Статті в журналах: "Non-reversible Markov chain"

1

Choi, Michael C. H., and Pierre Patie. "Analysis of non-reversible Markov chains via similarity orbits." Combinatorics, Probability and Computing 29, no. 4 (February 18, 2020): 508–36. http://dx.doi.org/10.1017/s0963548320000024.

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AbstractIn this paper we develop an in-depth analysis of non-reversible Markov chains on denumerable state space from a similarity orbit perspective. In particular, we study the class of Markov chains whose transition kernel is in the similarity orbit of a normal transition kernel, such as that of birth–death chains or reversible Markov chains. We start by identifying a set of sufficient conditions for a Markov chain to belong to the similarity orbit of a birth–death chain. As by-products, we obtain a spectral representation in terms of non-self-adjoint resolutions of identity in the sense of Dunford [21] and offer a detailed analysis on the convergence rate, separation cutoff and L2-cutoff of this class of non-reversible Markov chains. We also look into the problem of estimating the integral functionals from discrete observations for this class. In the last part of this paper we investigate a particular similarity orbit of reversible Markov kernels, which we call the pure birth orbit, and analyse various possibly non-reversible variants of classical birth–death processes in this orbit.

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2

Qin, Liang, Philipp Höllmer, and Werner Krauth. "Direction-sweep Markov chains." Journal of Physics A: Mathematical and Theoretical 55, no. 10 (February 16, 2022): 105003. http://dx.doi.org/10.1088/1751-8121/ac508a.

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Abstract We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the popular MCMC sweep methods for particle or spin indices. Direction-sweep MCMC can be applied to a wide range of reversible or non-reversible Markov chains, such as the Metropolis algorithm or the event-chain Monte Carlo algorithm. For a single two-dimensional tethered hard-disk dipole, we consider direction-sweep MCMC in the limit where restricted equilibrium is reached among the accessible configurations for a fixed direction before incrementing it. We show rigorously that direction-sweep MCMC leaves the stationary probability distribution unchanged and that it profoundly modifies the Markov-chain trajectory. Long excursions, with persistent rotation in one direction, alternate with long sequences of rapid zigzags resulting in persistent rotation in the opposite direction in the limit of small direction increments. The mapping to a Langevin equation then yields the exact scaling of excursions while the zigzags are described through a non-linear differential equation that is solved exactly. We show that the direction-sweep algorithm can have shorter mixing times than the algorithms with random updates of directions. We point out possible applications of direction-sweep MCMC in polymer physics and in molecular simulation.

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3

Höllmer, Philipp, A. C. Maggs, and Werner Krauth. "Hard-disk dipoles and non-reversible Markov chains." Journal of Chemical Physics 156, no. 8 (February 28, 2022): 084108. http://dx.doi.org/10.1063/5.0080101.

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We benchmark event-chain Monte Carlo (ECMC) algorithms for tethered hard-disk dipoles in two dimensions in view of application of ECMC to water models in molecular simulation. We characterize the rotation dynamics of dipoles through the integrated autocorrelation times of the polarization. The non-reversible straight, reflective, forward, and Newtonian ECMC algorithms are all event-driven and only move a single hard disk at any time. They differ only in their update rules at event times. We show that they realize considerable speedups with respect to the local reversible Metropolis algorithm with single-disk moves. We also find significant speed differences among the ECMC variants. Newtonian ECMC appears particularly well-suited for overcoming the dynamical arrest that has plagued straight ECMC for three-dimensional dipolar models with Coulomb interactions.

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4

Dobson, P., I. Fursov, G. Lord, and M. Ottobre. "Reversible and non-reversible Markov chain Monte Carlo algorithms for reservoir simulation problems." Computational Geosciences 24, no. 3 (March 13, 2020): 1301–13. http://dx.doi.org/10.1007/s10596-020-09947-4.

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5

Vialaret, Marie, and Florian Maire. "On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods." Methodology and Computing in Applied Probability 22, no. 3 (February 15, 2020): 1349–87. http://dx.doi.org/10.1007/s11009-019-09766-w.

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6

Yang, Shangze, Di Xiao, Xuesong Li, and Zhen Ma. "Markov Chain Investigation of Discretization Schemes and Computational Cost Reduction in Modeling Photon Multiple Scattering." Applied Sciences 8, no. 11 (November 19, 2018): 2288. http://dx.doi.org/10.3390/app8112288.

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Establishing fast and reversible photon multiple scattering algorithms remains a modeling challenge for optical diagnostics and noise reduction purposes, especially when the scattering happens within the intermediate scattering regime. Previous work has proposed and verified a Markov chain approach for modeling photon multiple scattering phenomena through turbid slabs. The fidelity of the Markov chain method has been verified through detailed comparison with Monte Carlo models. However, further improvement to the Markov chain method is still required to improve its performance in studying multiple scattering. The present research discussed the efficacy of non-uniform discretization schemes and analyzed errors induced by different schemes. The current work also proposed an iterative approach as an alternative to directly carrying out matrix inversion manipulations, which would significantly reduce the computational costs. The benefits of utilizing non-uniform discretization schemes and the iterative approach were confirmed and verified by comparing the results to a Monte Carlo simulation.

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7

Kijima, Masaaki. "On passage and conditional passage times for Markov chains in continuous time." Journal of Applied Probability 25, no. 2 (June 1988): 279–90. http://dx.doi.org/10.2307/3214436.

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Let X(t) be a temporally homogeneous irreducible Markov chain in continuous time defined on . For k < i < j, let H = {k + 1, ···, j − 1} and let kTij (jTik) be the upward (downward) conditional first-passage time of X(t) from i to j(k) given no visit to . These conditional passage times are studied through first-passage times of a modified chain HX(t) constructed by making the set of states absorbing. It will be shown that the densities of kTij and jTik for any birth-death process are unimodal and the modes kmij (jmik) of the unimodal densities are non-increasing (non-decreasing) with respect to i. Some distribution properties of kTij and jTik for a time-reversible Markov chain are presented. Symmetry among kTij, jTik, and is also discussed, where , and are conditional passage times of the reversed process of X(t).

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8

Kijima, Masaaki. "On passage and conditional passage times for Markov chains in continuous time." Journal of Applied Probability 25, no. 02 (June 1988): 279–90. http://dx.doi.org/10.1017/s0021900200040924.

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Let X(t) be a temporally homogeneous irreducible Markov chain in continuous time defined on . For k < i < j, let H = {k + 1, ···, j − 1} and let kTij ( jTik ) be the upward (downward) conditional first-passage time of X(t) from i to j(k) given no visit to . These conditional passage times are studied through first-passage times of a modified chain HX(t) constructed by making the set of states absorbing. It will be shown that the densities of kTij and jTik for any birth-death process are unimodal and the modes kmij ( jmik ) of the unimodal densities are non-increasing (non-decreasing) with respect to i. Some distribution properties of kTij and jTik for a time-reversible Markov chain are presented. Symmetry among kTij, jTik , and is also discussed, where , and are conditional passage times of the reversed process of X(t).

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9

Vermolen, Fred, and Ilkka Pölönen. "Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer." Journal of Mathematical Biology 80, no. 3 (December 19, 2019): 545–73. http://dx.doi.org/10.1007/s00285-019-01367-y.

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AbstractA spatial Markov-chain model is formulated for the progression of skin cancer. The model is based on the division of the computational domain into nodal points, that can be in a binary state: either in ‘cancer state’ or in ‘non-cancer state’. The model assigns probabilities for the non-reversible transition from ‘non-cancer’ state to the ‘cancer state’ that depend on the states of the neighbouring nodes. The likelihood of transition further depends on the life burden intensity of the UV-rays that the skin is exposed to. The probabilistic nature of the process and the uncertainty in the input data is assessed by the use of Monte Carlo simulations. A good fit between experiments on mice and our model has been obtained.

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10

Tran, Ha, and Kourosh Khoshelham. "Procedural Reconstruction of 3D Indoor Models from Lidar Data Using Reversible Jump Markov Chain Monte Carlo." Remote Sensing 12, no. 5 (March 5, 2020): 838. http://dx.doi.org/10.3390/rs12050838.

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Automated reconstruction of Building Information Models (BIMs) from point clouds has been an intensive and challenging research topic for decades. Traditionally, 3D models of indoor environments are reconstructed purely by data-driven methods, which are susceptible to erroneous and incomplete data. Procedural-based methods such as the shape grammar are more robust to uncertainty and incompleteness of the data as they exploit the regularity and repetition of structural elements and architectural design principles in the reconstruction. Nevertheless, these methods are often limited to simple architectural styles: the so-called Manhattan design. In this paper, we propose a new method based on a combination of a shape grammar and a data-driven process for procedural modelling of indoor environments from a point cloud. The core idea behind the integration is to apply a stochastic process based on reversible jump Markov Chain Monte Carlo (rjMCMC) to guide the automated application of grammar rules in the derivation of a 3D indoor model. Experiments on synthetic and real data sets show the applicability of the method to efficiently generate 3D indoor models of both Manhattan and non-Manhattan environments with high accuracy, completeness, and correctness.

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11

Brown, Garfield O., and Winston S. Buckley. "Experience rating with Poisson mixtures." Annals of Actuarial Science 9, no. 2 (July 16, 2015): 304–21. http://dx.doi.org/10.1017/s1748499515000019.

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AbstractWe propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

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12

Schmidt, A., F. Rottensteiner, U. Soergel, and C. Heipke. "Extraction of fluvial networks in lidar data using marked point processes." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3 (August 11, 2014): 297–304. http://dx.doi.org/10.5194/isprsarchives-xl-3-297-2014.

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We propose a method for the automatic extraction of fluvial networks in lidar data with the aim to obtain a connected network represented by the fluvial channels' skeleton. For that purpose we develop a two-step approach. First, we fit rectangles to the data using a stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. High gradients on the rectangles' border and non-overlapping areas of the objects are introduced as model in the optimization process. In a second step, we determine the principal axes of the rectangles and their intersection points. Based on this a network graph is constructed in which nodes represent junction points or end points, respectively, and edges in-between straight line segments. We evaluate our method on lidar data with a tidal channel network and show some preliminary results.

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13

Oh, Man-Suk, and Dong Wan Shin. "Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach." Journal of Applied Statistics 29, no. 5 (July 2002): 771–89. http://dx.doi.org/10.1080/02664760120098829.

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14

LIU, Yanming, Hailiang WEI, Lei SHI, and Bo YAO. "Adaptive protograph-based BICM-ID relying on the RJ-MCMC algorithm: a reliable and efficient transmission solution for plasma sheath channels." Plasma Science and Technology 24, no. 4 (April 1, 2022): 045001. http://dx.doi.org/10.1088/2058-6272/ac56ca.

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Abstract For reentry communication, owing to the influence of the highly dynamic plasma sheath (PS), the parasitic modulation effect can occur and the received phase shift keying (PSK) signal constellation can be severely rotated, leading to unacceptable demodulation performance degradation. In this work, an adaptive non-coherent bit-interleaved coded modulation with iterative decoding (BICM-ID) system with binary PSK (BPSK) modulation and protograph low-density parity-check under the PS channel is proposed. The proposed protograph-based BICM-ID (P-BICM-ID) system can achieve joint processing of demodulation and decoding, where the soft information is adaptively estimated by reversible-jump Markov chain Monte Carlo (RJ-MCMC) algorithms. Simulation results indicate that compared to existing algorithms, the proposed system can adapt well to the dynamic characteristics of the PS channel and can obtain a 5 dB performance improvement at a bit error rate of 10−6.

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15

Theorell, Axel, and Katharina Nöh. "Reversible jump MCMC for multi-model inference in Metabolic Flux Analysis." Bioinformatics 36, no. 1 (June 19, 2019): 232–40. http://dx.doi.org/10.1093/bioinformatics/btz500.

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Abstract Motivation The validity of model based inference, as used in systems biology, depends on the underlying model formulation. Often, a vast number of competing models is available, that are built on different assumptions, all consistent with the existing knowledge about the studied biological phenomenon. As a remedy for this, Bayesian Model Averaging (BMA) facilitates parameter and structural inferences based on multiple models simultaneously. However, in fields where a vast number of alternative, high-dimensional and non-linear models are involved, the BMA-based inference task is computationally very challenging. Results Here we use BMA in the complex setting of Metabolic Flux Analysis (MFA) to infer whether potentially reversible reactions proceed uni- or bidirectionally, using 13C labeling data and metabolic networks. BMA is applied on a large set of candidate models with differing directionality settings, using a tailored multi-model Markov Chain Monte Carlo (MCMC) approach. The applicability of our algorithm is shown by inferring the in vivo probability of reaction bidirectionalities in a realistic network setup, thereby extending the scope of 13C MFA from parameter to structural inference. Supplementary information Supplementary data are available at Bioinformatics online.

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16

Krivov, Sergei V. "Additive eigenvectors as optimal reaction coordinates, conditioned trajectories, and time-reversible description of stochastic processes." Journal of Chemical Physics 157, no. 1 (July 7, 2022): 014108. http://dx.doi.org/10.1063/5.0088061.

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A fundamental way to analyze complex multidimensional stochastic dynamics is to describe it as diffusion on a free energy landscape—free energy as a function of reaction coordinates (RCs). For such a description to be quantitatively accurate, the RC should be chosen in an optimal way. The committor function is a primary example of an optimal RC for the description of equilibrium reaction dynamics between two states. Here, additive eigenvectors (addevs) are considered as optimal RCs to address the limitations of the committor. An addev master equation for a Markov chain is derived. A stationary solution of the equation describes a sub-ensemble of trajectories conditioned on having the same optimal RC for the forward and time-reversed dynamics in the sub-ensemble. A collection of such sub-ensembles of trajectories, called stochastic eigenmodes, can be used to describe/approximate the stochastic dynamics. A non-stationary solution describes the evolution of the probability distribution. However, in contrast to the standard master equation, it provides a time-reversible description of stochastic dynamics. It can be integrated forward and backward in time. The developed framework is illustrated on two model systems—unidirectional random walk and diffusion.

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17

Schmidt, A., F. Rottensteiner, U. Soergel, and C. Heipke. "A GRAPH BASED MODEL FOR THE DETECTION OF TIDAL CHANNELS USING MARKED POINT PROCESSES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3/W3 (August 19, 2015): 115–21. http://dx.doi.org/10.5194/isprsarchives-xl-3-w3-115-2015.

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In this paper we propose a new method for the automatic extraction of tidal channels in digital terrain models (DTM) using a sampling approach based on marked point processes. In our model, the tidal channel system is represented by an undirected, acyclic graph. The graph is iteratively generated and fitted to the data using stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. The nodes of the graph represent junction points of the channel system and the edges straight line segments with a certain width in between. In each sampling step, the current configuration of nodes and edges is modified. The changes are accepted or rejected depending on the probability density function for the configuration which evaluates the conformity of the current status with a pre-defined model for tidal channels. In this model we favour high DTM gradient magnitudes at the edge borders and penalize a graph configuration consisting of non-connected components, overlapping segments and edges with atypical intersection angles. We present the method of our graph based model and show results for lidar data, which serve of a proof of concept of our approach.

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18

Rantini, Dwi, Nur Iriawan, and Irhamah Irhamah. "On the Reversible Jump Markov Chain Monte Carlo (RJMCMC) Algorithm for Extreme Value Mixture Distribution as a Location-Scale Transformation of the Weibull Distribution." Applied Sciences 11, no. 16 (August 10, 2021): 7343. http://dx.doi.org/10.3390/app11167343.

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Data with a multimodal pattern can be analyzed using a mixture model. In a mixture model, the most important step is the determination of the number of mixture components, because finding the correct number of mixture components will reduce the error of the resulting model. In a Bayesian analysis, one method that can be used to determine the number of mixture components is the reversible jump Markov chain Monte Carlo (RJMCMC). The RJMCMC is used for distributions that have location and scale parameters or location-scale distribution, such as the Gaussian distribution family. In this research, we added an important step before beginning to use the RJMCMC method, namely the modification of the analyzed distribution into location-scale distribution. We called this the non-Gaussian RJMCMC (NG-RJMCMC) algorithm. The following steps are the same as for the RJMCMC. In this study, we applied it to the Weibull distribution. This will help many researchers in the field of survival analysis since most of the survival time distribution is Weibull. We transformed the Weibull distribution into a location-scale distribution, which is the extreme value (EV) type 1 (Gumbel-type for minima) distribution. Thus, for the mixture analysis, we call this EV-I mixture distribution. Based on the simulation results, we can conclude that the accuracy level is at minimum 95%. We also applied the EV-I mixture distribution and compared it with the Gaussian mixture distribution for enzyme, acidity, and galaxy datasets. Based on the Kullback–Leibler divergence (KLD) and visual observation, the EV-I mixture distribution has higher coverage than the Gaussian mixture distribution. We also applied it to our dengue hemorrhagic fever (DHF) data from eastern Surabaya, East Java, Indonesia. The estimation results show that the number of mixture components in the data is four; we also obtained the estimation results of the other parameters and labels for each observation. Based on the Kullback–Leibler divergence (KLD) and visual observation, for our data, the EV-I mixture distribution offers better coverage than the Gaussian mixture distribution.

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19

Tran, H., and K. Khoshelham. "A STOCHASTIC APPROACH TO AUTOMATED RECONSTRUCTION OF 3D MODELS OF INTERIOR SPACES FROM POINT CLOUDS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2/W5 (May 29, 2019): 299–306. http://dx.doi.org/10.5194/isprs-annals-iv-2-w5-299-2019.

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<p><strong>Abstract.</strong> Automated reconstruction of 3D interior models has recently been a topic of intensive research due to its wide range of applications in Architecture, Engineering, and Construction. However, generation of the 3D models from LiDAR data and/or RGB-D data is challenged by not only the complexity of building geometries, but also the presence of clutters and the inevitable defects of the input data. In this paper, we propose a stochastic approach for automatic reconstruction of 3D models of interior spaces from point clouds, which is applicable to both Manhattan and non-Manhattan world buildings. The building interior is first partitioned into a set of 3D shapes as an arrangement of permanent structures. An optimization process is then applied to search for the most probable model as the optimal configuration of the 3D shapes using the reversible jump Markov Chain Monte Carlo (rjMCMC) sampling with the Metropolis-Hastings algorithm. This optimization is not based only on the input data, but also takes into account the intermediate stages of the model during the modelling process. Consequently, it enhances the robustness of the proposed approach to inaccuracy and incompleteness of the point cloud. The feasibility of the proposed approach is evaluated on a synthetic and an ISPRS benchmark dataset.</p>

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20

Wang, Yu, Guoqing Zhou, and Haotian You. "An Energy-Based SAR Image Segmentation Method with Weighted Feature." Remote Sensing 11, no. 10 (May 16, 2019): 1169. http://dx.doi.org/10.3390/rs11101169.

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To extract more structural features, which can contribute to segment a synthetic aperture radar (SAR) image accurately, and explore their roles in the segmentation procedure, this paper presents an energy-based SAR image segmentation method with weighted features. To precisely segment a SAR image, multiple structural features are incorporated into a block- and energy-based segmentation model in weighted way. In this paper, the multiple features of a pixel, involving spectral feature obtained from original SAR image, texture and boundary features extracted by a curvelet transform, form a feature vector. All the pixels’ feature vectors form a feature set of a SAR image. To automatically determine the roles of the multiple features in the segmentation procedure, weight variables are assigned to them. All the weight variables form a weight set. Then the image domain is partitioned into a set of blocks by regular tessellation. Afterwards, an energy function and a non-constrained Gibbs probability distribution are used to combine the feature and weight sets to build a block-based energy segmentation model with feature weighted on the partitioned image domain. Further, a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is designed to simulate from the segmentation model. In the RJMCMC algorithm, three move types were designed according to the segmentation model. Finally, the proposed method was tested on the SAR images, and the quantitative and qualitative results demonstrated its effectiveness.

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21

Fackeldey, K., A. Sikorski, and M. Weber. "Spectral clustering for non-reversible Markov chains." Computational and Applied Mathematics 37, no. 5 (August 28, 2018): 6376–91. http://dx.doi.org/10.1007/s40314-018-0697-0.

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22

Choi, Michael C. H. "Metropolis–Hastings reversiblizations of non-reversible Markov chains." Stochastic Processes and their Applications 130, no. 2 (February 2020): 1041–73. http://dx.doi.org/10.1016/j.spa.2019.04.006.

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23

Anandam, Victor. "Some potential-theoretic techniques in non-reversible Markov chains." Rendiconti del Circolo Matematico di Palermo 62, no. 2 (April 17, 2013): 273–84. http://dx.doi.org/10.1007/s12215-013-0124-8.

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24

Huang, Lu-Jing, and Yong-Hua Mao. "Variational principles of hitting times for non-reversible Markov chains." Journal of Mathematical Analysis and Applications 468, no. 2 (December 2018): 959–75. http://dx.doi.org/10.1016/j.jmaa.2018.08.036.

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Takahashi, Tsutomu, Yuka Kaiho, Yasushi Ishihara, Koichiro Obana, Seiichi Miura, Shuichi Kodaira, and Yoshiyuki Kaneda. "Trans-dimensional imaging of the random inhomogeneity structure in the southern Ryukyu arc, Japan." Geophysical Journal International 229, no. 2 (December 23, 2021): 1392–407. http://dx.doi.org/10.1093/gji/ggab518.

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SUMMARY The seismic velocity structure of the lithosphere shows various inhomogeneities over a wide range of scales, and such inhomogeneity causes complex seismic waves above a few hertz due to multiple scattering. Medium around active volcanoes and large faults tends to show strong random inhomogeneity in relatively small areas. For a more precise understanding of such random velocity inhomogeneities, it is necessary to estimate their detailed spatial variation without smoothing constraints. This study introduces a trans-dimensional approach for the 3-D imaging of random inhomogeneity using the reversible jump Markov chain Monte Carlo (rjMCMC) method, and set the number of structural parameters and their spatial layout as unknown parameters. Since the scale dependence of the random inhomogeneity is related to the frequency dependence of seismic wave scattering, the covariance matrix of the likelihood function was defined to be non-diagonal so that residuals at different frequencies in each ray path are correlated. A synthetic test showed this covariance matrix worked adequately for estimating parameters of a power-law-type spectrum of random inhomogeneity. Analysis of seismic data at the southern Ryukyu arc in the southwest Japan found anomalies with strong and weak inhomogeneities. A strongly inhomogeneous band with a width of 20–30 km was distributed in the Okinawa Trough at depths of 0–20 km. In part of this area, magma intrusions and associated complex structures have been detected by a seismic reflection survey. The scale of the structures discussed in this study is almost the same with that discussed in the reflection survey. The rjMCMC-based analysis made it possible to compare random inhomogeneities with the structural variations estimated by the deterministic seismic reflection survey. Since analyses of scattered seismic waves can examine much greater depths than seismic reflection surveys, further comparisons between the two methods in the shallow crust could provide useful insights for detailed interpretation of complex structures at deeper depth.

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Hordijk, Arie, and AD Ridder. "Insensitive bounds for the stationary distribution of non-reversible Markov chains." Journal of Applied Probability 25, no. 1 (March 1988): 9–20. http://dx.doi.org/10.2307/3214229.

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A general method is developed to compute easy bounds of the weighted stationary probabilities for networks of queues which do not satisfy the standard product form. The bounds are obtained by constructing approximating reversible Markov chains. Thus, the bounds are insensitive with respect to service-time distributions. A special representation, called the tree-form solution, of the stationary distribution is used to derive the bounds. The results are applied to an overflow model.

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27

Hordijk, Arie, and AD Ridder. "Insensitive bounds for the stationary distribution of non-reversible Markov chains." Journal of Applied Probability 25, no. 01 (March 1988): 9–20. http://dx.doi.org/10.1017/s0021900200040596.

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A general method is developed to compute easy bounds of the weighted stationary probabilities for networks of queues which do not satisfy the standard product form. The bounds are obtained by constructing approximating reversible Markov chains. Thus, the bounds are insensitive with respect to service-time distributions. A special representation, called the tree-form solution, of the stationary distribution is used to derive the bounds. The results are applied to an overflow model.

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28

Kontoyiannis, I., and S. P. Meyn. "Geometric ergodicity and the spectral gap of non-reversible Markov chains." Probability Theory and Related Fields 154, no. 1-2 (June 3, 2011): 327–39. http://dx.doi.org/10.1007/s00440-011-0373-4.

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29

Kijima, Masaaki. "Spectral structure of the first-passage-time densities for classes of Markov chains." Journal of Applied Probability 24, no. 3 (September 1987): 631–43. http://dx.doi.org/10.2307/3214095.

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Keilson [7] showed that for a birth-death process defined on non-negative integers with reflecting barrier at 0 the first-passage-time density from 0 to N (N to N + 1) has Pólya frequency of order infinity (is completely monotone). Brown and Chaganty [3] and Assaf et al. [1] studied the first-passage-time distribution for classes of discrete-time Markov chains and then produced the essentially same results as these through a uniformization. This paper addresses itself to an extension of Keilson's results to classes of Markov chains such as time-reversible Markov chains, skip-free Markov chains and birth-death processes with absorbing states. The extensions are due to the spectral representations of the infinitesimal generators governing these Markov chains. Explicit densities for those first-passage times are also given.

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30

Kijima, Masaaki. "Spectral structure of the first-passage-time densities for classes of Markov chains." Journal of Applied Probability 24, no. 03 (September 1987): 631–43. http://dx.doi.org/10.1017/s0021900200031363.

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Keilson [7] showed that for a birth-death process defined on non-negative integers with reflecting barrier at 0 the first-passage-time density from 0 to N (N to N + 1) has Pólya frequency of order infinity (is completely monotone). Brown and Chaganty [3] and Assaf et al. [1] studied the first-passage-time distribution for classes of discrete-time Markov chains and then produced the essentially same results as these through a uniformization. This paper addresses itself to an extension of Keilson's results to classes of Markov chains such as time-reversible Markov chains, skip-free Markov chains and birth-death processes with absorbing states. The extensions are due to the spectral representations of the infinitesimal generators governing these Markov chains. Explicit densities for those first-passage times are also given.

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31

Hallo, Miroslav, Walter Imperatori, Francesco Panzera, and Donat Fäh. "Joint multizonal transdimensional Bayesian inversion of surface wave dispersion and ellipticity curves for local near-surface imaging." Geophysical Journal International 226, no. 1 (March 26, 2021): 627–59. http://dx.doi.org/10.1093/gji/ggab116.

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Summary Physical properties of near-surface soil and rock layers play a fundamental role in the seismic site effects analysis, being an essential element of seismic hazard assessment. Site-specific mechanical properties (i.e. shear- and compressional-wave velocities and mass density) can be inferred from surface wave dispersion and horizontal-to-vertical or ellipticity data by non-linear inversion techniques. Nevertheless, results typically exhibit significant inherent non-uniqueness as different models may fit the data equally well. Standard optimization inversion techniques minimize data misfit, resulting in a single representative model, rejecting other models providing similar misfit values. An alternative inversion technique can be formulated in the Bayesian framework, where the posterior probability density on the model space is inferred. This paper introduces an inversion approach of surface wave dispersion and ellipticity data based on a novel multizonal transdimensional Bayesian formulation. In particular, we parametrize 1-D layered velocity models by the varying number of Voronoi nuclei, allowing us to treat the number of layers as an unknown parameter of the inverse problem. The chosen parametrization leads to the transdimensional formulation of the model space, sampled by a reversible jump Markov chain Monte Carlo algorithm to provide an ensemble of random samples following the posterior probability density of model parameters. The used type of the sampling algorithm controls a model complexity (i.e. the number of layers) self-adaptively based on the measured data's information content. The method novelty lies in the parsimonious selection of sampling models and in the multizonal formulation of prior assumptions on model parameters, the latter allows including additional site-specific constraints in the inversion. These assumptions may be based on, e.g. stratigraphic logs, standard penetration tests, known water table, and bedrock depth. The multizonal formulation fully preserves the validity of the transdimensional one, as demonstrated analytically. The resultant ensemble of model samples is a discrete approximation of the posterior probability density function of model parameters and associated properties (e.g. VS30, quarter-wavelength average velocity profile and theoretical SH-wave amplification function). Although the ultimate result is the posterior probability density function, some representative models are selected according to data fit and maximum of the posterior probability density function. We first validate our inversion approach based on synthetic tests and then apply it to field data acquired from the active seismic survey and single-station measurements of ambient vibrations at the SENGL seismic station site in central Switzerland.

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32

Gaudillière, A., and C. Landim. "A Dirichlet principle for non reversible Markov chains and some recurrence theorems." Probability Theory and Related Fields 158, no. 1-2 (January 13, 2013): 55–89. http://dx.doi.org/10.1007/s00440-012-0477-5.

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33

MONTENEGRO, RAVI. "Intersection Conductance and Canonical Alternating Paths: Methods for General Finite Markov Chains." Combinatorics, Probability and Computing 23, no. 4 (June 13, 2014): 585–606. http://dx.doi.org/10.1017/s096354831400025x.

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We extend the conductance and canonical paths methods to the setting of general finite Markov chains, including non-reversible non-lazy walks. The new path method is used to show that a known bound for the mixing time of a lazy walk on a Cayley graph with a symmetric generating set also applies to the non-lazy non-symmetric case, often even when there is no holding probability.

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34

Zaniolo, Orietta, Sorrel E. Wolowacz, and Lorenzo Pradelli. "Cost/effectiveness model of dabigatran in the prevention of venous thromboembolism in major orthopedic surgery: Adaptation for Italy." Farmeconomia. Health economics and therapeutic pathways 11, no. 2 (June 15, 2010): 91–101. http://dx.doi.org/10.7175/fe.v11i2.183.

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Venous thromboembolic events (VTE) represent a dangerous complication of major orthopedic surgery, especially in total hip replacement (THR) and total knee replacement (TKR) procedures. Dabigatran etexilate (DBG), a direct and reversible thrombin inhibitor, has proven its non-inferiority with respect to enoxaparin 40mg once-daily, a low molecular weight heparin (LMWH), in the prevention of VTE in patients undergoing THR and TKR, in the RE-NOVATE and RE-MODEL trials, respectively. The objective of this analysis was to estimate cost/effectiveness and cost/utility of DBG compared to standard care for the prevention of VTE in Italy. A decision analytic, Markov-chain based model, originally developed for the UK, was adapted to the Italian context. The adaptation involved cost and demographic characteristics, clinical and utility data were not altered. Costs were taken from national observational studies, where available. Otherwise, current prices and tariffs were applied. Resource consumption was derived from practice guidelines or taken from the UK model. According to the prevalent national practice, extended prophylaxis is considered for both surgical procedures. The time horizon of the analysis was patients’ lifetimes. In order to consider different alternatives for drug dispensation and, consequently, National Health Service acquisition costs, alternative scenarios were developed. A further scenario, excluding LMWHs administration costs (“worst-case” scenario), was considered. Compared to LMWHs, DBG was associated with an expected increase of 0.019 life-years (LYs) and 0.014 quality-adjusted life-years (QALYs) per THR patient and of 0.024 LYs and 0.019 QALYs per TKR patient. DBG-related costs were lower than LMWH in both procedures, with a mean difference ranging from 89 to 116 € for THR, and 107 to 142 for TKR, depending on the LMWH product. Higher acquisition costs for DBG were completely offset and inverted by avoided administration expenses and, to a lesser extent, by savings in VTE management. The results of alternative scenarios confirm the dominance of DBG, with a net saving ranging between 119 €, when both drugs were obtained by auction, and 32 €, when the auction price was applied but DBG was dispensed through territorial pharmacies. The corresponding estimates for TKR were 148 and 54 €. In the “worst-case” scenario, DBG was no longer dominant, with a cost per LYs of 2,788 and 4,514 € and a cost per QALY gained of 3,619 and 5,926 €, for TKR and THR respectively. In conclusion, DBG dominated LMWHs, and was cost-saving and non-inferior in terms of efficacy and safety, except for in the “worst-case” scenario, in which the incremental cost/effectiveness ratio estimate was lower than commonly accepted thresholds in health economics.

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35

Szewczak, Zbigniew S. "Berry–Esséen theorem for sample quantiles of asymptotically uncorrelated non reversible Markov chains." Communications in Statistics - Theory and Methods 46, no. 8 (May 5, 2016): 3985–4003. http://dx.doi.org/10.1080/03610926.2015.1076478.

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36

Rahimi Dalkhani, Amin, Xin Zhang, and Cornelis Weemstra. "On the Potential of 3D Transdimensional Surface Wave Tomography for Geothermal Prospecting of the Reykjanes Peninsula." Remote Sensing 13, no. 23 (December 4, 2021): 4929. http://dx.doi.org/10.3390/rs13234929.

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Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, surface waves retrieved through the application of seismic interferometry have also been exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a set of localized depth-dependent velocity profiles are obtained at the surface points. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation of the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. It also adapts model resolution to the amount of noise in the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from station–station cross correlations by the Reykjanes seismic network.

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37

Krauth, Werner. "Event-Chain Monte Carlo: Foundations, Applications, and Prospects." Frontiers in Physics 9 (June 1, 2021). http://dx.doi.org/10.3389/fphy.2021.663457.

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This review treats the mathematical and algorithmic foundations of non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC), a continuous-time lifted Markov chain that employs the factorized Metropolis algorithm. It analyzes a number of model applications and then reviews the formulation as well as the performance of ECMC in key models in statistical physics. Finally, the review reports on an ongoing initiative to apply ECMC to the sampling problem in molecular simulation, i.e., to real-world models of peptides, proteins, and polymers in aqueous solution.

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38

McDowell, Eoghan. "A Random Walk on the Indecomposable Summands of Tensor Products of Modular Representations of SL2 $\left ({\mathbb {F}_p}\right )$." Algebras and Representation Theory, March 12, 2021. http://dx.doi.org/10.1007/s10468-021-10034-0.

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AbstractIn this paper we introduce a novel family of Markov chains on the simple representations of SL2$\left ({\mathbb {F}_p}\right )$ F p in defining characteristic, defined by tensoring with a fixed simple module and choosing an indecomposable non-projective summand. We show these chains are reversible and find their connected components and their stationary distributions. We draw connections between the properties of the chain and the representation theory of SL2$\left ({\mathbb {F}_p}\right )$ F p , emphasising symmetries of the tensor product. We also provide an elementary proof of the decomposition of tensor products of simple SL2$\left ({\mathbb {F}_p}\right )$ F p -representations.

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39

Ghalenoei, Emad, Jan Dettmer, Mohammed Y. Ali, and Jeong Woo Kim. "Gravity and magnetic joint inversion for basement and salt structures with the reversible-jump algorithm." Geophysical Journal International, July 1, 2021. http://dx.doi.org/10.1093/gji/ggab251.

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Summary Gravity and magnetic data resolve the Earth with variable spatial resolution, and Earth structure exhibits both discontinuous and gradual features. Therefore, model parametrization complexity should be able to address such variability by locally adapting to the resolving power of the data. The reversible-jump Markov chain Monte Carlo (rjMcMC) algorithm provides variable spatial resolution that is consistent with data information. To address the prevalent non-uniqueness in joint inversion of potential field data, we employ a novel spatial partitioning with nested Voronoi cells that is explored by rjMcMC sampling. The nested Voronoi parametrization partitions the subsurface in terms of rock types, such as sedimentary, salt and basement rocks. Therefore, meaningful prior information can be specified for each type which reduces non-uniqueness. We apply nonoverlapping prior distributions for density contrast and susceptibility between rock types. In addition, the choice of noise parametrization can lead to significant trade-offs with model resolution and complexity. We adopt an empirical estimation of full data covariance matrices that include theory and observational errors to account for spatially correlated noise. The method is applied to 2D gravity and magnetic data to study salt and basement structures. We demonstrate that meaningful partitioning of the subsurface into sediment, salt, and basement structures is achieved by these advances without requiring regularization. Multiple simulated- and field-data examples are presented. Simulation results show clear delineation of salt and basement structures while resolving variable length scales. The field data show results that are consistent with observations made in the simulations. In particular, we resolve geologically plausible structures with varying length scales and clearly differentiate salt structure and basement topography.

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40

Müller, Stefan, and Badal Joshi. "Detailed Balance $$=$$ Complex Balance $$+$$ Cycle Balance: A Graph-Theoretic Proof for Reaction Networks and Markov Chains." Bulletin of Mathematical Biology 82, no. 9 (September 2020). http://dx.doi.org/10.1007/s11538-020-00792-1.

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Abstract We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, “formal balance,” and the new notion of “cycle balance” are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic (non-algebraic) proofs of a previous result (detailed balance = complex balance + formal balance), our main result (detailed balance = complex balance + cycle balance), and a corresponding result in the setting of continuous-time Markov chains.

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