Markov Chain Monte Carlo Approach Research Articles

First Light Curve Analysis of NSVS 8294044, V1023 Her, and V1397 Her Contact Binary Systems

The first photometric light curve investigation of the NSVS 8294044, V1023 Her, and V1397 Her binary systems is presented. We used ground-based observations for the NSVS 8294044 system and Transiting Exoplanet Survey Satellite data for V1023 Her and V1397 Her. The primary and secondary times of minima were extracted from all the data, and, by collecting the literature, a new ephemeris was computed for each system. Linear fits for the O − C diagrams were conducted using the Markov Chain Monte Carlo (MCMC) method. Light curve solutions were performed using the PHysics Of Eclipsing BinariEs Python code and the MCMC approach. The systems were found to be contact binary stars based on the fillout factor and mass ratio. V1023 Her showed the O’Connell effect, and a cold starspot on the secondary component was required for the light curve solution. The absolute parameters of the system were estimated based on an empirical relationship between orbital period and mass. We presented a new T–M equation based on a sample of 428 contact binary systems and found that our three target systems were in good agreement with the fit. The positions of the systems were also depicted on the M–L, M–R, q–L ratio, and M tot–J 0 diagrams in the logarithmic scales.

Bidirectional machine learning-assisted sensitivity-based stochastic searching approach for groundwater DNAPL source characterization.

In this study, we designed a machine learning-based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input-output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input-output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD-PSO-MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD-PSO-MC inversion outputs was more precise than that obtained using the multichain MCMC approach.

Exploring Universe acceleration through observational constraints via Hubble parameter reconstruction

In this article, we introduce an innovative parametric representation of the Hubble parameter, providing a model-independent means to explore the dynamics of an accelerating cosmos. The model's parameters are rigorously constrained through a Markov Chain Monte Carlo (MCMC) approach, leveraging a comprehensive dataset consisting of 31 data points from cosmic chronometers (CC), 1701 updated observations of Pantheon supernovae type Ia (SNeIa), and 6 data points from baryonic acoustic oscillations (BAO). Our analysis delves into the behavior of various cosmological parameters within the model, including the transition from a decelerating phase to an accelerating one, as well as the density parameters and the equation of state (EoS) parameter. The outcomes of our investigation reveal that the equation of state parameter aligns with characteristics reminiscent of the phantom model, supporting the prevailing understanding of our universe's current state of acceleration. This research contributes valuable insights into the ongoing cosmic expansion and underscores the utility of our novel parametric approach.

Stochastic seismic acoustic impedance inversion via a Markov-chain Monte Carlo method using a single GPU card

Seismic acoustic impedance inversion plays an important role in understanding subsurface structures and obtaining subsurface properties. The stochastic approach is one of the methods used for impedance inversion, and it aims to produce more reliable results by accounting for modeling uncertainty. Stochastic inversion represents the uncertainty of a subsurface model as a probability distribution and uses this distribution to estimate model parameters. In this study, seismic acoustic impedance inversion was performed using a Markov-chain Monte Carlo approach, which is a sampling method used in the stochastic process. Utilizing Bayesian inference based on prior information and observed data, we implemented acceptance probabilities and performed acoustic impedance inversion for field data through iterative calculations. We employed a single GPU card to execute the inversion algorithm and conducted a comparative analysis with the results obtained using a cluster composed of multiple CPU cores. Through a computational speed analysis, the efficiency of the algorithm using a GPU was verified, while uncertainty analysis was employed for algorithm validation. Through these analyses, we confirmed the feasibility of applying our developed GPU algorithm to tasks that require the inversion of extensive data, such as high-resolution seismic exploration and CO2 storage monitoring.

Hyper-local source strength retrieval and apportionment of black carbon in an urban area

Neighborhood-scale air pollution hotspots have recently been identified through detailed field campaigns, including the 100x100 Black Carbon Experiment which took place in West Oakland, CA, in 2017. Here, high-resolution nested atmospheric simulations are used together with a Bayesian inversion framework to estimate source apportionment at the hyper-local scale for a neighborhood in West Oakland. Forward simulations are performed with the Weather Research and Forecasting (WRF) model using 6 grid nests from 11.25 km to 2 m horizontal resolution. On the finest grid, building geometries are resolved using the immersed boundary method. Seven point sources and four line sources at known locations are included in the forward simulation for two 1-h periods during the 2017 field campaign. Data from 12 black carbon sensors are used to perform source inversion using a Markov Chain Monte Carlo approach, which provides a probability distribution for each of the 11 source strengths. From this, a most-likely plume can be created using the peaks of the distributions, and source apportionment can be estimated for each sensor. In addition, a composite plume can be constructed to indicate 90% confidence that concentrations are above or below a specified value. With this probabilistic analysis, it is possible to determine that more than half of the neighborhood has black carbon concentrations of higher than 0.4 μg/m3, with some areas higher than 3 μg/m3 during the time periods studied.

Simultaneously unveiling the EBL and intrinsic spectral parameters of gamma-ray sources with Hamiltonian Monte Carlo

The Extragalactic Background Light (EBL) is the main radiation field responsible for attenuating extragalactic gamma-ray emission at very high energies, but its precise spectral intensity is not fully determined. Therefore, disentangling propagation effects from the intrinsic spectral properties of gamma-ray sources (such as active galactic nuclei, AGN) is the primary challenge to interpret observations of these objects. We present a Bayesian and Markov Chain Monte Carlo approach to simultaneously infer parameters characterizing the EBL and the intrinsic spectra in a combined fit of a set of sources, which has the advantage of easily incorporating the uncertainties of both sets of parameters into one another through marginalization of the posterior distribution. Taking a sample of synthetic blazars observed by the ideal CTA configuration, we study the effects on the EBL constraints of combining multiple observations and varying their exposure. We also apply the methodology to a set of 65 gamma-ray spectra of 36 different AGNs measured by current Imaging Atmospheric Cherenkov Telescopes, using Hamiltonian Monte Carlo as a solution to the difficult task of sampling in spaces with a high number of parameters. We find robust constraints in the mid-IR region while simultaneously obtaining intrinsic spectral parameters for all of these objects. In particular, we identify Markarian 501 (Mkn 501) flare data (HEGRA/1997) as essential for constraining the EBL above 30 μm.

Anisotropic Reversible‐Jump McMC Shear‐Velocity Tomography of the Eastern Alpine Crust

AbstractThe eastern Alpine crust has been shaped by the continental collision of the European and Adriatic plates beginning at 35 Ma and was affected by a major reorganization after 20 Ma. To better understand how the eastern Alpine surface structures link with deep seated processes, we analyze the depth‐dependent seismic anisotropy based on Rayleigh wave propagation. Ambient noise recordings are evaluated to extract Rayleigh wave phase dispersion measurements. These are inverted in a two step approach for the azimuthally anisotropic shear velocity structure. Both steps are performed with a reversible jump Markov chain Monte Carlo (rj‐McMC) approach that estimates data errors and propagates the modeled uncertainties from the phase velocity maps into the depth inversion. A two layer structure of azimuthal anisotropy is imaged in the Alpine crust, with an orogen‐parallel upper crust and approximately orogen‐perpendicular layer in the lower crust and the uppermost mantle. In the upper layer, the anisotropy tends to follow major fault lines and may thus be an apparent, structurally driven anisotropy. The main foliation and fold axis orientations might contribute to the anisotropy. In the lower crust, the N‐S orientation of the fast axis is mostly confined to regions north of the Periadriatic Fault and may be related to European subduction. Outside the orogen, no clearly layered structure is identified. The anisotropy pattern in the northern Alpine foreland is found to be similar compared to SKS studies which is an indication of very homogeneous fast axis directions throughout the crust and the upper mantle.

Unveiling hidden companions in post-common-envelope binaries: A robust strategy and uncertainty exploration

Context. Some post-common-envelope binaries (PCEBs) are binary stars with short periods that exhibit significant period variations over long observational time spans. These eclipse timing variations (ETVs) are most likely to be accounted for by the presence of an unseen massive companion, potentially of planetary or substellar nature, and the light-travel time (LTT) effect. The existence of such companions challenges our current understanding of planetary formation and stellar evolution. Aims. In this study, our main objective is to describe the diversity of compatible nontransit companions around PCEBs and explore the robustness of the solutions by employing tools for uncertainty estimation. We select the controversial data of the QS Vir binary star, which previous studies have suggested hosts a planet. Methods. We employ a minimizing strategy, using genetic algorithms to explore the global parameter space followed by refinement of the solution using the simplex method. We evaluate errors through the classical Markov chain Monte Carlo (MCMC) approach and discuss the error range for parameters, considering the 1σ values obtained from the minimization. Results. Our results highlight the strong dependence of ETV models for close binaries on the dataset used, which leads to relatively loose constraints on the parameters of the unseen companion. We find that the shape of the O – C curve is influenced by the dataset employed. We propose an alternative method to evaluate errors on the orbital fits based on a grid search surrounding the best-fit values, obtaining a wider range of plausible solutions that are compatible with goodness-of-fit statistics. We also analyze how the parameter solutions are affected by the choice of the dataset, and find that this system continuously changes the compatible solutions as new data are obtained from eclipses. Conclusions. The best-fit parameters for QS Vir correspond to a low-mass stellar companion (57.71 Mjup ranging from ~40 to ~64 Mjup) on an eccentric orbit (e = 0.91−0.17+0.07) with a variety of potential periods (P = 16.69−0.42+0.47 yr.). Most solutions within 1σ exhibit regular orbits, despite their high eccentricity. Additional observations are required to accurately determine the period and other parameters of the unseen companion. In this context, we propose that a fourth body should not be modeled to fit the data, unless new observations considerably modify the computed orbital parameters. This methodology can be applied to other evolved binary stars suspected of hosting companions.

AT2022cmc: A Tidal Disruption Event with a Two-component Jet in a Bondi-profile Circumnuclear Medium

A supermassive black hole can launch a relativistic jet when it violently disrupts a star that passes too close. Such jetted tidal disruption events (TDEs) are rare and unique tools to investigate quiescent supermassive black holes, jet physics, and circumnuclear environments at high redshift. The newly discovered TDE AT2022cmc (z ∼ 1.193), providing rich multiband (X-ray, UV, optical, submillimeter, and radio) data, has been interpreted as the fourth on-axis jetted TDE. In this work, we constrain the circumnuclear medium (CNM) density profile with both a closure relation test and detailed forward shock model fit with a Markov Chain Monte Carlo approach to the multiband (optical, submillimeter, and radio) data of AT2022cmc. We find that the CNM density profile of AT2022cmc is n ∝ R −k with k ∼ 1.68, implying a Bondi accretion in history. Furthermore, our model fit result suggests a two-component jet in AT2022cmc, indicating similar jet physics to well-studied jetted TDE Sw J1644+57.

Global Parameters of Eight W UMa-type Binary Systems

Abstract Multiband photometric investigations for eight binary systems of the W Ursae Majoris-type are presented. Six systems are presented for the first time to analyze their light curves. All the analyzed systems have a temperature below 5000 K and an orbital period of less than 0.28 days. We extracted primary and secondary minima from the ground-based observations of these systems. According to a few observations reported in the literature, linear fits were considered in the O − C diagrams, and new ephemerides were presented. Light curve solutions were performed using the PHysics Of Eclipsing BinariEs code. The results of the mass ratio and fillout factor indicate that the systems are contact binary stars. Six of them showed the O’Connell effect, and a cold starspot on each companion was required for light curve solutions. Their absolute parameters were estimated and evaluated by two other methods. In this study, the empirical relationship between the orbital period and semimajor axis was updated using a sample consisting of 414 contact binary systems and the Monte Carlo Markov Chain approach. Also, using Machine Learning and the Artificial Neural Network model, the relationship between P–T 1–M 1 was updated for a better estimation of the mass of the primary star.

Frequentist and Bayesian Approaches in Modeling and Prediction of Extreme Rainfall Series: A Case Study from Southern Highlands Region of Tanzania

This study focuses on modeling and predicting extreme rainfall based on data from the Southern Highlands region, the critical for rain-fed agriculture in Tanzania. Analyzing 31 years of annual maximum rainfall data spanning from 1990 to 2020, the Generalized Extreme Value (GEV) model proved to be the best for modeling extreme rainfall in all stations. Three estimation methods–L-moments, maximum likelihood estimation (MLE), and Bayesian Markov chain Monte Carlo (MCMC)–were employed to estimate GEV parameters and future return levels. The Bayesian MCMC approach demonstrated superior performance by incorporating noninformative priors to ensure that the prior information had minimal influence on the analysis, allowing the observed data to play a dominant role in shaping the posterior distribution. Furthermore, return levels for various future periods were estimated, providing guidance for flood protection measures and infrastructure design. Trend analysis using p value, Kendall’s tau, and Sen’s slope indicated no statistically significant trends in rainfall patterns, although a weak positive trend in extreme rainfall events was observed, suggesting a gradual and modest increase over time. Overall, the study contributes valuable insights into extreme rainfall patterns and underscores the importance of L-moments in identifying the best fit distribution and Bayesian MCMC methodology for accurate parameter estimation and prediction, enabling effective measures and infrastructure planning in the region.

Development of a Simulator for Household Refrigerator Using Equation-Based Optimization Control with Bayesian Calibration

Conventional household refrigerators consist of a motor-driven compressor, evaporator, condenser, and expansion valve. To determine the optimal operation strategies of refrigerators, it is essential to investigate the overall system performance, using an appropriate simulator. This study proposed a data-driven simulator based on engineering features and machine learning algorithms for conventional household refrigerators. The most correlated variables for identifying the indoor temperature of refrigerators were identified using variable importance, and these were revealed to be the circulation fan speed, compressor operation status, and refrigerant flow direction. A data-driven simulator was constructed using Bayesian calibration, which considers the important variables, combined with a straightforward heat balance equation. The Markov Chain Monte Carlo approach was used to simultaneously calibrate three coefficients on the critical variables based on the heat balancing equation on each time step, which is consistent with the actual temperature of the container. The results revealed that the proposed approach (equation-based Bayesian calibration outperforms) standard machine learning algorithms, such as linear regression and random forest models, by 38.5%. Additionally, compared to the typical numerical analysis method, it can reduce the delivery time and effort required to develop a reliable simulator for household refrigerators.

Gaussian process metamodel and Markov chain Monte Carlo-based Bayesian inference framework for stochastic nonlinear model updating with uncertainties

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties; thus, a novel Bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the Bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffré–Menegotto–Pinto modeled steel-frame structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the Bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based Bayesian method effectively estimates the posterior PDF of unknown parameters and is appropriate for stochastic nonlinear model updating even with multisource uncertainties.

Watching the Universe’s acceleration era with the SKAO

ABSTRACT The possibility of watching the Universe expand in real time and in a model-independent way, first envisaged by Allan Sandage more than 60 yr ago and known as the redshift drift, is within reach of forthcoming astrophysical facilities, particularly the Extremely Large Telescope (ELT) and the Square Kilometre Array Observatory (SKAO). The latter, probing lower redshifts, enables us to watch the Universe’s acceleration era in real time, while the former does the same for the matter era. We use Fisher matrix analysis techniques, which we show to give comparable results to those of a Markov Chain Monte Carlo approach, to discuss forecasts for SKAO measurements of the redshift drift and their cosmological impact. We consider specific fiducial cosmological models but mainly rely on a more agnostic cosmographic series (which includes the deceleration and jerk parameters), and we also discuss prospects for measurements of the drift of the drift. Overall, our analysis shows that SKAO measurements, with a reasonable amount of observing time, can provide a competitive probe of the low-redshift accelerating Universe.

Euclid preparation. XXXIV. The effect of linear redshift-space distortions in photometric galaxy clustering and its cross-correlation with cosmic shear

The cosmological surveys that are planned for the current decade will provide us with unparalleled observations of the distribution of galaxies on cosmic scales, by means of which we can probe the underlying large-scale structure (LSS) of the Universe. This will allow us to test the concordance cosmological model and its extensions. However, precision pushes us to high levels of accuracy in the theoretical modelling of the LSS observables so that no biases are introduced into the estimation of the cosmological parameters. In particular, effects such as redshift-space distortions (RSD) can become relevant in the computation of harmonic-space power spectra even for the clustering of the photometrically selected galaxies, as has previously been shown in literature. In this work, we investigate the contribution of linear RSD, as formulated in the Limber approximation by a previous work, in forecast cosmological analyses with the photometric galaxy sample of the survey. We aim to assess their impact and to quantify the bias on the measurement of cosmological parameters that would be caused if this effect were neglected. We performed this task by producing mock power spectra for photometric galaxy clustering and weak lensing as is expected to be obtained from the survey. We then used a Markov chain Monte Carlo approach to obtain the posterior distributions of cosmological parameters from these simulated observations. When the linear RSD is neglected, significant biases are caused when galaxy correlations are used alone and when they are combined with cosmic shear in the so-called 3times 2pt approach. These biases can be equivalent to as much as $5\ when an underlying Lambda CDM cosmology is assumed When the cosmological model is extended to include the equation-of-state parameters of dark energy, the extension parameters can be shifted by more than $1\ sigma$.

COVID-19 vaccination implementation in 52 African countries: trajectory and implications for future pandemic preparedness

IntroductionTo end the COVID-19 pandemic, the WHO set a goal in 2021 to fully vaccinate 70% of the global population by mid-2022. We projected the COVID-19 vaccination trajectory in 52...

Characterizing the Seafloor Sediment Layer Using Teleseismic Body Waves Recorded by Ocean Bottom Seismometers

AbstractThis study presents an approach to better characterize the P‐wave and S‐wave velocity structure of the seafloor sediment layer using ocean bottom seismometers. The presence of low‐velocity seafloor sediment layers influences the observed seismic record at the seafloor over a broad frequency range, such that detailed knowledge of this sediment structure is essential to predict its effect on teleseismic records. We use the radial component of teleseismic P waves and autocorrelation functions of the radial, vertical, and pressure components of teleseismic P and S waves to obtain sediment layer models using the Markov chain Monte Carlo approach with parallel tempering. Synthetic tests show that the body waves constrain the P‐ and S‐wave impedances and travel times and the P‐ to S‐wave velocity ratio of the sediment layers. The proposed method resolves thin layers at a high resolution, including the uppermost thin (∼50 m to a few hundred meters) low S‐wave velocity layer. Real data applications at sites across the Pacific Ocean that are coincident with previous in situ studies demonstrate the effectiveness of this method in characterizing the seafloor sediment unit. The sediment models characterized by this new approach will allow us to more accurately predict and correct the effects of sediment layers in generating P‐ and S‐wave reverberations.

Probing accelerating cosmos via reconstructed Hubble parameter and its influence on f(T) gravity models

This article introduces a new way of studying the accelerating cosmos without relying on specific models. It proposes a new parametric form of the Hubble parameter (HP) and uses a Markov Chain Monte Carlo (MCMC) approach to determine the model parameters. The analysis incorporates a comprehensive dataset consisting of 34 cosmic chronometers (CC) data points, 40 non-correlated baryonic acoustic oscillations (BAO) points, and 1701 updated Pantheon+ supernovae type Ia (SNeIa) data points. The study investigates various aspects of the model's behavior, such as the transition from deceleration to acceleration, and the evolution of jerk and snap parameters. Constraints are applied to the model parameters as well as the Hubble constant (H0). Additionally, the parameter values obtained are used to study f(T) gravity models and compare them with observational data. This research provides valuable insights into the nature of the accelerating Universe and highlights the importance of using a parametrized approach in cosmological studies.

Bayesian extreme value analysis of extreme sea levels along the German Baltic coast using historical information

Abstract. Developed coastlines require considerable investments into coastal protection measures to mitigate the effects of flooding caused by extreme sea levels (ESLs). To maximize the effectiveness of these measures, accurate estimates of the underlying hazard are needed. These estimates are typically determined by performing extreme value analysis on a sample of events taken from tide-gauge observations. However, such records are often limited in duration, and the resulting estimates may be highly uncertain. Furthermore, short records make it difficult to assess whether exceptionally large events within the record are appropriate for analysis or should be disregarded as outliers. In this study, we explore how historical information can be used to address both of these issues for the case of the German Baltic coast. We apply a Bayesian Markov chain Monte Carlo approach to assess ESLs using both systematic tide-gauge observations and historical information at seven locations. Apart from the benefits provided by incorporating historical information in extreme value analysis, which include reduced estimate uncertainties and the reclassification of outliers into useful samples, we find that the current tide-gauge records in the region alone are insufficient for providing accurate estimates of ESLs for the planning of coastal protection. We find long-range dependence in the series of ESLs at the site of Travemünde, which suggests the presence of some long-term variability affecting events in the region. We show that ESL activity over the full period of systematic observation has been relatively low. Consequently, analyses which consider only these data are prone to underestimations.

Reliability and the engineering applications of the generalized half-normal model via an adaptive progressive hybrid censored mechanism

Recently, the generalized half-normal distribution with decreasing, increasing, and bathtub hazard function shapes was proposed, making it a more applicable, reliable, and flexible lifespan model. The task of estimating the unknown parameters and reliability features of the generalized half-normal distribution is looked at using adaptive progressively type-II hybrid censored data. The maximum likelihood and Bayesian estimation methods are both considered for this purpose. Two approximated confidence intervals, Bayes and highest posterior density intervals, are acquired for the various parameters. The Bayes estimates are obtained based on symmetric and asymmetric loss functions under the assumption of independent gamma priors. The Markov chain Monte Carlo approach is used to compute Bayes estimates as well as the various Bayes intervals. Monte Carlo experiments are used for assessing the efficiency of the various approaches. Finally, analysis is performed on two actual-life engineering datasets.