discrete fracture network technique is adopted to probabilistically describe various fracture parameters such as trace length, midpoint position or azimuthal angle. The reversible jump Markov chain Monte Carlo algorithm is applied to explore the target posterior distribution of model parameters of differing dimensionality, in which the number of fractures is assumed to be unknown. More specifically, the birth-death strategy is utilized to perturb the fracture number iteratively in the sampling process. The proposed methodology is applied with two different types of observational datasets, namely the head records from steady-state flow simulation and the acoustic impedance obtained from seismic inversion. The sampling results can successfully recover the fracture geometry in the observed domain, and the number of fractures in the system can be retrieved as well. Benchmarked on multiple Markov chain trials, the technique of parallel tempering can greatly improve the convergence efficiency and increase the diversity of sampled posterior models, through the random swapping of model states across the whole temperature ladder.

Size optimization of a stand-alone solar-wind-battery hybrid system for net zero energy buildings: A case study

In this research, a solar-wind-battery hybrid system (PV/WT/BS) is proposed to supply the electricity demand of a stand-alone net zero energy building. for estimating the output power of the hybrid system, wind speed and solar irradiance are measured throughout a year and their uncertainties are estimated by applying the Monte Carlo algorithm. The wind speed Wiebull distribution is estimated, and the solar irradiance distribution is obtained using a novel approach based on the sky cloudiness parameter. Moreover, to simulate the performance of the hybrid system components according to the actual conditions, their availability is calculated using failure and repair rates. The optimal size of the proposed hybrid system is calculated considering, for the first time, the reliability and system costs. The system's size is optimized through the consideration of key decision variables, including photovoltaic panel area, rated power, wind turbine tower height, and battery capacity. Two distinct optimization methods are employed: a single-objective approach utilizing Genetic Algorithm, where the total system cost is minimized with reliability as a constraint, and a double-objective approach using NSGA-II, considering both initial cost and reliability as objectives. The optimal system size is determined through an efficient decision-making process. A practical case study is conducted, monitoring wind speed, solar irradiance, and electricity demand of a residential building at 15-minute intervals over a year. The results reveal the efficacy of the optimization methods, with the single-objective approach yielding a total system cost of €75,495 and reliability of 95.19%, while the double-objective optimization achieves a cost of €73,460 and a reliability of 91.88%.

A Fast Monte Carlo Algorithm for Evaluating Matrix Functions with Application in Complex Networks

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods, which only work with one entry at a time, resulting in a significantly better convergence rate than the original approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with remarkable efficiency.

Emulation techniques for scenario and classical control design of tokamak plasmas

The optimization of scenarios and design of real-time-control in tokamaks, especially for machines still in design phase, requires a comprehensive exploration of solutions to the Grad–Shafranov (GS) equation over a high-dimensional space of plasma and coil parameters. Emulators can bypass the numerical issues in the GS equation, if a large enough library of equilibria is available. We train an ensemble of neural networks to emulate the typical shape-control targets (separatrix at midplane, X-points, divertor strike point, flux expansion, and poloidal beta) as a function of plasma parameters and active coil currents for the range of plasma configurations relevant to spherical tokamaks with a super-X divertor, with percent-level accuracy. This allows a quick calculation of the classical-control shape matrices, potentially allowing real-time calculation at any point in a shot with submillisecond latency. We devise a hyperparameter sampler to select the optimal network architectures and quantify uncertainties on the model predictions. To generate the relevant training set, we devise a Markov-chain Monte Carlo algorithm to produce large libraries of forward Grad–Shafranov solutions without the need for user intervention. The algorithm promotes equilibria with desirable properties, while avoiding parameter combinations resulting in problematic profiles or numerical issues in the integration of the GS equation.