Markov Chain Monte Carlo Approach Research Articles

The thermal state of Volgo–Uralia from Bayesian inversion of surface heat flow and temperature

SUMMARY Volgo–Uralia is the easternmost segment of the East European Craton. It accommodates the Volga–Ural petroleum province where the maturity of source rocks is tightly related to the temperature distribution in the crust. Numerous heat flow and temperature measurements have been reported for this region. However, no consistent geothermal model was presented for the Volgo–Uralian crustal block so far. In this study, we present a novel model of the Volgo–Uralian geothermal field where we aim to reconcile the reported heat flow and temperature data. The main goal of the study is to explore lateral variations of the unknown thermal parameters within Volgo–Uralia. For this purpose, we applied a Bayesian Markov Chain Monte Carlo approach where we used the known surface heat flow, surface temperature, lithosphere–asthenosphere boundary temperature and thicknesses of the Earth's lithospheric and crustal layers as input and investigated the possible lateral variations of crustal and lithospheric mantle thermal conductivities, crustal heat production and mantle heat flow. We implemented this methodology for a single-layer and multilayer crust and validated the obtained geothermal models with existing subsurface temperature measurements for the region. The results show that the Volgo–Uralian subcraton is characterized by significant lateral variations of crustal radiogenic heat production (RHP) and mantle heat flow. The variations of crustal and lithospheric mantle thermal conductivities are less pronounced. According to our model, the surface heat flow distribution is controlled mostly by crustal RHP which accounts for more than half of Volgo–Uralian surface heat flow. Validation of the models shows that single-layer and multilayer crustal models give roughly the same fit of measured and modelled temperatures. This implies that a single-layer crust with constant RHP can be considered a sufficient approximation for regional-scale geothermal modelling.

Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data

In this work, we presented the type I half logistic Burr-Weibull distribution, which is a unique continuous distribution. It offers several superior benefits in fitting various sorts of data. Estimates of the model parameters based on classical and nonclassical approaches are offered. Also, the Bayesian estimates of the model parameters were examined. The Bayesian estimate method employs the Monte Carlo Markov chain approach for the posterior function since the posterior function came from an uncertain distribution. The use of Monte Carlo simulation is to assess the parameters. We established the superiority of the proposed distribution by utilising real COVID-19 data from varied countries such as Saudi Arabia and Italy to highlight the relevance and flexibility of the provided technique. We proved our superiority using both real data.

High-contrast imaging of HD 29992 and HD 196385 with the Gemini Planet Imager

ABSTRACT Based on high-contrast images obtained with the Gemini Planet Imager (GPI), we report the discovery of two point-like sources at angular separations ρ ∼ 0.18 and 0.80 arcsec from the stars HD 29992 and HD 196385. A combined analysis of the new GPI observations and images from the literature indicates that the source close to HD 29992 could be a companion to the star. Concerning HD 196385, the small number of contaminants (∼0.5) suggests that the detected source may be gravitationally bound to the star. For both systems, we discarded the presence of other potential companions with m > 75 MJup at ρ ∼ 0.3–1.3 arcsec. From stellar model atmospheres and low-resolution GPI spectra, we derive masses of ∼0.2–0.3 M⊙ for these sources. Using a Markov-chain Monte Carlo approach, we performed a joint fit of the new astrometry measurements and published radial velocity data to characterize the possible orbits. For HD 196385B, the median dynamic mass is in agreement with that derived from model atmospheres, whilst for HD 29992B the orbital fit favours masses close to the brown dwarf regime (∼0.08 M⊙). HD 29992 and HD 196385 might be two new binary systems with M-type stellar companions. However, new high angular resolution images would help to confirm definitively whether the detected sources are gravitationally bound to their respective stars, and permit tighter constraints on the orbital parameters of both systems.

Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring

As an extension of the standard Weibull distribution, a new crucial distribution termed alpha power Weibull distribution has been presented. It can model decreasing, increasing, bathtub, and upside-down bathtub failure rates. This research investigates the estimation of model parameters and some of its reliability characteristics using progressively Type-II censored data. To get estimates of unknown parameters, reliability, and hazard rate functions, the maximum likelihood, and Bayesian estimation approaches are studied. To acquire estimated confidence intervals for unknown parameters and reliability characteristics, the maximum likelihood asymptotic properties are used. The Markov chain Monte Carlo approach is used in Bayesian estimation to provide Bayesian estimates under squared error and LINEX loss functions. Furthermore, the highest posterior density credible intervals of the parameters and reliability characteristics are determined. A Monte Carlo simulation study is used to investigate the accuracy of various point and interval estimators. In addition, various optimality criteria are used to choose the best progressive censoring schemes. Two real data from the engineering field are analyzed to demonstrate the applicability and significance of the proposed approaches. Based on numerical results, the Bayesian procedure for estimating the parameters and reliability characteristics of alpha power Weibull distribution is recommended. The analysis of two real data sets showed that the alpha power Weibull distribution is a good model to investigate engineering data in the presence of progressive Type-II censoring.

The Impacts of Air Quality on Vegetation Health in Dense Urban Environments: A Ground-Based Hyperspectral Imaging Approach

We examine the impact of changes in ozone (O3), particulate matter (PM2.5), temperature, and humidity on the health of vegetation in dense urban environments, using a very high-resolution, ground-based Visible and Near-Infrared (VNIR, 0.4–1.0 μm with a spectral resolution of 0.75 nm) hyperspectral camera deployed by the Urban Observatory (UO) in New York City. Images were captured at 15 min intervals from 08h00 to 18h00 for 30 days between 3 May and 6 June 2016 with each image containing a mix of dense built structures, sky, and vegetation. Vegetation pixels were identified using unsupervised k-means clustering of the pixel spectra and the time dependence of the reflection spectrum of a patch of vegetation at roughly 1 km from the sensor that was measured across the study period. To avoid illumination and atmospheric variability, we introduce a method that measures the ratio of vegetation pixel spectra to the spectrum of a nearby building surface at each time step relative to that ratio at a fixed time. This “Compound Ratio” exploits the (assumed) static nature of the building reflectance to isolate the variability of vegetation reflectance. Two approaches are used to quantify the health of vegetation at each time step: (a) a solar-induced fluorescence indicator (SIFi) calculated as the simple ratio of the amplitude of the Compound Ratio at 0.75 μm and 0.9 μm, and (b) Principal Component Analysis (PCA) decomposition designed to capture more global spectral features. The time dependence of these vegetation health indicators is compared to that of O3, PM2.5, temperature, and humidity values from a distributed and publicly available in situ air quality sensor network. Assuming a linear relationship between vegetation health indicators and air quality indicators, we find that changes in both SIF indicator values and PC amplitudes show a strong correlation (r2 value of 40% and 47%, respectively) with changes in air quality, especially in comparison with nearby buildings used as controls (r2 value of 1% and 4%, respectively, and with all molecular correlations consistent with zero to within 3σ uncertainty). Using the SIF indicator, O3 and temperature exhibit a positive correlation with changes in photosynthetic rate in vegetation, while PM2.5 and humidity exhibit a negative correlation. We estimate full covariant uncertainties on the coefficients using a Markov Chain Monte Carlo (MCMC) approach and demonstrate that these correlations remain statistically significant even when controlling for the effects of diurnal sun-sensor geometry and temperature variability. This work highlights the importance of quantifying the effects of various air quality parameters on vegetation health in urban environments in order to uncover the complexity, covariance, and interdependence of the numerous factors involved.

An Integrated Bayesian and Machine Learning Approach Application to Identification of Groundwater Contamination Source Parameters

The identification of groundwater contamination source parameters is an important prerequisite for the control and risk assessment of groundwater contamination. This study developed an innovative approach for the optimal design of observation well locations and the high-precision identification of groundwater contamination source parameters. The approach involves Bayesian theory and integrates Markov Chain Monte Carlo, Bayesian design, information entropy, machine learning, and surrogate modeling. The optimal observation well locations are determined by information entropy, which is adopted to mine valuable information about unknown groundwater contamination source parameters from measurements of contaminant concentration according to Bayesian design. After determining the optimal observation well locations, the identification of groundwater contamination source parameters is implemented through a Bayesian-based Differential Evolution Adaptive Metropolis with Discrete Sampling–Markov Chain Monte Carlo approach. However, the processes of both determination and identification are time-consuming because the original simulation model (that is, the contaminant transport model) needs to be invoked multiple times. To overcome this challenge, a machine learning approach, that is, Multi-layer Perceptron, is used to build a surrogate model for the original simulation model, which can greatly accelerate the determination and identification processes. Finally, two hypothetical numerical case studies involving homogeneous and heterogeneous cases are used to verify the performance of the proposed approach. The results show that the optimal design of observation well locations and high-precision identification of groundwater contamination source parameters can be implemented accurately and effectively by using the proposed approach. In summary, this study highlights that the integrated Bayesian and machine learning approach provides a promising solution for high-precision identification of groundwater contamination source parameters.

Ensemble Markov Chain Monte Carlo with Teleporting Walkers

We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in which one chain's state is cloned as another's is deleted. This effective teleportation of states can overcome issues of metastability in the underlying chain, as the scheme enjoys rapid mixing once the modes of the target density have been populated. We derive a mean-field limit for the evolution of the ensemble. We analyze the global and local convergence of this mean-field limit, showing asymptotic convergence independent of the spectral gap of the underlying Markov chain, and moreover we interpret the limiting evolution as a gradient flow. We explain how interaction can be applied selectively to a subset of state variables in order to maintain advantage on very high-dimensional problems. Finally we present the application of our methodology to Bayesian hyperparameter estimation for Gaussian process regression.

Towards reliable uncertainty quantification for hydrologic predictions, Part I: Development of a particle copula Metropolis Hastings method

In this study, a particle copula Metropolis-Hastings (PCMH) approach was developed for reliable uncertainty quantification of hydrological predictions. The proposed PCMH approach employs a mixed particle evolution scheme, which integrates the Gaussian perturbation and copula-based dependent sampling methods. The Metropolis ratio is then employed to determine the acceptance of the candidate samples. The applicability of PCMH is elaborated for a long-term data assimilation case at the River Ouse in UK. Multiple hydrological models and different uncertainty settings in inputs, outputs and sample sizes are tested by the PCMH, particle filter (PF) and particle Markov chain Monte Carlo (PMCMC) approaches. The results indicate that the developed PCMH approach is able to generate more reliable results with less accuracy fluctuation than PF and PMCMC for both deterministic and probabilistic predictions from all the hydrological models. The mean values and the associated variation intervals of NSE over the total 270 runs for PCMH, PF and PMCMC are 0.752 (variation interval of [0.534, 0.866]), 0.661 (variation interval of [0.080, 0.879]), and 0.655 (variation interval of [0.247, 0.824]), respectively. For the probabilistic predictions evaluated by CRPS, the mean values and fluctuation ranges from PCMH, PF and PMCMC are respectively 15.215 ([8.624,31.549]), 18.758 ([8.595, 43.536]), 19.308 ([10.848, 37.799]). These results suggested that the proposed PCMH method would be more robust than PF and PMCMC in generating reliable hydrologic predictions and be less influenced by the hydrologic model structures, uncertainty scenarios, and its inherent randomness. Moreover, the PCMH method can also show better robustness than the copula-based particle filter method since the particle evolution scheme of PCMH would balance extreme samples from copula sampling procedure by mixing samples from Gaussian perturbation and remove unacceptable candidates through the Metropolis acceptance criterion.

A Bayesian approach to infer recombination patterns in coronaviruses

As shown during the SARS-CoV-2 pandemic, phylogenetic and phylodynamic methods are essential tools to study the spread and evolution of pathogens. One of the central assumptions of these methods is that the shared history of pathogens isolated from different hosts can be described by a branching phylogenetic tree. Recombination breaks this assumption. This makes it problematic to apply phylogenetic methods to study recombining pathogens, including, for example, coronaviruses. Here, we introduce a Markov chain Monte Carlo approach that allows inference of recombination networks from genetic sequence data under a template switching model of recombination. Using this method, we first show that recombination is extremely common in the evolutionary history of SARS-like coronaviruses. We then show how recombination rates across the genome of the human seasonal coronaviruses 229E, OC43 and NL63 vary with rates of adaptation. This suggests that recombination could be beneficial to fitness of human seasonal coronaviruses. Additionally, this work sets the stage for Bayesian phylogenetic tracking of the spread and evolution of SARS-CoV-2 in the future, even as recombinant viruses become prevalent.

Contact tracing of COVID-19 in Karnataka, India: Superspreading and determinants of infectiousness and symptomatic infection.

BackgroundIndia has experienced the second largest outbreak of COVID-19 globally, yet there is a paucity of studies analysing contact tracing data in the region which can optimise public health interventions (PHI’s).MethodsWe analysed contact tracing data from Karnataka, India between 9 March and 21 July 2020. We estimated metrics of transmission including the reproduction number (R), overdispersion (k), secondary attack rate (SAR), and serial interval. R and k were jointly estimated using a Bayesian Markov Chain Monte Carlo approach. We studied determinants of risk of further transmission and risk of being symptomatic using Poisson regression models.FindingsUp to 21 July 2020, we found 111 index cases that crossed the super-spreading threshold of ≥8 secondary cases. Among 956 confirmed traced cases, 8.7% of index cases had 14.4% of contacts but caused 80% of all secondary cases. Among 16715 contacts, overall SAR was 3.6% [95% CI, 3.4–3.9] and symptomatic cases were more infectious than asymptomatic cases (SAR 7.7% vs 2.0%; aRR 3.63 [3.04–4.34]). As compared to infectors aged 19–44 years, children were less infectious (aRR 0.21 [0.07–0.66] for 0–5 years and 0.47 [0.32–0.68] for 6–18 years). Infectors who were confirmed ≥4 days after symptom onset were associated with higher infectiousness (aRR 3.01 [2.11–4.31]). As compared to asymptomatic cases, symptomatic cases were 8.16 [3.29–20.24] times more likely to cause symptomatic infection in their secondary cases. Serial interval had a mean of 5.4 [4.4–6.4] days, and case fatality rate was 2.5% [2.4–2.7] which increased with age.ConclusionWe found significant heterogeneity in the individual-level transmissibility of SARS-CoV-2 which could not be explained by the degree of heterogeneity in the underlying number of contacts. To strengthen contact tracing in over-dispersed outbreaks, testing and tracing delays should be minimised and retrospective contact tracing should be implemented. Targeted measures to reduce potential superspreading events should be implemented. Interventions aimed at children might have a relatively small impact on reducing transmission owing to their low symptomaticity and infectivity. We propose that symptomatic cases could cause a snowballing effect on clinical severity and infectiousness across transmission generations; further studies are needed to confirm this finding.

Locating and Quantifying Methane Emissions by Inverse Analysis of Path-Integrated Concentration Data Using a Markov-Chain Monte Carlo Approach.

The action to reduce anthropogenic greenhouse gas emissions is severely constrained by the difficulty of locating sources and quantifying their emission rates. Methane emissions by the energy sector are of particular concern. We report results achieved with a new area monitoring approach using laser dispersion spectroscopy to measure path-averaged concentrations along multiple beams. The method is generally applicable to greenhouse gases, but this work is focused on methane. Nineteen calibrated methane releases in four distinct configurations, including three separate blind trials, were made within a flat test area of 175 m by 175 m. Using a Gaussian plume gas dispersion model, driven by wind velocity data, we calculate the data anticipated for hundreds of automatically proposed candidate source configurations. The Markov-chain Monte Carlo analysis finds source locations and emission rates whose calculated path-averaged concentrations are consistent with those measured and associated uncertainties. This approach found the correct number of sources and located them to be within <9 m in more than 75% of the cases. The relative accuracy of the mass emission rate results was highly correlated to the localization accuracy and better than 30% in 70% of the cases. The discrepancies for mass emission rates were <2 kg/h for 95% of the cases.

Statistical Inference for the Gompertz Distribution Based on Adaptive Type-II Progressive Censoring Scheme

The topic of estimating the parameters of Gompertz distribution using an adaptive Type-II progressively censored data are described in this paper. The unknown parameters, the reliability, and the hazard functions are estimated using maximum likelihood and Bayesian estimation methods. The approximate confidence intervals of them are then determined. Furthermore, the Markov chain Monte Carlo approach is used to perform a Bayesian estimate procedure and compute the credible intervals. Finally, a Monte Carlo simulation study is done to assess the performance of the two estimating methods, and a numerical example with real data is shown to demonstrate the procedures’ utility.

Morpho-Statistical Description of Networks Through Graph Modelling and Bayesian Inference

Collaboration graphs are relevant sources of information to understand behavioural tendencies of groups of individuals. The study of these graphs enables figuring out factors that may affect the efficiency and the sustainability of cooperative work. For example, such a collaboration involves researchers who develop relationships with their external counterparts to address scientific challenges. As relations and projects change over time, the evolution of social structures must be tackled. We propose a statistical approach considering different structural collaboration patterns and captures the dynamic of the relational structures over the years. Our approach combines spatial processes modelling and Exponential Random Graph Models used to analyse social processes. Since the normalising constant involved in classical Markov Chain Monte Carlo (MCMC) approaches is intractable, the inference remains challenging. To overcome this issue, we propose a Bayesian tool that relies on the recent ABC Shadow algorithm. The method is illustrated on real data sets from an open archive of scholarly documents. Through a simple formalism, our approach highlights the interactions between the different types of social relations at stake in the collaboration network.

Estimation and Prediction for Algorithmic Models of Investor Behavior

We propose a Markov chain Monte Carlo (MCMC) algorithm for estimating the parameters of algorithmic models of investor behavior. We show that this method can successfully infer the relative importance of each heuristic among a large cross-section of investors, even when the number of observations per investor is quite small. We also compare the accuracy of the MCMC approach to regression analysis in predicting the relative importance of heuristics at the individual and aggregate levels and conclude that MCMC predicts aggregate weights more accurately while regression outperforms in predicting individual weights.

Bayesian MCMC Approach to Learning About the SIR Model

Abstract: This project aims to study the parameters of the Deterministic SIR(Susceptible → Infected → Recovered) model of COVID-19 in a Bayesian MCMC framework. Several deterministic mathematical models are being developed everyday to forecast the spread of COVID-19 correctly. Here, I have tried to model and study the parameters of the SIR Infectious disease model using the Bayesian Framework and Markov-Chain Monte-Carlo (MCMC) techniques. I have used Bayesian Inference to predict the Basic Reproductive Rate ࢚ࡾ in real time using and following this, demonstrated the process of how the parameters of the SIR Model can be estimated using Bayesian Statistics and Markov-Chain Monte-Carlo Methods. Keywords: COVID-19, Bayesian Inference, Dynamical Systems, SIR Model, Basic Reproductive Rate, Markov-Chain MonteCarlo(MCMC)

ALMA Images the Eccentric HD 53143 Debris Disk

We present ALMA 1.3 mm observations of the HD 53143 debris disk—the first infrared or millimeter image produced of this ∼1 Gyr old solar analog. Previous HST STIS coronagraphic imaging did not detect flux along the minor axis of the disk, which could suggest a face-on geometry with two clumps of dust. These ALMA observations reveal a disk with a strikingly different structure. In order to fit models to the millimeter visibilities and constrain the uncertainties on the disk parameters, we adopt a Markov Chain Monte Carlo approach. This is the most eccentric debris disk observed to date with a forced eccentricity of 0.21 ± 0.02, nearly twice that of the Fomalhaut debris disk, and also displays an apocenter glow. Although this eccentric model fits the outer debris disk well, significant interior residuals remain, which may suggest a possible edge-on inner disk, which remains unresolved in these observations. Combined with the observed structure difference between HST and ALMA, these results suggest a potential previous scattering event or dynamical instability in this system. We also note that the stellar flux changes considerably over the course of our observations, suggesting flaring at millimeter wavelengths. Using simultaneous TESS observations, we determine the stellar rotation period to be 9.6 ± 0.1 days.

A time-domain multisource Bayesian/Markov chain Monte Carlo formulation of time-lapse seismic waveform inversion

Seismic waveform inversion has been shown to be well-suited for identification and characterization of time-lapse changes in a reservoir. However, the subtle medium variations associated with enhanced oil recovery and/or [Formula: see text] storage problems give uncertainty quantification within such inverse approaches a heightened importance. To analyze both of these features of the time-lapse inverse problem, we formulate a Bayesian full-waveform inversion (FWI) procedure, based on a Markov chain Monte Carlo (MCMC) algorithm. The formulation uses several existing strategies, such as the use of a double-difference time-lapse FWI (DDFWI), incorporation of time-domain multisource data, and application of a local-updating target-oriented inversion. However, it incorporates these within a stochastic framework, involving computation of model covariance with an adaptive Metropolis algorithm, and a method to estimate data error statistics based on the features of time-lapse difference data that is incorporated. A random walk Metropolis-Hastings MCMC is adopted for optimization. In conventional, i.e., deterministic, DDFWI, inversions are carried out for the baseline and monitoring models; in the MCMC approach, a deterministic FWI procedure is carried out for the baseline model, and the MCMC algorithm is applied in the monitoring inversion stage; and the final time-lapse model is the difference between these. A feasibility study is carried out using synthetic 2D acoustic models and data, including time-lapse model estimation and uncertainty quantification. We compare the MCMC approach with conventional deterministic optimization DDFWI and remark on benefits derived, which appear to justify the expanded complexity and cost of a global approach. In addition to the availability of posterior distributions, which are critical for the assessment of the estimations, we observe that the MCMC approach tends to produce monitoring images with clearer edges and fewer coherent errors.

Metropolis-Hastings Markov Chain Monte Carlo Approach to Simulate van Genuchten Model Parameters for Soil Water Retention Curve

The soil water retention curve (SWRC) is essential for assessing water flow and solute transport in unsaturated media. The van Genuchten (VG) model is widely used to describe the SWRC; however, estimation of its effective hydraulic parameters is often prone to error, especially when data exist for only a limited range of matric potential. We developed a Metropolis-Hastings algorithm of the Markov chain Monte Carlo (MH-MCMC) approach using R to estimate VG parameters, which produces a numerical estimate of the joint posterior distribution of model parameters, including fully-quantified uncertainties. When VG model parameters were obtained using complete range of soil water content (SWC) data (i.e., from saturation to oven dryness), the MH-MCMC approach returned similar accuracy as the widely used non-linear curve-fitting program RETC (RETention Curve), but avoiding non-convergence issues. When VG model parameters were obtained using 5 SWC data measured at matric potential of around −60, −100, −200, −500, and −15,000 cm, the MH-MCMC approach was more robust than the RETC program. The performance of MH-MCMC are generally good (R2 &gt; 0.95) for all 8 soils, whereas the RETC underperformed for coarse-textured soils. The MH-MCMC approach was used to obtain VG model parameters for all 1871 soils in the National Cooperative Soil Characterization dataset with SWC measured at matric potentials of −60 cm, −100 cm, −330 cm, and −15,000 cm; the results showed that the simulated SWC by MH-MCMC model were highly consistent with the measured SWC at corresponding matric potential. Altogether, our new MH-MCMC approach to solving the VG model is more robust to limited coverage of soil matric potential when compared to the RETC procedures, making it an effective alternative to traditional water retention solvers. We developed an MH-MCMC code in R for solving VG model parameters, which can be found at the GitHub repository.

An MCMC approach to the three-dimensional structure of the Milky Way bulge using OGLE-IV δ Scuti stars

ABSTRACT We present an analysis of high-latitude δ Scuti stars (|b| &amp;gt; 1°) in the Galactic bulge region (−8${_{.}^{\circ}}$3 &amp;lt; l &amp;lt; 9${_{.}^{\circ}}$4) using a clean sample of the photometric data of 7440 stars recently released by the OGLE-IV project. The geometrical parameters of the bulge are determined based on Maximum Likelihood (ML) analysis in five-dimensional parameter space. More refined values of these parameters as well as their uncertainties are obtained from a fully Bayesian Markov chain Monte Carlo (MCMC) analysis. Approximating the bulge as an ellipsoid, the distribution of the number density of stars as a function of Galacto-centric distance has been modelled using three distribution functions: two Exponential ($\rm E_{1},\rm E_{2}$) types and one Gaussian ($\rm G$) type. Based on the AIC and BIC values, the exponential model $\rm E_{1}$ is chosen as the best statistical model for the parameter values obtained from the MCMC analysis. The MCMC analysis yields the following results: the mean distance to the Galactic Centre (GC) is found to be R0 = 8.034 ± 0.012stat ± 0.586sys kpc; the bulge δ Scuti distribution has a triaxial shape with normalized (a ≡ 1) axes ratios (a: b: c) as 1.000 ± 0.005: 0.348 ± 0.002: 0.421 ± 0.002. Here a is the semi-major axis lying in the Galactic plane and pointing towards us; b and c are the two semi-minor axes, the former lying in the Galactic plane and the later perpendicular to it. Smaller values of b as compared to a obtained for Galacto-centric distances R ≥ 2.0 kpc indicate the presence of a bar-like structure of the bulge with a bar angle of 22${_{.}^{\circ}}$006 ± 2${_{.}^{\circ}}$078.

The Photometric Study of Six W UMa Systems and Investigation of the Mass–Radius Relations for Contact Binary Stars

We present the photometric analysis of six short-period systems (EI Oct, V336 TrA, NX Boo, V356 Boo, PS Boo, and V2282 Cyg). This is the first photometric analysis of these systems except for V336 TrA. Observations were conducted for 27 nights at three observatories in the northern and southern hemispheres. We calculated a new ephemeris for each of the systems using our minimum times and additional literature. The Markov Chain Monte Carlo (MCMC) approach was used to determine the eclipse timing variation trends of the systems. We found a likely orbital growth for V336 TrA and PS Boo; four other systems show a linear trend in orbital period changes, which is most likely due to the accumulation of measurement errors in their linear ephemeris parameters. The light curve analysis was performed using the Physics of Eclipsing Binaries (PHOEBE) 2.3.59 version code with the MCMC approach. The absolute parameters of the systems were calculated by using the Gaia Early Data Release 3 (EDR3) parallax. The positions of the systems were also depicted on the Hertzsprung–Russell (H-R) and diagrams. According to a sample, we were able to present relations for the mass–radius (M–R) relationships of contact binary systems. There is also a strong relationship between the mass ratio and the radius ratio in the W UMa systems for which we also provided a new relation. We compared the M–R updated relationships in this study with seven systems in other studies obtained using the spectroscopic method. In addition, we estimated some of the absolute parameters for 1734 EW systems, based on the new relationships.