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Journal articles on the topic 'Gaussian; Markov chain Monte Carlo methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Wang, Zheng, Shanxiang Lyu, and Ling Liu. "Learnable Markov Chain Monte Carlo Sampling Methods for Lattice Gaussian Distribution." IEEE Access 7 (2019): 87494–503. http://dx.doi.org/10.1109/access.2019.2925530.

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Ahmadian, Yashar, Jonathan W. Pillow, and Liam Paninski. "Efficient Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains." Neural Computation 23, no. 1 (2011): 46–96. http://dx.doi.org/10.1162/neco_a_00059.

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Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using e

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Wang, Zheng. "Markov Chain Monte Carlo Methods for Lattice Gaussian Sampling: Convergence Analysis and Enhancement." IEEE Transactions on Communications 67, no. 10 (2019): 6711–24. http://dx.doi.org/10.1109/tcomm.2019.2926470.

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Whiley, Matt, and Simon P. Wilson. "Parallel algorithms for Markov chain Monte Carlo methods in latent spatial Gaussian models." Statistics and Computing 14, no. 3 (2004): 171–79. http://dx.doi.org/10.1023/b:stco.0000035299.51541.5e.

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Geweke, John, and Hisashi Tanizaki. "On markov chain monte carlo methods for nonlinear and non-gaussian state-space models." Communications in Statistics - Simulation and Computation 28, no. 4 (1999): 867–94. http://dx.doi.org/10.1080/03610919908813583.

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Jiao, Zhun, and Rong Zhang. "Improved Particle Filter for Integrated Navigation System." Applied Mechanics and Materials 543-547 (March 2014): 1278–81. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1278.

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As a new method for dealing with any nonlinear or non-Gaussian distributions, based on the Monte Carlo methods and Bayesian filtering, particle filters (PF) are favored by researchers and widely applied in many fields. Based on particle filtering, an improved particle filter (IPF) proposal distribution is presented. Evaluation of the weights is simplified and other improved techniques including the residual resampling step and Markov Chain Monte Carlo method are introduced for SINS/GPS integrated navigation system. The simulation results confirm that the improved particle filter outperforms th

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Lu, Dan, Daniel Ricciuto, Anthony Walker, Cosmin Safta, and William Munger. "Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods." Biogeosciences 14, no. 18 (2017): 4295–314. http://dx.doi.org/10.5194/bg-14-4295-2017.

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Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of

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Durante, Daniele. "Conjugate Bayes for probit regression via unified skew-normal distributions." Biometrika 106, no. 4 (2019): 765–79. http://dx.doi.org/10.1093/biomet/asz034.

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Summary Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically taken to be Gaussians, with the likelihood induced by probit or logit regressions for the responses. In this updating, the apparent absence of a tractable posterior has motivated a variety of computational methods,

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Peng, Li Feng, Guo Shao Su, and Wei Zhao. "Fast Analysis of Structural Reliability Using Gaussian Process Classification Based Dynamic Response Surface Method." Applied Mechanics and Materials 501-504 (January 2014): 1067–70. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.1067.

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The performance function of large-scale complicated engineering structure is always highly nonlinear and implicit, and its reliability needs to be evaluated through a time-consuming Finite Element method (FEM). A new method, Gaussian process classification (GPC) dynamic response surface based on Monte Carlo Simulation (MCS) was proposed. Small training samples were created using FEM and Markov chain. Then, the most probable point (MPP) is predicted quickly using MCS without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPC by using information

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Tilmann, F. J., H. Sadeghisorkhani, and A. Mauerberger. "Another look at the treatment of data uncertainty in Markov chain Monte Carlo inversion and other probabilistic methods." Geophysical Journal International 222, no. 1 (2020): 388–405. http://dx.doi.org/10.1093/gji/ggaa168.

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SUMMARY In probabilistic Bayesian inversions, data uncertainty is a crucial parameter for quantifying the uncertainties and correlations of the resulting model parameters or, in transdimensional approaches, even the complexity of the model. However, in many geophysical inference problems it is poorly known. Therefore, it is common practice to allow the data uncertainty itself to be a parameter to be determined. Although in principle any arbitrary uncertainty distribution can be assumed, Gaussian distributions whose standard deviation is then the unknown parameter to be estimated are the usual

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Noh, S. J., Y. Tachikawa, M. Shiiba, and S. Kim. "Applying sequential Monte Carlo methods into a distributed hydrologic model: lagged particle filtering approach with regularization." Hydrology and Earth System Sciences Discussions 8, no. 2 (2011): 3383–420. http://dx.doi.org/10.5194/hessd-8-3383-2011.

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Abstract. Applications of data assimilation techniques have been widely used to improve hydrologic prediction. Among various data assimilation techniques, sequential Monte Carlo (SMC) methods, known as "particle filters", provide the capability to handle non-linear and non-Gaussian state-space models. In this paper, we propose an improved particle filtering approach to consider different response time of internal state variables in a hydrologic model. The proposed method adopts a lagged filtering approach to aggregate model response until uncertainty of each hydrologic process is propagated. T

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Cai, Rong-Gen, and Tao Yang. "Standard sirens and dark sector with Gaussian process." EPJ Web of Conferences 168 (2018): 01008. http://dx.doi.org/10.1051/epjconf/201816801008.

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The gravitational waves from compact binary systems are viewed as a standard siren to probe the evolution of the universe. This paper summarizes the potential and ability to use the gravitational waves to constrain the cosmological parameters and the dark sector interaction in the Gaussian process methodology. After briefly introducing the method to reconstruct the dark sector interaction by the Gaussian process, the concept of standard sirens and the analysis of reconstructing the dark sector interaction with LISA are outlined. Furthermore, we estimate the constraint ability of the gravitatio

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Cui, Kai. "Semiparametric Gaussian Variance-Mean Mixtures for Heavy-Tailed and Skewed Data." ISRN Probability and Statistics 2012 (December 23, 2012): 1–18. http://dx.doi.org/10.5402/2012/345784.

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There is a need for new classes of flexible multivariate distributions that can capture heavy tails and skewness without being so flexible as to fully incur the curse of dimensionality intrinsic to nonparametric density estimation. We focus on the family of Gaussian variance-mean mixtures, which have received limited attention in multivariate settings beyond simple special cases. By using a Bayesian semiparametric approach, we allow the data to infer about the unknown mixing distribution. Properties are considered and an approach to posterior computation is developed relying on Markov chain Mo

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Chin, T. M., M. J. Turmon, J. B. Jewell, and M. Ghil. "An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems." Monthly Weather Review 135, no. 1 (2007): 186–202. http://dx.doi.org/10.1175/mwr3353.1.

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Abstract Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF.

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Aleardi, Mattia, Fabio Ciabarri, and Timur Gukov. "A two-step inversion approach for seismic-reservoir characterization and a comparison with a single-loop Markov-chain Monte Carlo algorithm." GEOPHYSICS 83, no. 3 (2018): R227—R244. http://dx.doi.org/10.1190/geo2017-0387.1.

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We have evaluated a two-step Bayesian algorithm for seismic-reservoir characterization, which, thanks to some simplifying assumptions, is computationally very efficient. The applicability and reliability of this method are assessed by comparison with a more sophisticated and computer-intensive Markov-chain Monte Carlo (MCMC) algorithm, which in a single loop directly estimates petrophysical properties and lithofluid facies from prestack data. The two-step method first combines a linear rock-physics model (RPM) with the analytical solution of a linearized amplitude versus angle (AVA) inversion,

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Wu, Chen, Li, and Peng. "Acoustic Impedance Inversion Using Gaussian Metropolis–Hastings Sampling with Data Driving." Energies 12, no. 14 (2019): 2744. http://dx.doi.org/10.3390/en12142744.

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The Markov chain Monte Carlo (MCMC) method based on Metropolis–Hastings (MH) sampling is a popular approach in solving seismic acoustic impedance (AI) inversion problem, as it can improve the inversion resolution by statistical prior information. However, the sampling function of the traditional MH sampling is a fixed parameter distribution. The parameter ignores the statistical information of AI that expands sampling range and reduces the inversion efficiency and resolution. To reduce the sampling range and improve the efficiency, we apply the statistical information of AI to the sampling fun

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Maniatis, G., N. Demiris, A. Kranis, G. Banos, and A. Kominakis. "Comparison of inference methods of genetic parameters with an application to body weight in broilers." Archives Animal Breeding 58, no. 2 (2015): 277–86. http://dx.doi.org/10.5194/aab-58-277-2015.

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Abstract. REML (restricted maximum likelihood) has become the standard method of variance component estimation in animal breeding. Inference in Bayesian animal models is typically based upon Markov chain Monte Carlo (MCMC) methods, which are generally flexible but time-consuming. Recently, a new Bayesian computational method, integrated nested Laplace approximation (INLA), has been introduced for making fast non-sampling-based Bayesian inference for hierarchical latent Gaussian models. This paper is concerned with the comparison of estimates provided by three representative programs (ASReml, W

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Noh, S. J., Y. Tachikawa, M. Shiiba, and S. Kim. "Applying sequential Monte Carlo methods into a distributed hydrologic model: lagged particle filtering approach with regularization." Hydrology and Earth System Sciences 15, no. 10 (2011): 3237–51. http://dx.doi.org/10.5194/hess-15-3237-2011.

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Abstract. Data assimilation techniques have received growing attention due to their capability to improve prediction. Among various data assimilation techniques, sequential Monte Carlo (SMC) methods, known as "particle filters", are a Bayesian learning process that has the capability to handle non-linear and non-Gaussian state-space models. In this paper, we propose an improved particle filtering approach to consider different response times of internal state variables in a hydrologic model. The proposed method adopts a lagged filtering approach to aggregate model response until the uncertaint

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19

Beneš, Viktor, Karel Bodlák, Jesper Møller, and Rasmus Waagepetersen. "A CASE STUDY ON POINT PROCESS MODELLING IN DISEASE MAPPING." Image Analysis & Stereology 23, no. 3 (2011): 159. http://dx.doi.org/10.5566/ias.v24.p159-168.

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We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis (TBE), and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence of the risk on the covariates. Instead of using the common area level approaches we base the analysis on a Bayesian approach for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using Markov chain Monte

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Li, Xin, and Albert C. Reynolds. "A Gaussian Mixture Model as a Proposal Distribution for Efficient Markov-Chain Monte Carlo Characterization of Uncertainty in Reservoir Description and Forecasting." SPE Journal 25, no. 01 (2019): 001–36. http://dx.doi.org/10.2118/182684-pa.

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Summary Generating an estimate of uncertainty in production forecasts has become nearly standard in the oil industry, but is often performed with procedures that yield at best a highly approximate uncertainty quantification. Formally, the uncertainty quantification of a production forecast can be achieved by generating a correct characterization of the posterior probability-density function (PDF) of reservoir-model parameters conditional to dynamic data and then sampling this PDF correctly. Although Markov-chain Monte Carlo (MCMC) provides a theoretically rigorous method for sampling any targe

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Ruchi, Sangeetika, Svetlana Dubinkina, and Jana de Wiljes. "Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation." Nonlinear Processes in Geophysics 28, no. 1 (2021): 23–41. http://dx.doi.org/10.5194/npg-28-23-2021.

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Abstract. Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte

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Girolami, Mark, and Simon Rogers. "Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors." Neural Computation 18, no. 8 (2006): 1790–817. http://dx.doi.org/10.1162/neco.2006.18.8.1790.

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It is well known in the statistics literature that augmenting binary and polychotomous response models with gaussian latent variables enables exact Bayesian analysis via Gibbs sampling from the parameter posterior. By adopting such a data augmentation strategy, dispensing with priors over regression coefficients in favor of gaussian process (GP) priors over functions, and employing variational approximations to the full posterior, we obtain efficient computational methods for GP classification in the multiclass setting.1 The model augmentation with additional latent variables ensures full a po

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Madan, Hennadii, Franjo Pernuš, and Žiga Špiclin. "Reference-free error estimation for multiple measurement methods." Statistical Methods in Medical Research 28, no. 7 (2018): 2196–209. http://dx.doi.org/10.1177/0962280217754231.

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We present a computational framework to select the most accurate and precise method of measurement of a certain quantity, when there is no access to the true value of the measurand. A typical use case is when several image analysis methods are applied to measure the value of a particular quantitative imaging biomarker from the same images. The accuracy of each measurement method is characterized by systematic error (bias), which is modeled as a polynomial in true values of measurand, and the precision as random error modeled with a Gaussian random variable. In contrast to previous works, the r

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Feng, Xia, Timothy DelSole, and Paul Houser. "Comparison of Seasonal Potential Predictability of Precipitation." Journal of Climate 27, no. 11 (2014): 4094–110. http://dx.doi.org/10.1175/jcli-d-13-00489.1.

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Abstract Three methods for estimating potential seasonal predictability of precipitation from a single realization of daily data are assessed. The estimation methods include a first-order Markov chain model proposed by Katz (KZ), and an analysis of covariance (ANOCOVA) method and a bootstrap method proposed by the authors. The assessment is based on Monte Carlo experiments, ensemble atmospheric general circulation model (AGCM) simulations, and observation-based data. For AGCM time series, ANOCOVA produces the most accurate estimates of weather noise variance, despite the fact that it makes the

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Lu, Rong, Jennifer L. Miskimins, and Mikhail Zhizhin. "Learning from Nighttime Observations of Gas Flaring in North Dakota for Better Decision and Policy Making." Remote Sensing 13, no. 5 (2021): 941. http://dx.doi.org/10.3390/rs13050941.

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In today’s oil industry, companies frequently flare the produced natural gas from oil wells. The flaring activities are extensive in some regions including North Dakota. Besides company-reported data, which are compiled by the North Dakota Industrial Commission, flaring statistics such as count and volume can be estimated via Visible Infrared Imaging Radiometer Suite nighttime observations. Following data gathering and preprocessing, Bayesian machine learning implemented with Markov chain Monte Carlo methods is performed to tackle two tasks: flaring time series analysis and distribution approx

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Gangopadhyay, A., and W. C. Gau. "Bayesian Nonparametric Approach to Credibility Modelling." Annals of Actuarial Science 2, no. 1 (2007): 91–114. http://dx.doi.org/10.1017/s1748499500000270.

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ABSTRACTCurrent methods in credibility theory often rely on parametric models, e.g., a linear function of past experience. During the last decade, the existence of high speed computers and statistical software packages allowed the introduction of more sophisticated and flexible modelling strategies. In recent years, some of these techniques, which made use of the Markov Chain Monte Carlo (MCMC) approach to modelling, have been incorporated in credibility theory. However, very few of these methods made use of additional covariate information related to risk, or collection of risks; and at the s

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Vehtari, Aki, and Jouko Lampinen. "Bayesian Model Assessment and Comparison Using Cross-Validation Predictive Densities." Neural Computation 14, no. 10 (2002): 2439–68. http://dx.doi.org/10.1162/08997660260293292.

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In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate because it describes the uncertainty in the estimate. The distributions of the expected utility estimates can also be used to compare models, for example, by computing the probability of one model having a better expected

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Miller, S. M., A. M. Michalak, and P. J. Levi. "Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions." Geoscientific Model Development 7, no. 1 (2014): 303–15. http://dx.doi.org/10.5194/gmd-7-303-2014.

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Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include nonnegativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination

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Potthast, Roland, Anne Walter, and Andreas Rhodin. "A Localized Adaptive Particle Filter within an Operational NWP Framework." Monthly Weather Review 147, no. 1 (2019): 345–62. http://dx.doi.org/10.1175/mwr-d-18-0028.1.

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Particle filters are well known in statistics. They have a long tradition in the framework of ensemble data assimilation (EDA) as well as Markov chain Monte Carlo (MCMC) methods. A key challenge today is to employ such methods in a high-dimensional environment, since the naïve application of the classical particle filter usually leads to filter divergence or filter collapse when applied within the very high dimension of many practical assimilation problems (known as the curse of dimensionality). The goal of this work is to develop a localized adaptive particle filter (LAPF), which follows clos

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Mendoza, Alberto, Lassi Roininen, Mark Girolami, Jere Heikkinen, and Heikki Haario. "Statistical methods to enable practical on-site tomographic imaging of whole-core samples." GEOPHYSICS 84, no. 3 (2019): D89—D100. http://dx.doi.org/10.1190/geo2018-0436.1.

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Statistical methods enable the use of portable industrial scanners with sparse measurements, suitable for fast on-site whole-core X-ray computed tomography (CT), as opposed to conventional (medical) devices that use dense measurements. This approach accelerates an informed first-stage general assessment of core samples. To that end, this novel industrial tomographic measurement principle is feasible for rock-sample imaging, in conjunction with suitable forms of priors in Bayesian inversion algorithms. Gaussian, Cauchy, and total variation priors yield different inversion characteristics for si

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Arjas, Arttu, Andreas Hauptmann, and Mikko J. Sillanpää. "Estimation of dynamic SNP-heritability with Bayesian Gaussian process models." Bioinformatics 36, no. 12 (2020): 3795–802. http://dx.doi.org/10.1093/bioinformatics/btaa199.

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Abstract Motivation Improved DNA technology has made it practical to estimate single-nucleotide polymorphism (SNP)-heritability among distantly related individuals with unknown relationships. For growth- and development-related traits, it is meaningful to base SNP-heritability estimation on longitudinal data due to the time-dependency of the process. However, only few statistical methods have been developed so far for estimating dynamic SNP-heritability and quantifying its full uncertainty. Results We introduce a completely tuning-free Bayesian Gaussian process (GP)-based approach for estimati

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Pfreundschuh, Simon, Patrick Eriksson, David Duncan, Bengt Rydberg, Nina Håkansson, and Anke Thoss. "A neural network approach to estimating a posteriori distributions of Bayesian retrieval problems." Atmospheric Measurement Techniques 11, no. 8 (2018): 4627–43. http://dx.doi.org/10.5194/amt-11-4627-2018.

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Abstract. A neural-network-based method, quantile regression neural networks (QRNNs), is proposed as a novel approach to estimating the a posteriori distribution of Bayesian remote sensing retrievals. The advantage of QRNNs over conventional neural network retrievals is that they learn to predict not only a single retrieval value but also the associated, case-specific uncertainties. In this study, the retrieval performance of QRNNs is characterized and compared to that of other state-of-the-art retrieval methods. A synthetic retrieval scenario is presented and used as a validation case for the

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Lenoir, Guillaume, and Michel Crucifix. "A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis." Nonlinear Processes in Geophysics 25, no. 1 (2018): 175–200. http://dx.doi.org/10.5194/npg-25-175-2018.

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Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform equivalent of the extended Lomb–Scargle periodogram defined in Part 1 of this study (Lenoir and Crucifix, 2018). The signal being analysed is modelled as the sum of a locally periodic component in the time–frequency pl

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Hassan, Masoud M. "A Fully Bayesian Logistic Regression Model for Classification of ZADA Diabetes Dataset." Science Journal of University of Zakho 8, no. 3 (2020): 105–11. http://dx.doi.org/10.25271/sjuoz.2020.8.3.707.

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Classification of diabetes data with existing data mining and machine learning algorithms is challenging and the predictions are not always accurate. We aim to build a model that effectively addresses these challenges (misclassification) and can accurately diagnose and classify diabetes. In this study, we investigated the use of Bayesian Logistic Regression (BLR) for mining such data to diagnose and classify various diabetes conditions. This approach is fully Bayesian suited for automating Markov Chain Monte Carlo (MCMC) simulation. Using Bayesian methods in analysing medical data is useful be

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Pollard, David, Won Chang, Murali Haran, Patrick Applegate, and Robert DeConto. "Large ensemble modeling of the last deglacial retreat of the West Antarctic Ice Sheet: comparison of simple and advanced statistical techniques." Geoscientific Model Development 9, no. 5 (2016): 1697–723. http://dx.doi.org/10.5194/gmd-9-1697-2016.

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Abstract. A 3-D hybrid ice-sheet model is applied to the last deglacial retreat of the West Antarctic Ice Sheet over the last ∼ 20 000 yr. A large ensemble of 625 model runs is used to calibrate the model to modern and geologic data, including reconstructed grounding lines, relative sea-level records, elevation–age data and uplift rates, with an aggregate score computed for each run that measures overall model–data misfit. Two types of statistical methods are used to analyze the large-ensemble results: simple averaging weighted by the aggregate score, and more advanced Bayesian techniques invo

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Miller, S. M., A. M. Michalak, and P. J. Levi. "Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions." Geoscientific Model Development Discussions 6, no. 3 (2013): 4531–62. http://dx.doi.org/10.5194/gmdd-6-4531-2013.

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Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include non-negativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examinatio

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Chen, Jinsong, G. Michael Hoversten, Kerry Key, Gregg Nordquist, and William Cumming. "Stochastic inversion of magnetotelluric data using a sharp boundary parameterization and application to a geothermal site." GEOPHYSICS 77, no. 4 (2012): E265—E279. http://dx.doi.org/10.1190/geo2011-0430.1.

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We developed a Bayesian model to invert magnetotelluric (MT) data using a 2D sharp boundary parameterization. We divided the 2D cross section into layers and considered the locations of interfaces and resistivity of the regions formed by the interfaces as random variables. We assumed that those variables are independent in the vertical direction and dependent along the lateral direction, whose spatial dependence is described by either pairwise difference or multivariate Gaussian priors. We used a parallel, adaptive finite-element algorithm to rapidly forward simulate frequency-domain MT respon

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Blatter, Daniel, Anandaroop Ray, and Kerry Key. "Two-dimensional Bayesian inversion of magnetotelluric data using trans-dimensional Gaussian processes." Geophysical Journal International 226, no. 1 (2021): 548–63. http://dx.doi.org/10.1093/gji/ggab110.

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SUMMARY Bayesian inversion of electromagnetic data produces crucial uncertainty information on inferred subsurface resistivity. Due to their high computational cost, however, Bayesian inverse methods have largely been restricted to computationally expedient 1-D resistivity models. In this study, we successfully demonstrate, for the first time, a fully 2-D, trans-dimensional Bayesian inversion of magnetotelluric (MT) data. We render this problem tractable from a computational standpoint by using a stochastic interpolation algorithm known as a Gaussian process (GP) to achieve a parsimonious para

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Ghofrani, Faeze, Qing He, Reza Mohammadi, Abhishek Pathak, and Amjad Aref. "Bayesian Survival Approach to Analyzing the Risk of Recurrent Rail Defects." Transportation Research Record: Journal of the Transportation Research Board 2673, no. 7 (2019): 281–93. http://dx.doi.org/10.1177/0361198119844241.

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This paper develops a Bayesian framework to explore the impact of different factors and to predict the risk of recurrence of rail defects, based upon datasets collected from a US Class I railroad between 2011 and 2016. To this end, this study constructs a parametric Weibull baseline hazard function and a proportional hazard (PH) model under a Gaussian frailty approach. The analysis is performed using Markov chain Monte Carlo simulation methods and the fit of the model is checked using a Cox–Snell residual plot. The results of the model show that the recurrence of a defect is correlated with di

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Fang, Zhilong, Curt Da Silva, Rachel Kuske, and Felix J. Herrmann. "Uncertainty quantification for inverse problems with weak partial-differential-equation constraints." GEOPHYSICS 83, no. 6 (2018): R629—R647. http://dx.doi.org/10.1190/geo2017-0824.1.

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In statistical inverse problems, the objective is a complete statistical description of unknown parameters from noisy observations to quantify uncertainties in unknown parameters. We consider inverse problems with partial-differential-equation (PDE) constraints, which are applicable to many seismic problems. Bayesian inference is one of the most widely used approaches to precisely quantify statistics through a posterior distribution, incorporating uncertainties in observed data, modeling kernel, and prior knowledge of parameters. Typically when formulating the posterior distribution, the PDE c

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Pollard, D., W. Chang, M. Haran, P. Applegate, and R. DeConto. "Large ensemble modeling of last deglacial retreat of the West Antarctic Ice Sheet: comparison of simple and advanced statistical techniques." Geoscientific Model Development Discussions 8, no. 11 (2015): 9925–63. http://dx.doi.org/10.5194/gmdd-8-9925-2015.

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Abstract. A 3-D hybrid ice-sheet model is applied to the last deglacial retreat of the West Antarctic Ice Sheet over the last ~ 20 000 years. A large ensemble of 625 model runs is used to calibrate the model to modern and geologic data, including reconstructed grounding lines, relative sea-level records, elevation-age data and uplift rates, with an aggregate score computed for each run that measures overall model-data misfit. Two types of statistical methods are used to analyze the large-ensemble results: simple averaging weighted by the aggregate score, and more advanced Bayesian techniques i

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Ju, Feng, Ru An, and Yaxing Sun. "Immune Evolution Particle Filter for Soil Moisture Data Assimilation." Water 11, no. 2 (2019): 211. http://dx.doi.org/10.3390/w11020211.

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Data assimilation (DA) has been widely used in land surface models (LSM) to improve model state estimates. Among various DA methods, the particle filter (PF) with Markov chain Monte Carlo (MCMC) has become increasingly popular for estimating the states of the nonlinear and non-Gaussian LSMs. However, the standard PF always suffers from the particle impoverishment problem, characterized by loss of particle diversity. To solve this problem, an immune evolution particle filter with MCMC simulation inspired by the biological immune system, entitled IEPFM, is proposed for DA in this paper. The meri

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Posselt, Derek J., and Gerald G. Mace. "MCMC-Based Assessment of the Error Characteristics of a Surface-Based Combined Radar–Passive Microwave Cloud Property Retrieval." Journal of Applied Meteorology and Climatology 53, no. 8 (2014): 2034–57. http://dx.doi.org/10.1175/jamc-d-13-0237.1.

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AbstractCollocated active and passive remote sensing measurements collected at U.S. Department of Energy Atmospheric Radiation Measurement Program sites enable simultaneous retrieval of cloud and precipitation properties and air motion. Previous studies indicate the parameters of a bimodal cloud particle size distribution can be effectively constrained using a combination of passive microwave radiometer and radar observations; however, aspects of the particle size distribution and particle shape are typically assumed to be known. In addition, many retrievals assume the observation and retrieva

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Lenoir, Guillaume, and Michel Crucifix. "A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 1: Frequency analysis." Nonlinear Processes in Geophysics 25, no. 1 (2018): 145–73. http://dx.doi.org/10.5194/npg-25-145-2018.

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Abstract. We develop a general framework for the frequency analysis of irregularly sampled time series. It is based on the Lomb–Scargle periodogram, but extended to algebraic operators accounting for the presence of a polynomial trend in the model for the data, in addition to a periodic component and a background noise. Special care is devoted to the correlation between the trend and the periodic component. This new periodogram is then cast into the Welch overlapping segment averaging (WOSA) method in order to reduce its variance. We also design a test of significance for the WOSA periodogram,

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Heydenreich, Sven, Benjamin Brück, and Joachim Harnois-Déraps. "Persistent homology in cosmic shear: Constraining parameters with topological data analysis." Astronomy & Astrophysics 648 (April 2021): A74. http://dx.doi.org/10.1051/0004-6361/202039048.

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In recent years, cosmic shear has emerged as a powerful tool for studying the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods such as peak count statistics offer competitive results. Here we show that persistent homology, a tool from topological data analysis, can extract more cosmological information than previous methods from the same data set. For this, we use persistent Betti numbers to efficiently summarise the full topological structure of weak lensing aperture mass maps. This method can be seen as a

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Martikainen, J., K. Muinonen, A. Penttilä, A. Cellino, and X. B. Wang. "Asteroid absolute magnitudes and phase curve parameters from Gaia photometry." Astronomy & Astrophysics 649 (May 2021): A98. http://dx.doi.org/10.1051/0004-6361/202039796.

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Aims. We perform light curve inversion for 491 asteroids to retrieve phase curve parameters, rotation periods, pole longitudes and latitudes, and convex and triaxial ellipsoid shapes by using the sparse photometric observations from Gaia Data Release 2 and the dense ground-based observations from the DAMIT database. We develop a method for the derivation of reference absolute magnitudes and phase curves from the Gaia data, allowing for comparative studies involving hundreds of asteroids. Methods. For both general convex shapes and ellipsoid shapes, we computed least-squares solutions using eit

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Fernández Martínez, Juan Luis, Tapan Mukerji, Esperanza García Gonzalo, and Amit Suman. "Reservoir characterization and inversion uncertainty via a family of particle swarm optimizers." GEOPHYSICS 77, no. 1 (2012): M1—M16. http://dx.doi.org/10.1190/geo2011-0041.1.

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History matching provides to reservoir engineers an improved spatial distribution of physical properties to be used in forecasting the reservoir response for field management. The ill-posed character of the history-matching problem yields nonuniqueness and numerical instabilities that increase with the reservoir complexity. These features might cause local optimization methods to provide unpredictable results not being able to discriminate among the multiple models that fit the observed data (production history). Also, the high dimensionality of the inverse problem impedes estimation of uncert

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Basson, Abigail R., Fabio Cominelli, and Alexander Rodriguez-Palacios. "‘Statistical Irreproducibility’ Does Not Improve with Larger Sample Size: How to Quantify and Address Disease Data Multimodality in Human and Animal Research." Journal of Personalized Medicine 11, no. 3 (2021): 234. http://dx.doi.org/10.3390/jpm11030234.

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Poor study reproducibility is a concern in translational research. As a solution, it is recommended to increase sample size (N), i.e., add more subjects to experiments. The goal of this study was to examine/visualize data multimodality (data with >1 data peak/mode) as cause of study irreproducibility. To emulate the repetition of studies and random sampling of study subjects, we first used various simulation methods of random number generation based on preclinical published disease outcome data from human gut microbiota-transplantation rodent studies (e.g., intestinal inflammation and univa

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Ruchi, Sangeetika, and Svetlana Dubinkina. "Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling." Nonlinear Processes in Geophysics 25, no. 4 (2018): 731–46. http://dx.doi.org/10.5194/npg-25-731-2018.

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Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable Markov chain Monte Carlo (MCMC) methods are computationally expensive. Sequential ensemble methods such as ensemble Kalman filters and particle filters provide a favorable alternative. However, ensemble Kalman filter has an assumption of Gaussianity. Ensemble transform particle filter does not have this assumption and has proven to be highly beneficial for an initial condition estimation and a sm

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Athreya, K. B., Mohan Delampady, and T. Krishnan. "Markov Chain Monte Carlo methods." Resonance 8, no. 4 (2003): 17–26. http://dx.doi.org/10.1007/bf02883528.

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