Bayesian Inference for Stochastic Multipath Radio Channel Models

Sampling technique is one of the asymptotically unbiased estimation approaches for inference in Bayesian probabilistic models. Markov chain Monte Carlo (MCMC) is a kind of sampling methods, which is widely used in the inference of complex probabilistic models. However, current MCMC methods can incur high autocorrelation of samples, which means that the samples generated by MCMC samplers are far from independent. In this paper, we propose the neural networks Langevin Monte Carlo (NNLMC) which makes full use of the flexibility of neural networks and the high efficiency of the Langevin dynamics sampling to construct a new MCMC sampling method. We propose the new update function to generate samples and employ appropriate loss functions to improve the performance of NNLMC during the process of sampling. We evaluate our method on a large diversity of challenging distributions and real datasets. Our results show that NNLMC is able to sample from the target distribution with low autocorrelation and rapid convergence, and outperforms the state-of-the-art MCMC samplers.

In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo (MCMC) sampling strategies have become the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density functions (PDFs). However, these algorithms have been shown to be inefficient when sampling from high-dimensional posterior distributions or exhibit multimodality and/or strong parameter correlations. In such contexts, transitional MCMC (TMCMC) provides a more efficient alternative. Despite the recent applicability for Bayesian updating and model selection across a variety of disciplines, TMCMC may require a prohibitive number of tempering stages when the prior pdf is significantly different from the target posterior. Furthermore, the need to start with an initial set of samples from the prior distribution may present a challenge when dealing with implicit priors, e.g., based on feasible regions. Finally, TMCMC cannot be used for inverse problems with improper prior PDFs that represent a lack of prior knowledge on all or a subset of parameters. A generalization of TMCMC is proposed that alleviates such challenges and limitations toward providing a more robust and efficient tempering sampling strategy. We present convergence analysis, proving that the distance between the intermediate distributions and the target posterior distribution monotonically decreases as the algorithm proceeds. We also demonstrate the advantages of the proposed generalization through a series of test problems and an engineering application in the oil and gas industry.

The Bayesian framework is commonly used to quantify uncertainty in seismic inversion. To perform Bayesian inference, Markov chain Monte Carlo (MCMC) algorithms are regarded as the gold standard technique for sampling from the posterior probability distribution. Consistent MCMC methods have trouble for complex, high-dimensional models, and most methods scale poorly to large datasets, such as those arising in seismic inversion. As an alternative, approximate MCMC methods based on unadjusted Langevin dynamics offer scalability and more rapid sampling at the cost of biased inference. However, when assessing the quality of approximate MCMC samples for characterizing the posterior distribution, most diagnostics fail to account for these biases. In this work, we introduce the kernel Stein discrepancy (KSD) as a diagnostic tool to determine the convergence of MCMC samples for Bayesian seismic inversion. We demonstrate the use of the KSD for measuring sample quality and selecting the optimal Langevin MCMC algorithm for two Gaussian Bayesian inference problems.

In-line inspection (ILI) data is commonly used in corrosion growth models (CGMs) to predict the corrosion growth in energy pipelines. A hierarchical stochastic corrosion growth model is considered in this paper which considers the variations in the corrosion growth, both spatially and temporally, the inherent measurement error of the ILI tools as well as the model uncertainties. These uncertainties are represented as unknown model variables and are often inferred using a Bayesian method [1], [2] and samples of the unknown parameters’ posterior probability density functions (PDFs) are obtained using Markov Chain Monte Carlo (MCMC) sampling techniques [3]. ILIs can result in massive data sets. In order for MCMC-based inference techniques to yield reasonably accurate results, many samples (approaching infinity) are required. This fact in addition to the massive data sets exponentially increases the scale of the inference problem from an attainable solution to a potentially impossible one that is limited by today’s computing power. For this reason, MCMC-based inference techniques can become inefficient in the cases where ILI datasets are large. The objective is to propose variational inference (VI) as an alternative to MCMC to determine a Bayesian solution for the unknown parameters in complex stochastic CGMs. VI produces approximations of the posterior PDFs by treating the inference as an optimization problem. Variational inference emerged from machine learning for Bayesian inference of large data sets; therefore, it is an appropriate tool to use in the analysis of mass pipeline inspection data[4]–[7]. This paper introduces VI to solve the inference problem and provide a solution for a hierarchical stochastic CGM to describe the defect-specific corrosion growth experienced in pipelines based on excessively large ILI datasets. To gauge the accuracy of the VI implementation in the model, the results are compared to a set of values generated using a stochastic gamma process that represents the corrosion growth process experienced by the pipe.

Global illumination algorithms using Markov chain Monte Carlo (MCMC) sampling are well-known for their efficiency in scenes with complex light transport. Samples in such algorithms are generated as a history of Markov chain states so that they are distributed according to the contributions to the image. The whole process is done based only on the information of the path contributions and user-defined transition probabilities from one state to the others. In light transport simulation, however, there is more information that can be used to improve the efficiency of path sampling. A notable example is multiple importance sampling (MIS) in bidirectional path tracing, which utilizes the probability densities of constructing a given path with different estimators. While MIS is a powerful ordinary Monte Carlo method, how to incorporate such additional information into MCMC sampling has been an open problem. We introduce a novel MCMC sampling framework, primary space serial tempering , which fuses the ideas of MCMC sampling and MIS for the first time. The key idea is to explore not only the sample space using a Markov chain, but also different estimators to generate samples by utilizing the information already available for MIS. Based on this framework, we also develop a novel rendering algorithm, multiplexed Metropolis light transport , which automatically and adaptively constructs paths with appropriate techniques as predicted by MIS. The final algorithm is very easy to implement, yet in many cases shows comparable (or even better) performance than significantly more complex MCMC rendering algorithms.

This chapter provides a brief introduction to the use of Bayesian graphical models in R. In these models, parameters are treated as random quantities on an equal footing with the random variables. This allows complex stochastic systems to modeled, often using Markov chain Monte Carlo (MCMC) sampling methods. We first consider a series of examples, ranging from simple repeated sampling, linear regression models, random coefficient regression models, to the chest clinic example of Chap. 3. We formulate these as Bayesian graphical models, and represent them graphically in a compact form using plates. We then describe a special case, in which the unknown parameters are all discrete, and explain how probability propagation methods described in Chap. 3 may be used to compute the posterior distributions. We then turn to the general case, when MCMC sampling is required, and explain the computations involved in Metropolis-Hastings sampling and Gibbs sampling. Finally we illustrate a Bayesian linear regression analysis using the R2WinBUGS package.

This article is a review article on the optimal Markov chain Monte Carlo (MCMC) sampling. The focus is on homogeneous Markov chains. This article first reviews the problem of finding the optimal transition matrix, which is defined to minimize the asymptotic variance of MCMC estimators. The article later reviews the locally optimal sampler (LOS), an MCMC sampling that performs local updates based on the optimal transition matrix. We conducted a simulation study to compare the LOS with the Metropolis–Hastings and the Gibbs Sampler. The LOS was shown to provide an improved rate of convergence over these two most popular sampling schemes. The implementation of the LOS requires only minor modifications in existing Gibbs sampling code. WIREs Comput Stat 2013. doi: 10.1002/wics.1265This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

RNA exosomes are large multi-subunit protein complexes involved in controlled and processive 3' to 5' RNA degradation. Exosomes form large molecular chambers and harbor multiple nuclease sites as well as RNA binding regions. This makes a quantitative kinetic analysis of RNA degradation with reliable parameter and error estimates challenging. For instance, recent quantitative biochemical assays revealed that degradation speed and efficiency depend on various factors, such as the type of RNA binding caps and the RNA length. We propose the combination of a differential equation model with Bayesian Markov Chain Monte Carlo (MCMC) sampling for a more robust and reliable analysis of such complex kinetic systems. Using the exosome as a paradigm, it is shown that conventional “best fit” approaches to parameter estimation are outperformed by the MCMC method. The parameter distribution returned by MCMC sampling allows for a reliable and meaningful comparison of the data from different time series. In the case of the exosome, we find that the cap structures of the exosome have a direct effect on the recruitment and degradation of RNA, and that these effects are RNA length-dependent. The described approach can be widely applied to any processive reaction with a similar kinetics like the XRN1-dependent RNA degradation, RNA/DNA synthesis by polymerases, and protein synthesis by the ribosome.

Identification of contaminant sources in rivers is crucial for river protection and emergency response. This study presents an innovative approach for identifying river pollution sources by using Bayesian inference and cellular automata (CA) modeling. A general Bayesian framework is proposed that combines the CA model with observed data to identify unknown sources of river pollution. To reduce the computational burden of the Bayesian inference, a CA contaminant transport model is developed to efficiently simulate pollutant concentration values in the river. These simulated concentration values are then used to calculate the likelihood function of available measurements. The Markov chain Monte Carlo (MCMC) method is used to produce the posterior distribution of contaminant source parameters, which is a sampling-based method that enables the estimation of complex posterior distributions. The suggested methodology is applied to a real case study of the Fen River in Yuncheng City, Shanxi Province, Northern China, and it estimates the release time, release mass, and source location with relative errors below 19%. The research indicates that the proposed methodology is an effective and flexible way to identify the location and concentrations of river contaminant sources.

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global analysis of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalizing flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

We present a new galaxy survey simulation package, which combines the power of Markov Chain Monte Carlo (MCMC) sampling with a robust and adaptable model of galaxy evolution. The aim of this code is to aid in the characterization and study of new and existing galaxy surveys. In this paper we briefly describe the MCMC implementation and the survey simulation methodology and associated tools. A test case of this full suite was to constrain the evolution of the IR Luminosity Function (LF) based on the HerMES (Herschel SPIRE) survey of the Spitzer First Look Survey field. The initial results are consistent with previous studies, but our more general approach should be of wider benefit to the community.

Many researchers tend to evaluate the performance of their state-of-the-art MIMO antenna array designs using either stochastic or ray-tracing channel modeling tools. These channel models are mainly categorized into deterministic and stochastics channel models. In this paper, we investigate these two categories in terms of the MIMO channel capacity and evaluate the performance of a miniaturized MIMO antenna array in an indoor offices scenario. The effects of the number of transmitters and receivers, spatial location, 3D radiation patterns, polarization, and S-parameters are evaluated for an indoor office model and the IEEE TGn-B indoor stochastic channel model. The ray-tracing software, Wireless InSite, is used as the deterministic channel modeling tool while MIMObit is used as the stochastic channel modeling tool.

Variable selection is very important in many fields, and for its resolution many procedures have been proposed and investigated. Among them are Bayesian methods that use Markov chain Monte-Carlo (MCMC) sampling algorithms. A problem with MCMC sampling, however, is that it cannot guarantee that the samples are exactly from the target distributions. This drawback is overcome by related methods known as perfect sampling algorithms. In this paper, we propose the use of two perfect sampling algorithms to perform variable selection within the Bayesian framework. They are the sandwiched coupling from the past (CFTP) algorithm and the Gibbs coupler. We focus our attention to scenarios where the model coefficients and noise variance are known. We indicate the condition under which the sandwiched CFTP can be applied. Most importantly, we design a detailed scheme to adapt the Gibbs coupler algorithm to variable selection. In addition, we discuss the possibilities of applying perfect sampling when the model coefficients and noise variance are unknown. Test results that show the performance of the algorithms are provided.

Context.The characterization of the interior of an exoplanet is an inverse problem. The solution requires statistical methods such as Bayesian inference. Current methods employ Markov chain Monte Carlo (MCMC) sampling to infer the posterior probability of the planetary structure parameters for a given exoplanet. These methods are time-consuming because they require the evaluation of a planetary structure model ~105times.Aims.To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks to calculate the posterior probability of the planetary structure parameters.Methods.Conditional invertible neural networks (cINNs) are a special type of neural network that excels at solving inverse problems. We constructed a cINN following the framework for easily invertible architectures (FreIA). This neural network was then trained on a database of 5.6 × 106internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius, and elemental composition of the host star). We also show how observational uncertainties can be accounted for.Results.The cINN method was compared to a commonly used Metropolis-Hastings MCMC. To do this, we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability distributions of the internal structure parameters from both methods are very similar; the largest differences are seen in the exoplanet water content. Thus, cINNs are a possible alternative to the standard time-consuming sampling methods. cINNs allow infering the composition of an exoplanet that is orders of magnitude faster than what is possible using an MCMC method. The computation of a large database of internal structures to train the neural network is still required, however. Because this database is only computed once, we found that using an invertible neural network is more efficient than an MCMC when more than ten exoplanets are characterized using the same neural network.

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