Adaptive Markov Research Articles

GAME MODEL OF ONTOLOGICAL PROJECT SUPPORT

Context. In today’s information society with advanced telecommunications through mobile devices and computer networks, it is important to form a variety of virtual organizations and communities. Such virtual associations of people by professional or other interests are designed to quickly solve various tasks: to perform project tasks, create startups to attract investors, network marketing, distance learning, solving complex problems in science, economics and public administration , construction of various Internet services, discussion of political and social processes, etc.
 Objective of the study is to develop an adaptive Markov recurrent method based on the stochastic approximation of the modified condition of complementary non-rigidity, valid at Nash equilibrium points for solving the problem of game coverage of projects.
 Method. In this work the multiagent game model for formation of virtual teams of executors of projects on the basis of libraries of subject ontologies is developed. The competencies and abilities of agents required to carry out projects are specified by sets of ontologies. Intelligent agents randomly, simultaneously and independently choose one of the projects at discrete times. Agents who have chosen the same project determine the current composition of the team of its executors. For agents’ teams, a current penalty is calculated for insufficient coverage of competencies by the combined capabilities of agents. This penalty is used to adaptively recalculate mixed player strategies. The probabilities of selecting those teams whose current composition has led to a reduction in the fine for non-coverage of ontologies are increasing. During the repetitive stochastic game, agents will form vectors of mixed strategies that will minimize average penalties for non-coverage of projects.
 Results. For solve the problem of game coverage of projects, an adaptive Markov recurrent method based on the stochastic approximation of the modified condition of complementary non-rigidity, valid at Nash equilibrium points, was developed.
 Conclusions. Computer simulation confirmed the possibility of using the stochastic game model to form teams of project executors with the necessary ontological support in conditions of uncertainty. The convergence of the game method is ensured by compliance with the fundamental conditions and limitations of stochastic optimization. The reliability of experimental studies is confirmed by the repeatability of the results obtained for different sequences of random variables.

An adaptive Markov chain algorithm applied over map-matching of vehicle trip GPS data

ABSTRACT Markov chains have frequently been applied to match the probable routes with a set of GPS trip data that a pilot vehicle is emitting over a specific graph road network. This class of map-matching (MM) algorithms presently demonstrates and involve statistical and ad-hoc measures to drive the Markov chain transitional probabilities in picking the best route combinations constrained over the graph road network. In this study, we have devised an adaptive scheme to modify the Markov Chain (MC) kernel window as we move along the GPS samples to reduce the mistakes that can happen by the use of narrower MC widths. The measure for temporarily increasing the MC window width is chosen to be the ratio between the geodesic distance of current route to the actual geodesic distance between each pair of GPS samples. This adaptive use of MC has shown to have hardened the results significantly with tolerable computational cost increase. The details of the overall algorithm are depicted by the example routes extracted from various vehicle trips and the results are shown to validate the usefulness of the algorithm in practice.

Bayesian non‐linear quantile effects on modelling realized kernels

AbstractThis article examines the non‐linear responses of a stock market's realized measure of volatility to its potential factors across different quantile levels. Specifically, we apply the threshold quantile autoregressive model with exogenous variables and GARCH specification to model the realized kernel series of the Nikkei 225 stock market. Using this model, we investigate the relationship between the realized kernel series and its lagged one autoregressive effect, intraday returns, and abnormal trading volume. Applying an adaptive Markov chain Monte Carlo sampling scheme, our results confirm the existence of volatility clustering, a leverage effect, and a negative and asymmetric impact of trading volume on market volatility. We discover that the asymmetric characteristic of the news impact curve of the stock market varies over different quantile levels. This finding provides an in‐depth understanding about how stock volatility reacts to its determinants and how stock markets operate under different market conditions.

Bssm: Bayesian Inference of Non-linear and Non-Gaussian State Space Models in R

We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and the extended Kalman filter. The package accommodates also discretely observed latent diffusion processes. The inference is based on fully automatic, adaptive Markov chain Monte Carlo (MCMC) on the hyperparameters, with optional importance sampling post-correction to eliminate any approximation bias. The package implements also a direct pseudo-marginal MCMC and a delayed acceptance pseudo-marginal MCMC using intermediate approximations. The package offers an easy-to-use interface to define models with linear-Gaussian state dynamics with non-Gaussian observation models, and has an Rcpp interface for specifying custom non-linear and diffusion models.

On the convergence of stochastic approximations under a subgeometric ergodic Markov dynamic

IIn this paper, we extend the framework of the convergence ofstochastic approximations. Such a procedure is used in many methods such as parameters estimation inside a Metropolis Hastings algorithm, stochastic gradient descent or stochastic Expectation Maximization algorithm. It is given by θ n+1 = θn + ∆ n+1 H θn (X n+1) , where (Xn)n∈N is a sequence of random variables following a parametric distribution which depends on (θn)n∈N, and (∆n)n∈N is a step sequence. The convergence of such a stochastic approximation has already been proved under an assumption of geometric ergodicity of the Markov dynamic. However, in many practical situations this hypothesis is not satisfied, for instance for any heavy tail target distribution in a Monte Carlo Metropolis Hastings algorithm. In this paper, we relax this hypothesis and prove the convergence of the stochastic approximation by only assuming a subgeometric ergodicity of the Markov dynamic. This result opens up the possibility to derive more generic algorithms with proven convergence. As an example, we first study an adaptive Markov Chain Monte Carlo algorithm where the proposal distribution is adapted by learning the variance of a heavy tail target distribution. We then apply our work to the Independent Component Analysis when a positive heavy tail noise leads to a subgeometric dynamic in an Expectation Maximization algorithm.

Integrating public health policies in the epidemiological modeling of hepatitisC with LEHC tool: application in Austria.

SummaryBackgroundEliminating hepatitis C requires addressing issues other than medicines or therapies. Public health policies focused on the hepatitis C virus (HCV) must be emphasized and worked to know the impacts on its epidemiologic dynamics. This research aims to provide a tool to evaluate and simulate alternatives by redefining policies meeting specific needs in each country towards the HCV elimination target by 2030.MethodsThe development of a gamified model with 24 public health policies focused on HCV was conducted to evaluate the impact of measures in the disease epidemiologic dynamics. The Let’s End HepC (LEHC) project encompassed key populations (people who inject drugs [PWID], prisoners, blood products and remnant population) in Austria and other countries, presenting prospects for every year from 2019 to 2030. The LEHC epidemiological model comprised an integrated solution for HCV, with adaptive conjoint analysis (ACA) and Markov chains constituting its main processes.ResultsDespite Austria’s efforts towards achieving the HCV elimination goal by 2030, the LEHC model forecast quantitative analysis predicts that it is still not enough to meet the target; however, prospects are very optimistic if public health policies are adapted to the country’s needs, being possible to achieve the goal as early as 2026.ConclusionIn Austria, the LEHC tool allowed to forecast the HCV elimination year anticipation to 2026, instead of being achieved after 2030. This target will only be valid if adequate management of the 24 public health policies focused on this pathology is further implemented.

Sensitivity Analysis and Uncertainty Parameter Quantification in a Regression Model: The Case of Deforestation in Tanzania

Sep 2020, Published Oct 2020AbstractIn this paper a multiple regression model for the economic factors and policy that influence therate of deforestation in Tanzania is formulated. Sensitivity analysis for parameters of explanatoryvariables using one-at-a time and direct methods is carried out and the model is fitted by classicalleast square (LSQ) and Markov Chain Monte Carlo (MCMC) methods. Uncertainty quantificationof parameters by adaptive Markov Chain Monte Carlo methods is performed. The coefficient ofdetermination indicates that 87% of deforestation rate is explained by explanatory variablescaptured in the model. Household poverty rate is found to be the most sensitive factor todeforestation, while purchasing power is the least sensitive in both methods. Model validationindicates a good agreement between the collected data and the predicted data by the model andMarkoc Chain Monte Carlo method yielded a good sample mix. Thus, the study recommends thatsince economic activities tend to increase the rate of deforestation, then policy and decisionmakingprocesses should link the country’s desire for economic growth and environmentalmanagement.
 Keywords: deforestation; economic factors; Markov Chain Monte Carlo methods; regressionmodel; sensitivity;

In search of lost mixing time: adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very largep

SummaryThe availability of datasets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these datasets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. We propose new adaptive Markov chain Monte Carlo algorithms to address this shortcoming. The adaptive design of these algorithms exploits the observation that in large-$p$, small-$n$ settings, the majority of the $p$ variables will be approximately uncorrelated a posteriori. The algorithms adaptively build suitable nonlocal proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems and speed-ups of up to four orders of magnitude are observed.

Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts

This study proposes a class of nonlinear hysteretic integer-valued GARCH models in order to describe the occurrence of weekly dengue hemorrhagic fever cases via three meteorological covariates: precipitation, average temperature, and relative humidity. The proposed model adopts the hysteretic three-regime switching mechanism with a buffer zone that are able to explain various characteristics. This allows for having consecutive zeros in the lower regime and large counts to appear up in the upper regime. These nonlinear hysteretic integer-valued GARCH models include Poisson, negative binomial, and log-linked forms. We utilize adaptive Markov chain Monte Carlo simulations for making inferences and prediction and employ two Bayesian criteria for model comparisons and the relative root mean squared prediction error for evaluation. Simulation and analytic results emphasize that the hysteretic negative binomial integer-valued GARCH model is superior to other models and successfully offers an alternative nonlinear integer-valued GARCH model to better describe larger values of counts.

An adaptive Markov Chain approach for probabilistic forecasting of categorical events

Abstract Categorical probabilistic prediction is widely used for terrestrial and space weather forecasting as well as for other environmental forecasts. One example is a warning system for geomagnetic disturbances caused by space weather, which are often classified on a 10-level scale. The simplest approach assumes that the transition probabilities are stationary in time – the Homogeneous Markov Chain (HMC). We extend this approach by developing a flexible Non-Homogeneous Markov Chain (NHMC) model using Bayesian non-parametric estimation to describe the time-varying transition probabilities. The transition probabilities are updated using a modified Bayes’ rule that gradually forgets transitions in the distant past, with a tunable memory parameter. The approaches were tested by making daily geomagnetic state forecasts at lead times of 1-4 days and verified over the period 2000-2019 using the Rank Probability Score (RPS). Both HMC and NHMC models were found to be skilful at all lead times when compared with climatological forecasts. The NHMC forecasts with an optimal memory parameter of ~100 days were found to be substantially more skilful than the HMC forecasts, with an RPS skill for the NHMC of 10.5% and 5.6% for lead times of 1 and 4 days ahead, respectively. The NHMC is thus a viable alternative approach for forecasting geomagnetic disturbances, and could provide a new benchmark for producing operational forecasts. The approach is generic and applicable to other forecasts including discrete weather regimes or hydrological conditions, e.g. wet and dry days.

Bayesian Semi-Parametric Realized Conditional Autoregressive Expectile Models for Tail Risk Forecasting

AbstractA new model framework called Realized Conditional Autoregressive Expectile is proposed, whereby a measurement equation is added to the conventional Conditional Autoregressive Expectile model. A realized measure acts as the dependent variable in the measurement equation, capturing the contemporaneous dependence between it and the latent conditional expectile; it also drives the expectile dynamics. The usual grid search and asymmetric least squares optimization, to estimate the expectile level and parameters, suffers from convergence issues leading to inefficient estimation. This article develops an alternative random walk Metropolis stochastic target search method, incorporating an adaptive Markov Chain Monte Carlo sampler, which leads to improved accuracy in estimation of the expectile level and model parameters. The sampling properties of this method are assessed via a simulation study. In a forecast study applied to several market indices and asset return series, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed model class.

Bayesian cumulative shrinkage for infinite factorizations.

The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.

A Bayesian approach to discrete multiple outcome network meta-analysis.

In this paper we suggest a new Bayesian approach to network meta-analysis for the case of discrete multiple outcomes. The joint distribution of the discrete outcomes is modeled through a Gaussian copula with binomial marginals. The remaining elements of the hierarchial random effects model are specified in a standard way, with the logit of the success probabilities given by the sum of a baseline log-odds and random effects comparing the log-odds of each treatment against the reference and having a Gaussian distribution centered at the vector of pooled effects. An adaptive Markov Chain Monte Carlo algorithm is devised for running posterior inference. The model is applied to two datasets from Cochrane reviews, already analysed in two papers so to assess and compare its performance. We implemented the model in a freely available R package called netcopula.

Cost-effectiveness of social oocyte freezing in Germany: estimates based on a Markov model.

Is oocyte freezing for non-medical reasons-the so-called "social freezing" (SF)-cost-effective compared to standard in vitro fertilization (IVF)/intracytoplasmic sperm injection (ICSI) in Germany today? We developed a model based on three strategies for women planning to postpone pregnancy. In each strategy, women actively practiced contraception until 40 then tried to conceive naturally for 1year. If unsuccessful, women using strategy I (oocyte cryopreservation) attempted ICSI with frozen oocytes in the 2nd year, while women using strategy II (no action) further attempted natural conception. In strategy III (IVF/ICSI), women underwent 1year of IVF/ICSI. If still unsuccessful, each strategy was followed by attempting natural conception again until 45. We used an adaptive Markov model to estimate and compare live birth rates and cost-effectiveness measures. For strategy I, cumulative live birth rates at age 45 generally declined with the woman's age at freezing and were between 71.4% (25years) and 67.6% (38years), while the cumulative success rate was 51.5% for strategy II and 60.8% for strategy III. The costs per live birth of egg freezing were age-dependent ranging between 22,418 € (30years) and 25,590 € (38years). The costs for strategy III were lower at 20,293 € per live birth. Based on our results, social freezing in Germany may lead to additional pregnancies among women over 40 but also to significantly higher costs, since given the current live birth success rates and pricing, social freezing does not appear to be cost-effective.

Bayesian parameter estimation for the SWIFT model of eye-movement control during reading

Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.

A low-complexity algorithm for the joint antenna selection and user scheduling in multi-cell multi-user downlink massive MIMO systems

The massive MIMO (multiple-input multiple-output) technology plays a key role in the next-generation (5G) wireless communication systems, which are equipped with a large number of antennas at the base station (BS) of a network to improve cell capacity for network communication systems. However, activating a large number of BS antennas needs a large number of radio-frequency (RF) chains that introduce the high cost of the hardware and high power consumption. Our objective is to achieve the optimal combination subset of BS antennas and users to approach the maximum cell capacity, simultaneously. However, the optimal solution to this problem can be achieved by using an exhaustive search (ES) algorithm by considering all possible combinations of BS antennas and users, which leads to the exponential growth of the combinatorial complexity with the increasing of the number of BS antennas and active users. Thus, the ES algorithm cannot be used in massive MIMO systems because of its high computational complexity. Hence, considering the trade-off between network performance and computational complexity, we proposed a low-complexity joint antenna selection and user scheduling (JASUS) method based on Adaptive Markov Chain Monte Carlo (AMCMC) algorithm for multi-cell multi-user massive MIMO downlink systems. AMCMC algorithm is helpful for selecting combination subset of antennas and users to approach the maximum cell capacity with consideration of the multi-cell interference. Performance analysis and simulation results show that AMCMC algorithm performs extremely closely to ES-based JASUS algorithm. Compared with other algorithms in our experiments, the higher cell capacity and near-optimal system performance can be obtained by using the AMCMC algorithm. At the same time, the computational complexity is reduced significantly by combining with AMCMC.

Quantile forecasting based on a bivariate hysteretic autoregressive model with GARCH errors and time ‐varying correlations

AbstractTo understand and predict chronological dependence in the second‐order moments of asset returns, this paper considers a multivariate hysteretic autoregressive (HAR) model with generalized autoregressive conditional heteroskedasticity (GARCH) specification and time‐varying correlations, by providing a new method to describe a nonlinear dynamic structure of the target time series. The hysteresis variable governs the nonlinear dynamics of the proposed model in which the regime switch can be delayed if the hysteresis variable lies in a hysteresis zone. The proposed setup combines three useful model components for modeling economic and financial data: (1) the multivariate HAR model, (2) the multivariate hysteretic volatility models, and (3) a dynamic conditional correlation structure. This research further incorporates an adapted multivariate Student t innovation based on a scale mixture normal presentation in the HAR model to tolerate for dependence and different shaped innovation components. This study carries out bivariate volatilities, Value at Risk, and marginal expected shortfall based on a Bayesian sampling scheme through adaptive Markov chain Monte Carlo (MCMC) methods, thus allowing to statistically estimate all unknown model parameters and forecasts simultaneously. Lastly, the proposed methods herein employ both simulated and real examples that help to jointly measure for industry downside tail risk.

NON-MATRIX FACTORIZATION FOR BLIND IMAGE SEPARATION

Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding fractions from the mixture, nonnegative matrix factions ( NMF ) is suitable as a candidate for the linear spectral mixture mode, has been applied to the unmixing hyperspectral data. Unfortunately, the local minima is cause by the nonconvexity of the objective function makes the solution nonunique, thus only the nonnegativity constraint is not sufficient enough to lead to a well define problems. Therefore, two inherent characteristic of hyperspectal data, piecewise smoothness ( both temporal and spatial ) of spectral data and sparseness of abundance fraction of every material, are introduce to the NMF. The adaptive potential function from discontinuity adaptive Markov random field model is used to describe the smoothness constraint while preserving discontinuities is spectral data. At the same time two NMF algorithms, non smooth NMS and NMF with sparseness constraint, are used to quantify the degree of sparseness of material abundances. Experiment using the synthetic and real data demonstrate the proposed algorithms provides an effective unsupervised technique for hyperspectial unmixing.

Probabilistic Inference on Noisy Time Series (PINTS)

Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of the underlying system based on observed time series. For both statistical and mechanistic models, inference involves finding parameter values, or distributions of parameters values, for which model outputs are consistent with observations. A wide variety of inference techniques are available and different approaches are suitable for different classes of problems. This variety presents a challenge for researchers, who may not have the resources or expertise to implement and experiment with these methods. PINTS (Probabilistic Inference on Noisy Time Series - https://github.com/pints-team/pints is an open-source (BSD 3-clause license) Python library that provides researchers with a broad suite of non-linear optimisation and sampling methods. It allows users to wrap a model and data in a transparent and straightforward interface, which can then be used with custom or pre-defined error measures for optimisation, or with likelihood functions for Bayesian inference or maximum-likelihood estimation. Derivative-free optimisation algorithms - which work without harder-to-obtain gradient information - are included, as well as inference algorithms such as adaptive Markov chain Monte Carlo and nested sampling which estimate distributions over parameter values. By making these statistical techniques available in an open and easy-to-use framework, PINTS brings the power of modern statistical techniques to a wider scientific audience.

Adaptive Markov chain Monte Carlo algorithms for Bayesian inference: recent advances and comparative study

Condition assessments of structures require prediction models such as empirical model and numerical simulation model. Generally, these prediction models have model parameters to be estimated from experimental data. Bayesian inference is the formal statistical framework to estimate the model parameters and their uncertainties. As a result, uncertainties associated with the model and measurement can be accounted for decision making. Markov Chain Monte Carlo (MCMC) algorithms have been widely employed. However, there still remain some implementation issues from the inappropriate selection of the proposal mechanism in Markov chain. Since the posterior density for a given problem is often problem-dependent and unknown, users require a trial-and-error approach to select and tune optimal proposal mechanism. To relieve this difficulty, various adaptive MCMC algorithms have been recently appeared. Users must understand their mechanism and limitations before applying the algorithms to their problems. However, there is no comprehensive work to provide detailed exposition and their performance comparison together. This study aims to bring together different adaptive MCMC algorithms with the goal of providing their mechanisms and evaluating their performances through comparative study. Three algorithms are chosen as the representative proposal mechanism. From comparative studies, the discussions were drawn in terms of performances, simplicity and computational costs for less-experienced users.