Markov Chain Monte Carlo Techniques Research Articles

Statistical Evaluations and Applications for IER Parameters from Generalized Progressively Type-II Hybrid Censored Data

Generalized progressively Type-II hybrid strategy has been suggested to save both the duration and cost of a life test when the experimenter aims to score a fixed number of failed units. In this paper, using this mechanism, the maximum likelihood and Bayes inferential problems for unknown model parameters, in addition to both reliability, and hazard functions of the inverted exponentiated Rayleigh model, are acquired. Applying the observed Fisher data and delta method, the normality characteristic of the classical estimates is taken into account to derive confidence intervals for unknown parameters and several indice functions. In Bayes’ viewpoint, through independent gamma priors against both symmetrical and asymmetrical loss functions, the Bayes estimators of the unknown quantities are developed. Because the Bayes estimators are acquired in complicated forms, a hybrid Monte-Carlo Markov-chain technique is offered to carry out the Bayes estimates as well as to create the related highest posterior density interval estimates. The precise behavior of the suggested estimation approaches is assessed using wide Monte Carlo simulation experiments. Two actual applications based on actual data sets from the mechanical and chemical domains are examined to show how the offered methodologies may be used in real current events.

Object based Bayesian full-waveform inversion for shear elastography

We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the posterior probability of parameter fields representing the geometry of the anomalies and their shear moduli. To construct a prior probability, we exploit the topological energies of associated objective functions. We demonstrate the approach on synthetic two dimensional tests with smooth and irregular shapes. Sampling the posterior distribution by Markov Chain Monte Carlo (MCMC) techniques we obtain statistical information on the shear moduli and the geometrical properties of the anomalies. General affine-invariant ensemble MCMC samplers are adequate for shapes characterized by parameter sets of low to moderate dimension. However, MCMC methods are computationally expensive. For simple shapes, we devise a fast optimization scheme to calculate the maximum a posteriori (MAP) estimate representing the most likely parameter values. Then, we approximate the posterior distribution by a Gaussian distribution found by linearization about the MAP point to capture the main mode at a low computational cost.

Yield Curve Models with Regime Changes: An Analysis for the Brazilian Interest Rate Market

This study examines the effectiveness of various specifications of the dynamic Nelson–Siegel term structure model in analyzing the term structure of Brazilian interbank deposits. A key contribution of our research is the incorporation of regime changes and other time-varying parameters in the model, both when relying solely on observed yields and when incorporating macroeconomic variables. By allowing parameters in the latent factors to adapt to changes in persistence patterns and the overall shape of the yield curve, these mechanisms enhance the model’s flexibility. To evaluate the performance of the models, we conducted assessments based on their in-sample fit and out-of-sample forecast accuracy. Our estimation approach involved Bayesian procedures utilizing Markov Chain Monte Carlo techniques. The results highlight that models incorporating macro factors and greater flexibility demonstrated superior in-sample fit compared to other models. However, when it came to out-of-sample forecasts, the performance of the models was influenced by the forecast horizon and maturity. Models incorporating regime switching exhibited better performance overall. Notably, for long maturities with a one-month ahead forecast horizon, the model incorporating regime changes in both the latent and macro factors emerged as the top performer. On the other hand, for a twelve-month horizon, the model incorporating regime switching solely in the macro factors demonstrated superior performance across most maturities. These findings have significant implications for the development of trading and hedging strategies in interest rate derivative instruments, particularly in emerging markets that are more prone to regime changes and structural breaks.

Alleviating estimation problems in small sample structural equation modeling-A comparison of constrained maximum likelihood, Bayesian estimation, and fixed reliability approaches.

Small sample structural equation modeling (SEM) may exhibit serious estimation problems, such as failure to converge, inadmissible solutions, and unstable parameter estimates. A vast literature has compared the performance of different solutions for small sample SEM in contrast to unconstrained maximum likelihood (ML) estimation. Less is known, however, on the gains and pitfalls of different solutions in contrast to each other. Focusing on three current solutions-constrained ML, Bayesian methods using Markov chain Monte Carlo techniques, and fixed reliability single indicator (SI) approaches-we bridge this gap. When doing so, we evaluate the potential and boundaries of different parameterizations, constraints, and weakly informative prior distributions for improving the quality of the estimation procedure and stabilizing parameter estimates. The performance of all approaches is compared in a simulation study. Under conditions with low reliabilities, Bayesian methods without additional prior information by far outperform constrained ML in terms of accuracy of parameter estimates as well as the worst-performing fixed reliability SI approach and do not perform worse than the best-performing fixed reliability SI approach. Under conditions with high reliabilities, constrained ML shows good performance. Both constrained ML and Bayesian methods exhibit conservative to acceptable Type I error rates. Fixed reliability SI approaches are prone to undercoverage and severe inflation of Type I error rates. Stabilizing effects on Bayesian parameter estimates can be achieved even with mildly incorrect prior information. In an empirical example, we illustrate the practical importance of carefully choosing the method of analysis for small sample SEM. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

3-D imaging of the Balmuccia peridotite body (Ivrea–Verbano zone, NW-Italy) using controlled source seismic data

SUMMARY We provide new results from a controlled-source seismic experiment on the deepest part of the Val Sesia crust–mantle section of the Ivrea–Verbano zone (IVZ) in the Italian Alps. The IVZ is a tilted, almost complete section through the continental crust and exposes gabbros and peridotites in the structurally deepest level, coinciding with high-resolution gravity anomalies imaging the Ivrea geophysical body. The seismic experiment SEIZE (SEismic imaging of the Ivrea ZonE) was conducted along two crossing profiles: an NNE-SSW profile of ∼11 km length and an E-W profile of ∼16 km length. 432 vibration points were recorded with 110 receivers resulting in 24 392 traveltime picks. Inversion methods using Markov chain Monte Carlo techniques have been used to derive an isotropic 3-D P-wave velocity model based on first break traveltimes (refracted phases) from controlled source seismic data. Resulting seismic P-wave velocities (Vp ) range from 4.5 to 7.5 km s−1, with an expected general trend of increasing velocities with depth. A sharp velocity change from low Vp in the West to high Vp in the East marks the Insubric Zone (ISZ), the Europe–Adria plate boundary. The most prominent feature of the 3-D tomography model is a high-velocity body (Vp increases from 6 to 7.5 km s−1) that broadens downwards. Its pointy shape peaks the surface East of Balmuccia at a location coincident with the exposed Balmuccia peridotite. Considering rock physics, high-resolution gravity and other geophysical data, we interpret this high-velocity body as dominantly composed of peridotite. The dimension of this seismically imaged peridotite material is far bigger than interpreted from geological cross-sections and requires a revision of previous models. The interpretation of ultramafic bodies in the IVZ as fragments of mantle peridotites interfingered in the crust during pre-Permian accretion is not supported by the new data. Instead, we revive a model that the contact between the Balmuccia peridotite and the Permian mafic magmas might represent a fossil continental crust–mantle transition zone.

Evidence for the Self-organized Criticality Phenomenon in the Prompt Phase of Short Gamma-Ray Bursts

The prompt phase of gamma-ray bursts (GRBs) contains essential information regarding their physical nature and central engine, which are as yet unknown. In this paper, we investigate the self-organized criticality phenomenon in GRB prompt phases as done in X-ray flares of GRBs. We obtain the differential and cumulative distributions of 243 short GRB pulses, such as peak flux, FWHM, rise time, decay time, and peak time in the fourth BATSE Time-Tagged Event Catalog with the Markov Chain Monte Carlo technique. It is found that these distributions can be well described by power-law models. In particular, comparisons are made with 182 short GRB pulses in the third Swift GRB Catalog from 2004 December to 2019 July. The results are essentially consistent with the BATSE ones. We notice that there is no obvious power-law index evolution across different energy bands for either BATSE or Swift short GRBs. The joint analysis suggests that the GRB prompt phase can be explained by a fractal-diffusive self-organized criticality system with the spatial dimension S = 3 and the classical diffusion β = 1. Our findings show that GRB prompt phases and X-ray flares possess the very same magnetically dominated stochastic process and mechanism.

Maximum Product Spacings Estimator for Fuzzy Data Using Inverse Lindley Distribution

The article addresses the problem of parameter estimation of the inverse Lindley distribution when the observations are fuzzy. The estimation of the unknown model parameter was performed using both classical and Bayesian methods. In the classical approach, the estimation of the population parameter is performed using the maximum likelihood (ML) method and the maximum product of distances (MPS) method. In the Bayesian setup, the estimation is obtained using the squared error loss function (SELF) with the Markov Chain Monte Carlo (MCMC) technique. Asymptotic confidence intervals and highest posterior density (HPD) credible intervals for the unknown parameter are also obtained. The performances of the estimators are compared based on their MSEs. Finally, a real data set is analyzed for numerical illustration of the above estimation methods.

Multipole expansion for 21 cm intensity mapping power spectrum: Forecasted cosmological parameters estimation for the SKA observatory

ABSTRACTThe measurement of the large-scale distribution of neutral hydrogen in the late Universe, obtained with radio telescopes through the hydrogen 21 cm line emission, has the potential to become a key cosmological probe in the upcoming years. We explore the constraining power of 21 cm intensity mapping observations on the full set of cosmological parameters that describe the ΛCDM model. We assume a single-dish survey for the SKA Observatory and simulate the 21 cm linear power spectrum monopole and quadrupole within six redshift bins in the range $z$ = 0.25–3. Forecasted constraints are computed numerically through Markov Chain Monte Carlo techniques. We extend the sampler CosmoMC by implementing the likelihood function for the 21 cm power spectrum multipoles. We assess the constraining power of the mock data set alone and combined with Planck 2018 CMB observations. We find that 21 cm multipoles observations alone are enough to obtain constraints on the cosmological parameters comparable with other probes. Combining the 21 cm data set with CMB observations results in significantly reduced errors on all the cosmological parameters. The strongest effect is on Ωch2 and H0, for which the error is reduced by almost a factor four. The percentage errors we estimate are $\sigma _{\Omega _ch^2} = 0.25~{{\ \rm per\ cent}}$ and $\sigma _{H_0} = 0.16~{{\ \rm per\ cent}}$, to be compared with the Planck only results $\sigma _{\Omega _ch^2} = 0.99~{{\ \rm per\ cent}}$ and $\sigma _{H_0} = 0.79~{{\ \rm per\ cent}}$. We conclude that 21 cm SKAO observations will provide a competitive cosmological probe, complementary to CMB and, thus, pivotal for gaining statistical significance on the cosmological parameters constraints, allowing a stress test for the current cosmological model.

Panel threshold model with covariate-dependent thresholds and its application to the cash flow/investment relationship

Abstract This paper introduces a panel threshold model with covariate-dependent and time-varying thresholds (PTCT), which extends the classical panel threshold model of Hansen, B. E. 1999. “Threshold Effects in Non-dynamic Panels: Estimation, Testing, and Inference.” Journal of Econometrics 93: 345–68 to a framework with multiple covariate-dependent and time-varying thresholds. Based on the within-group transformation and Markov chain Monte Carlo (MCMC) technique, we develop methods for estimation and inference for threshold parameters in the proposed panel threshold model. We also suggest test statistics for threshold effect, threshold constancy, and for determining the number of thresholds. Monte Carlo simulations indicate that the estimation, inference and testing procedures work well in finite samples. Empirically, using the same data as in Hansen, B. E. 1999. “Threshold Effects in Non-dynamic Panels: Estimation, Testing, and Inference.” Journal of Econometrics 93: 345–68 we revisit the cash flow/investment relationship and find quite different results.

Supplementing recurrent neural networks with annealing to solve combinatorial optimization problems

Combinatorial optimization problems can be solved by heuristic algorithms such as simulated annealing (SA) which aims to find the optimal solution within a large search space through thermal fluctuations. This algorithm generates new solutions through Markov-chain Monte Carlo techniques which can result in severe limitations, such as slow convergence and a tendency to stay within the same local search space at small temperatures. To overcome these shortcomings, we use the variational classical annealing (VCA) framework that combines autoregressive recurrent neural networks (RNNs) with traditional annealing to sample solutions that are uncorrelated. In this paper, we demonstrate the potential of using VCA as an approach to solving real-world optimization problems. We explore VCA’s performance in comparison with SA at solving three popular optimization problems: the maximum cut problem (Max-Cut), the nurse scheduling problem (NSP), and the traveling salesman problem (TSP). For all three problems, we find that VCA outperforms SA on average in the asymptotic limit by one or more orders of magnitude in terms of relative error. Interestingly, we reach large system sizes of up to 256 cities for the TSP. We also conclude that in the best case scenario, VCA can serve as a great alternative when SA fails to find the optimal solution.

Efficient gravitational wave searches with pulsar timing arrays using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) by looking for correlated deviations in pulse arrival times. Current Bayesian searches use Markov Chain Monte Carlo (MCMC) methods, which struggle to sample the large number of parameters needed to model the PTA and GW signals. As the data span and number of pulsars increase, this problem will only worsen. An alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC), utilizes Hamiltonian dynamics to produce sample proposals informed by first-order gradients of the model likelihood. This in turn allows it to converge faster to high dimensional distributions. We implement HMC as an alternative sampling method in our search for an isotropic stochastic GW background, and show that this method produces equivalent statistical results to similar analyses run with standard MCMC techniques, while requiring 100-200 times fewer samples. We show that the speed of HMC sample generation scales as $\mathcal{O}(N_\mathrm{psr}^{5/4})$ where $N_\mathrm{psr}$ is the number of pulsars, compared to $\mathcal{O}(N_\mathrm{psr}^2)$ for MCMC methods. These factors offset the increased time required to generate a sample using HMC, demonstrating the value of adopting HMC techniques for PTAs.

Lognormal seminumerical simulations of the Lyman α forest: comparison with full hydrodynamic simulations

ABSTRACTObservations of the Lyman α (Ly α) forest in spectra of distant quasars enable us to probe the matter power spectrum at relatively small scales. With several upcoming surveys, it is expected that there will be a many-fold increase in the quantity and quality of data, and hence it is important to develop efficient simulations to forward model these data sets. One such seminumerical method is based on the assumption that the baryonic densities in the intergalactic medium (IGM) follow a lognormal distribution. In this work, we test the robustness of the lognormal model of the Ly α forest in recovering a set of IGM parameters by comparing with high-resolution Sherwood smoothed particle hydrodynamics (SPH) simulations. We study the recovery of the parameters T0 (temperature of the mean-density IGM), γ (slope of the temperature–density relation), and Γ12 (hydrogen photoionization rate) at z ∼ 2.5 using a Markov chain Monte Carlo technique for parameter estimation. Using three flux statistics, the probability distribution, the mean flux, and the power spectrum, values of all three parameters, T0, γ, and Γ12, implied in the SPH simulations are recovered within 1 − σ (∼9, 4, and 1 per cent, respectively) of the median (best-fitting) values. We verify the validity of our results at different baryon smoothing filter, signal-to-noise ratio, box size and resolution, and data seed and confirm that the lognormal model can be used as an efficient tool for modelling the Ly α transmitted flux at z ∼ 2.5.

Reliability analysis of two Gompertz populations under joint progressive type-ii censoring scheme based on binomial removal

ABSTRACT Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies.

Enhanced conformational exploration of protein loops using a global parameterization of the backbone geometry.

Flexible loops are paramount to protein functions, with action modes ranging from localized dynamics contributing to the free energy of the system, to large amplitude conformational changes accounting for the repositioning whole secondary structure elements or protein domains. However, generating diverse and low energy loops remains a difficult problem. This work introduces a novel paradigm to sample loop conformations, in the spirit of the hit-and-run (HAR) Markov chain Monte Carlo technique. The algorithm uses a decomposition of the loop into tripeptides, and a novel characterization of necessary conditions for Tripeptide Loop Closure to admit solutions. Denoting m the number of tripeptides, the algorithm works in an angular space of dimension 12 m. In this space, the hyper-surfaces associated with the aforementioned necessary conditions are used to run a HAR-like sampling technique. On classical loop cases up to 15 amino acids, our parameter free method compares favorably to previous work, generating more diverse conformational ensembles. We also report experiments on a 30 amino acids long loop, a size not processed in any previous work.

Photometric Calibrations of M-dwarf Metallicity with Markov Chain Monte Carlo and Bayesian Inference

Knowledge of stellar atmospheric parameters (T eff, , [Fe/H]) of M dwarfs can be used to constrain both theoretical stellar models and Galactic chemical evolutionary models, and guide exoplanet searches, but their determination is difficult due to the complexity of the spectra of their cool atmospheres. In our ongoing effort to characterize M dwarfs, and in particular their chemical composition, we carried out multiband photometric calibrations of metallicity for early- and intermediate-type M dwarfs. The third Gaia data release provides high-precision astrometry and three-band photometry. This information, combined with the 2MASS and CatWISE2020 infrared photometric surveys and a sample of 4919 M dwarfs with metallicity values determined with high-resolution spectroscopy by The Cannon and APOGEE spectra, allowed us to study the effect of the metallicity in color–color and color–magnitude diagrams. We divided this sample into two subsamples: we used 1000 stars to train the calibrations with Bayesian statistics and Markov Chain Monte Carlo techniques, and the remaining 3919 stars to check the accuracy of the estimations. We derived several photometric calibrations of metallicity applicable to M dwarfs in the range of −0.45 ≤ [Fe/H] ≤ + 0.45 dex and spectral types down to M5.0 V that yield uncertainties down to the 0.10 dex level. Lastly, we compared our results with other photometric estimations published in the literature for an additional sample of 46 M dwarfs in wide binary systems with FGK-type primary stars and found a great predictive performance.

A Gender Study of Food Stress and Implications for International Students Acculturation

Acculturative stress can be a big problem for international students. Among the adaptation difficulties they may face, adjusting to new foods in a new environment is crucial to their well-being. Existing studies related to dietary acculturation point to gender differences, mostly on objective health impacts. Using the information processing approach, this study aims to examine the subjective perception of dietary acculturation difficulties, with a focus on the influence of social connectedness. Using the Bayesian inference approach with the Hamiltonian Markov Chain Monte Carlo (MCMC) technique on a sample of 268 students from a Japanese international university, we found that female students are more likely to have perceived difficulties in the process of adjusting to new foods, but social connectedness lessens this effect. We also found no significant differences between domestic and international students regarding perceived difficulties of food adjustment in this study site, likely due to its highly multicultural environment. We suggest international universities provide better information about the food situations on campuses, especially for female students, and organize more cultural exchange events and food-related social activities to help students overcome barriers of food stress.

Computational Analysis for Fréchet Parameters of Life from Generalized Type-II Progressive Hybrid Censored Data with Applications in Physics and Engineering

Generalized progressive hybrid censored procedures are created to reduce test time and expenses. This paper investigates the issue of estimating the model parameters, reliability, and hazard rate functions of the Fréchet (Fr) distribution under generalized Type-II progressive hybrid censoring by making use of the Bayesian estimation and maximum likelihood methods. The appropriate estimated confidence intervals of unknown quantities are likewise built using the frequentist estimators’ normal approximations. The Bayesian estimators are created using independent gamma conjugate priors under the symmetrical squared-error loss. The Bayesian estimators and the associated greatest posterior density intervals cannot be computed analytically since the joint likelihood function is obtained in complex form, but they may be assessed using Monte Carlo Markov chain (MCMC) techniques. Via extensive Monte Carlo simulations, the actual behavior of the proposed estimation methodologies is evaluated. Four optimality criteria are used to choose the best censoring scheme out of all the options. To demonstrate how the suggested approaches may be utilized in real scenarios, two real applications reflecting the thirty successive values of precipitation in Minneapolis–Saint Paul for the month of March as well as the number of vehicle fatalities for thirty-nine counties in South Carolina during 2012 are examined.

Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data

In life-testing investigations, accelerated life testing is crucial since it reduces both time and costs. In this study, constant-stress partially accelerated life tests using adaptive progressively Type I censored samples are taken into account. This is accomplished under the assumption that the lifespan of products under normal use conditions follows the inverse Weibull distribution. In addition to using the maximum likelihood approach, the maximum product of the spacing procedure is utilized to obtain the point and interval estimates of the model parameters as well as the acceleration factor. Employing the premise of independent gamma priors, the Bayes point estimates using the squared error loss function and the Bayes credible intervals are obtained based on both the likelihood and product of spacing functions via the Markov chain Monte Carlo technique. To assess the effectiveness of the various approaches, a simulation study is used because it is not possible to compare the findings theoretically. To demonstrate the applicability of the various approaches, two real datasets for the lifetime of micro-droplets in the ambient environment and light-emitting diode failure data are investigated. Based on the numerical results, to estimate the parameters and acceleration factor of the inverse Weibull distribution based on the suggested scheme with constant-stress partially accelerated life tests, it is recommended to utilize the Bayesian estimation approach.

Classical and Bayesian inferences on the stress-strength reliability $ {R = P[Y < X < Z]} $ in the geometric distribution setting

<abstract><p>The subject matter described herein includes the analysis of the stress-strength reliability of the system, in which the discrete strength of the system is impacted by two random discrete stresses. The reliability function of such systems is denoted by $ R = P[Y < X < Z] $, where $ X $ is the strength of the system and $ Y $ and $ Z $ are the stresses. We look at how $ X $, $ Y $ and $ Z $ fit into a well-known discrete distribution known as the geometric distribution. The stress-strength reliability of this form is not widely studied in the current literature, and research in this area has only considered the scenario when the strength and stress variables follow a continuous distribution, although it is essentially nil in the case of discrete stress and strength. There are numerous applications wherein a system is exposed to external stress, and its functionality depends on whether its intrinsic physical strength falls within specific stress limits. Furthermore, the continuous measurement of stress and strength variables presents inherent difficulties and inconveniences in such scenarios. For the suggested distribution, we obtain the maximum likelihood estimate of the variable $ R $, as well as its asymptotic distribution and confidence interval. Additionally, in the classical setup, we find the boot-p and boot-t confidence intervals for $ R $. In the Bayesian setup, we utilize the widely recognized Markov Chain Monte Carlo technique and the Lindley approximation method to find the Bayes estimate of $ R $ under the squared error loss function. A Monte Carlo simulation study and real data analysis are demonstrated to show the applicability of the suggested model in the real world.</p></abstract>

Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II progressive censoring data

This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice.