Stochastic approximation cut algorithm for inference in modularized Bayesian models

Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model and prevent feedback from suspect modules, using a cut model. After observing data, this leads to the cut distribution which normally does not have a closed form. Previous studies have proposed algorithms to sample from this distribution, but these algorithms have unclear theoretical convergence properties. To address this, we propose a new algorithm called the stochastic approximation cut (SACut) algorithm as an alternative. The algorithm is divided into two parallel chains. The main chain targets an approximation to the cut distribution; the auxiliary chain is used to form an adaptive proposal distribution for the main chain. We prove convergence of the samples drawn by the proposed algorithm and present the exact limit. Although SACut is biased, since the main chain does not target the exact cut distribution, we prove this bias can be reduced geometrically by increasing a user-chosen tuning parameter. In addition, parallel computing can be easily adopted for SACut, which greatly reduces computation time.

Internet of things-assisted integrated framework for electronic market application

Purpose The widespread use of the internet and the rapid development of the internet of things in information technology have increased the need for network-enabled marketing. It is important to service a broad class involving logistics, buyer, seller and end-users. During various phases of the sales, purchases and marketing process, IoT will influence decision-making. Electronic commerce is a new form of trade under the development of modern information technology. Design/methodology/approach In this paper, the integrated neutrosophic framework based on the internet of things (INF-IoT) has been proposed to support marketers and companies to make a powerful marketing strategy using identified data from IoT devices. Findings The experimental results show that the proposed method has high performance and very efficient. Originality/value This approach may reduce business activity to its core components, which include, in the simplest case, a value proposal, distribution channels and customers, and explain how a network of multi-actors generates a product and services, distributes and uses the value in production. Furthermore, an efficient interface is provided by the logistic module to maintain an order list.

Markov chain Monte Carlo for petrophysical inversion

Stochastic petrophysical inversion is a method to predict reservoir properties from seismic data. Recent advances in stochastic optimization allow generating multiple realizations of rock and fluid properties conditioned on seismic data. To match the measured data and represent the uncertainty of the model variables, a large number of realizations is generally required. Stochastic sampling and optimization of spatially correlated models are computationally demanding. Monte Carlo methods allow quantifying the uncertainty of the model variables but are impractical for high-dimensional models with spatially correlated variables. We propose a Bayesian approach based on an efficient implementation of the Markov chain Monte Carlo method for the inversion of seismic data for the prediction of reservoir properties. The proposed Bayesian approach includes an explicit vertical correlation model in the proposal distribution. It is applied trace by trace and the lateral continuity model is imposed by using the previously simulated values at the adjacent traces as conditioning data for simulating the initial model at the current trace. The methodology is first presented for a one-dimensional problem to test the vertical correlation and it is extended to two-dimensional problems by including the lateral correlation and comparing two novel implementations based on sequential sampling. The proposed method is applied to synthetic data to estimate the posterior distribution of the petrophysical properties conditioned on the measured seismic data. The results are compared with a McMC implementation without lateral correlation and demonstrate the advantage of integrating a spatial correlation model.

Bayesian Estimation of Agent-Based Models via Adaptive Particle Markov Chain Monte Carlo

Over the last decade, agent-based models in economics have reached a state of maturity that brought the tasks of statistical inference and goodness-of-fit of such models on the agenda of the research community. While most available papers have pursued a frequentist approach adopting either likelihood-based algorithms or simulated moment estimators, here we explore Bayesian estimation using a Markov chain Monte Carlo approach (MCMC). One major problem in the design of MCMC estimators is finding a parametrization that leads to a reasonable acceptance probability for new draws from the proposal density. With agent-based models the appropriate choice of the proposal density and its parameters becomes even more complex since such models often require a numerical approximation of the likelihood. This brings in additional factors affecting the acceptance rate as it will also depend on the approximation error of the likelihood. In this paper, we take advantage of a number of recent innovations in MCMC: We combine Particle Filter Markov Chain Monte Carlo as proposed by Andrieu et al. (J R Stat Soc B 72(Part 3):269–342, 2010) with adaptive choice of the proposal distribution and delayed rejection in order to identify an appropriate design of the MCMC estimator. We illustrate the methodology using two well-known behavioral asset pricing models.

Informed Proposal Monte Carlo

Summary Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search and sampling algorithms is to build in as much external information about the problem as possible. In the special case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done through the choice of proposal distribution, and we show how this way of adding more information about the problem can be made particularly efficient when based on an approximate physics model of the problem. A highly nonlinear inverse scattering problem with a high-dimensional model space serves as an illustration of the gain of efficiency through this approach.

A Neural Network MCMC Sampler That Maximizes Proposal Entropy

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the efficiency of MCMC methods. Augmenting samplers with neural networks can potentially improve their efficiency. Previous neural network-based samplers were trained with objectives that either did not explicitly encourage exploration, or contained a term that encouraged exploration but only for well structured distributions. Here we propose to maximize proposal entropy for adapting the proposal to distributions of any shape. To optimize proposal entropy directly, we devised a neural network MCMC sampler that has a flexible and tractable proposal distribution. Specifically, our network architecture utilizes the gradient of the target distribution for generating proposals. Our model achieved significantly higher efficiency than previous neural network MCMC techniques in a variety of sampling tasks, sometimes by more than an order magnitude. Further, the sampler was demonstrated through the training of a convergent energy-based model of natural images. The adaptive sampler achieved unbiased sampling with significantly higher proposal entropy than a Langevin dynamics sample. The trained sampler also achieved better sample quality.

Distribution-Dependent Weighted Union Bound

In this paper, we deal with the classical Statistical Learning Theory’s problem of bounding, with high probability, the true risk R(h) of a hypothesis h chosen from a set H of m hypotheses. The Union Bound (UB) allows one to state that PLR^(h),δqh≤R(h)≤UR^(h),δph≥1−δ where R^(h) is the empirical errors, if it is possible to prove that P{R(h)≥L(R^(h),δ)}≥1−δ and P{R(h)≤U(R^(h),δ)}≥1−δ, when h, qh, and ph are chosen before seeing the data such that qh,ph∈[0,1] and ∑h∈H(qh+ph)=1. If no a priori information is available qh and ph are set to 12m, namely equally distributed. This approach gives poor results since, as a matter of fact, a learning procedure targets just particular hypotheses, namely hypotheses with small empirical error, disregarding the others. In this work we set the qh and ph in a distribution-dependent way increasing the probability of being chosen to function with small true risk. We will call this proposal Distribution-Dependent Weighted UB (DDWUB) and we will retrieve the sufficient conditions on the choice of qh and ph that state that DDWUB outperforms or, in the worst case, degenerates into UB. Furthermore, theoretical and numerical results will show the applicability, the validity, and the potentiality of DDWUB.

A Robust Solution to Variational Importance Sampling of Minimum Variance

Importance sampling is a Monte Carlo method where samples are obtained from an alternative proposal distribution. This can be used to focus the sampling process in the relevant parts of space, thus reducing the variance. Selecting the proposal that leads to the minimum variance can be formulated as an optimization problem and solved, for instance, by the use of a variational approach. Variational inference selects, from a given family, the distribution which minimizes the divergence to the distribution of interest. The Rényi projection of order 2 leads to the importance sampling estimator of minimum variance, but its computation is very costly. In this study with discrete distributions that factorize over probabilistic graphical models, we propose and evaluate an approximate projection method onto fully factored distributions. As a result of our evaluation it becomes apparent that a proposal distribution mixing the information projection with the approximate Rényi projection of order 2 could be interesting from a practical perspective.

Particle Gibbs sampling for Bayesian phylogenetic inference

Motivation The combinatorial sequential Monte Carlo (CSMC) has been demonstrated to be an efficient complementary method to the standard Markov chain Monte Carlo (MCMC) for Bayesian phylogenetic tree inference using biological sequences. It is appealing to combine the CSMC and MCMC in the framework of the particle Gibbs (PG) sampler to jointly estimate the phylogenetic trees and evolutionary parameters. However, the Markov chain of the PG may mix poorly for high dimensional problems (e.g. phylogenetic trees). Some remedies, including the PG with ancestor sampling and the interacting particle MCMC, have been proposed to improve the PG. But they either cannot be applied to or remain inefficient for the combinatorial tree space. Results We introduce a novel CSMC method by proposing a more efficient proposal distribution. It also can be combined into the PG sampler framework to infer parameters in the evolutionary model. The new algorithm can be easily parallelized by allocating samples over different computing cores. We validate that the developed CSMC can sample trees more efficiently in various PG samplers via numerical experiments. Availability and implementation The implementation of our method and the data underlying this article are available at https://github.com/liangliangwangsfu/phyloPMCMC. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.