Markov Chain Monte Carlo Estimation Research Articles

Interrater Reliability for Interdependent Social Network Data: A Generalizability Theory Approach

We propose interrater reliability coefficients for observational interdependent social network data, which are dyadic data from a network of interacting subjects that are observed by external raters. Using the social relations model, dyadic scores of subjects’ behaviors during these interactions can be decomposed into actor, partner, and relationship effects. These effects constitute different facets of theoretical interest about which researchers formulate research questions. Based on generalizability theory, we extended the social relations model with rater effects, resulting in a model that decomposes the variance of dyadic observational data into effects of actors, partners, relationships, raters, and their statistical interactions. We used the variances of these effects to define intraclass correlation coefficients (ICCs) that indicate the extent the actor, partner, and relationship effects can be generalized across external raters. We proposed Markov chain Monte Carlo estimation of a Bayesian hierarchical linear model to estimate the ICCs, and tested their bias and coverage in a simulation study. The method is illustrated using data on social mimicry.

Building a simpler moderated nonlinear factor analysis model with Markov Chain Monte Carlo estimation.

Moderated nonlinear factor analysis (MNLFA) has emerged as an important and flexible data analysis tool, particularly in integrative data analysis setting and psychometric studies of measurement invariance and differential item functioning. Substantive applications abound in the literature and span a broad range of disciplines. MNLFA unifies item response theory, multiple group, and multiple indicator multiple cause modeling traditions, and it extends these frameworks by conceptualizing latent variable heterogeneity as a source of differential item functioning. The purpose of this article was to illustrate a flexible Markov chain Monte Carlo-based approach to MNLFA that offers statistical and practical enhancements to likelihood-based estimation while remaining plug and play with established analytic practices. Among other things, these enhancements include (a) missing data handling functionality for incomplete moderators, (b) multiply imputed factor score estimates that integrate into existing multiple imputation inferential methods, (c) support for common data types, including normal/continuous, nonnormal/continuous, binary, ordinal, multicategorical nominal, count, and two-part constructions for floor and ceiling effects, (d) novel residual diagnostics for identifying potential sources of differential item function, (e) manifest-by-latent variable interaction effects that replace complex moderation function constraints, and (f) integration with familiar regression modeling strategies, including graphical diagnostics. A real data analysis example using the Blimp software application illustrates these features. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Convergence speed and approximation accuracy of numerical MCMC

Abstract When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the $\chi^2$ metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims.

Bayesian Inference for Long Memory Stochastic Volatility Models

We explore the application of integrated nested Laplace approximations for the Bayesian estimation of stochastic volatility models characterized by long memory. The logarithmic variance persistence in these models is represented by a Fractional Gaussian Noise process, which we approximate as a linear combination of independent first-order autoregressive processes, lending itself to a Gaussian Markov Random Field representation. Our results from Monte Carlo experiments indicate that this approach exhibits small sample properties akin to those of Markov Chain Monte Carlo estimators. Additionally, it offers the advantages of reduced computational complexity and the mitigation of posterior convergence issues. We employ this methodology to estimate volatility dependency patterns for both the SP&500 index and major cryptocurrencies. We thoroughly assess the in-sample fit and extend our analysis to the construction of out-of-sample forecasts. Furthermore, we propose multi-factor extensions and apply this method to estimate volatility measurements from high-frequency data, underscoring its exceptional computational efficiency. Our simulation results demonstrate that the INLA methodology achieves comparable accuracy to traditional MCMC methods for estimating latent parameters and volatilities in LMSV models. The proposed model extensions show strong in-sample fit and out-of-sample forecast performance, highlighting the versatility of the INLA approach. This method is particularly advantageous in high-frequency contexts, where the computational demands of traditional posterior simulations are often prohibitive.

Multivariate Moment Least-Squares Variance Estimators for Reversible Markov Chains

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. Berg and Song introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from Berg and Song. We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN. Supplemental materials for this article are available online.

Practical Implementation of Advanced Causal Inference Method: Development of an R Package for Bayesian Marginal Structural Models with Time-Varying Treatment

Background: Observational studies offer a viable, efficient, and low-cost design to readily gather evidence on exposure effects. Although more practical, the exposure mechanism is non-randomized and causal inference methods are required to draw causal conclusions. Objectives: Bayesian approaches to causal inference have unique estimation features that are useful in many settings; however, there is a lack of open-access software packages to carry out these analyses. Our project seeks to address this gap by developing a user-friendly R package named “bayesmsm” for the implementation of the Bayesian Marginal Structural Models for longitudinal observational data with extensions to handle right-censoring which is common for longitudinal health data. This R package provides an elegant approach to conduct Bayesian causal inference with time-varying exposure and confounding. Methods: We use simulated datasets to assess the performance of the package and to illustrate its use. This package first implements Bayesian parametric treatment assignment weight estimation through Markov Chain Monte Carlo (MCMC) computation. It then uses Bayesian non-parametric bootstrap to maximize the utility function with respect to the causal effect. The bootstrap calculation process was optimized for performance through parallel computing. The package has additional features, including handling right-censored data and generating analysis summaries and visualizations. Results: Using simulated datasets with and without right-censoring, the subject-specific treatment assignment weights were estimated using the package's weight estimation functions. The Bayesian posterior bootstrap results were further visualized by functions built within this package. Conclusions: The “bayesmsm” package provides a reliable tool to implement complex Bayesian Marginal Structural Model analysis. Future work will focus on extending this package to handle time-to-event data.

Regularized Bayesian algorithms for Q-matrix inference based on saturated cognitive diagnosis modelling.

Q-matrices are crucial components of cognitive diagnosis models (CDMs), which are used to provide diagnostic information and classify examinees according to their attribute profiles. The absence of an appropriate Q-matrix that correctly reflects item-attribute relationships often limits the widespread use of CDMs. Rather than relying on expert judgment for specification and post-hoc methods for validation, there has been a notable shift towards Q-matrix estimation by adopting Bayesian methods. Nevertheless, their dependency on Markov chain Monte Carlo (MCMC) estimation requires substantial computational burdens and their exploratory tendency is unscalable to large-scale settings. As a scalable and efficient alternative, this study introduces the partially confirmatory framework within a saturated CDM, where the Q-matrix can be partially defined by experts and partially inferred from data. To address the dual needs of accuracy and efficiency, the proposed framework accommodates two estimation algorithms-an MCMC algorithm and a Variational Bayesian Expectation Maximization (VBEM) algorithm. This dual-channel approach extends the model's applicability across a variety of settings. Based on simulated and real data, the proposed framework demonstrated its robustness in Q-matrix inference.

Radiation mechanism of twin kilohertz quasi-periodic oscillations in neutron star low-mass X-ray binaries

Context. The connection between quasi-periodic oscillations (QPOs) and magnetic fields has been investigated in various celestial bodies. Magnetohydrodynamic (MHD) waves have been employed to explain the simultaneous upper and lower kilohertz (kHz) QPOs. Nevertheless, the intricate and undefined formation pathways of twin kHz QPOs present a compelling avenue for exploration. This study area holds great interest as it provides an opportunity for deriving crucial parameters related to compact stars. Aims. We strive to develop a self-consistent model elucidating the radiation mechanism of twin kHz QPOs, which we then compare it with observations. Methods. A sample of 28 twin kHz QPOs detected from the X-ray binary 4U 1636–53 was used for a comparison with the results of the Markov chain Monte Carlo calculations based on our model of the radiation mechanism of twin kHz QPOs, which is related to twin MHD waves. Results. We obtained 28 groups of parameters of 4U 1636–53 and a tight exponential fit between the flux and the temperature of seed photons to Compton up-scattering and find that the electron temperature in the corona around the neutron star decreases with increasing seed photon temperature. Conclusions. The origin of twin kHz QPOs are dual disturbances that arise from twin MHD waves that are generated at the innermost radius of an accretion disc. The seed photons can be transported through a high temperature corona and are Compton up-scattered. The photons that vary the frequencies of twin MHD waves lead to the observed twin kHz QPOs.

Peer effects affect the adaptation behaviour of rural residents to geohazards in China: a new policy pathway

ABSTRACT Disaster prevention and mitigation (DPM) is one of the responses to extreme climate change impacts and depends on the adoption of risk adaptation behaviour by rural residents. While residents exhibit a high willingness to adapt, they also show low behaviour with reference to DPM. While adaptation behaviour of individuals has been studied extensively, the mutual impact of adaptation behaviour among residents has so far been neglected in the literature. Evaluating this interaction could serve as an important foundation for refining disaster reduction policies. Drawing on social cognitive theory, we propose a novel theoretical framework to analyze peer effects on individual decision-making in DPM. Using data gathered from 536 respondents in Sichuan Province, China, this paper adopts the Bayes Markov chain Monte Carlo estimation method to perform a regression of the spatial probit model. Further, the propensity score matching model was used to explore peer effects on the transformation between residents’ willingness to actual behaviour. Results indicate significant and robust peer effects on DPM behaviour among residents. A heterogeneity test indicated that peer effects are predominantly observed among residents with low and medium social status perception and not in those with high social status perception. Peer effects have a significant and positive influence on the transformation from residents’ willingness to their behaviour. Residents are not completely independent in their decision-making, and complex social mechanisms dictate rational and irrational choices of behaviour. Therefore, it is necessary to fully consider positive peer effects on residents in the formulation of policies. Key policy insights Focusing on the adaptation behaviours and peer effects of rural residents is conducive to improving the public's acceptance of disaster reduction policies. It is difficult for homogenization policies to accurately meet the needs of rural residents in China, and the response to geohazard events requires diversified local policies. Through peer effect, the government can create a kind of environmental soft pressure and promote the transformation of residents’ willingness into behaviour. Due to peer effects, the government can utilize the leading role of a small number of target groups to reduce the cost of implementing disaster reduction policies.

B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics.

Throughout an organism's life, a multitude of complex and interdependent biological systems transition through biophysical processes that serve as indicators of the underlying biological states. Inferring these latent, unobserved states is a goal of modern biology and neuroscience. However, in many experimental setups, we can at best obtain discrete snapshots of the system at different times and for different individuals. This challenge is particularly relevant in the study of Alzheimer's Disease (AD) progression, where we observe the aggregation of pathology in brain donors, but the underlying disease state is unknown. This paper proposes a biophysically motivated Bayesian framework (B-BIND: Biophysical Bayesian Inference for Neurodegenerative Dynamics), where the disease state is modeled and continuously inferred from observed quantifications of multiple AD pathological proteins. Inspired by biophysical models, we describe pathological burden as an exponential process. The progression of AD is modeled by assigning a latent score, termed pseudotime, to each pathological state, creating a pseudotemporal order of donors based on their pathological burden. We study the theoretical properties of the model using linearization to reveal convergence and identifiability properties. We provide Markov chain Monte Carlo estimation algorithms, illustrating the effectiveness of our approach with multiple simulation studies across various data conditions. Applying this methodology to data from the Seattle Alzheimer's Disease Brain Cell Atlas, we infer the pseudotime ordering of donors. Finally, we analyze the information within each pathological feature to refine the model, focusing on the most informative pathologies. This framework lays the groundwork for continuous pseudotime modeling in the analysis of neurodegenerative diseases.

Is the availability and quality of local early childhood education and care services associated with young children's mental health at school entry?

PurposeThis study investigated the relationship between geographic availability (and quality) of local early childhood education and care services and children's early mental health outcomes for all children entering their first year of full-time school in Melbourne, Australia. MethodsWe capitalise on a unique population linked dataset, the Australian Early Development Census – Built Environment, which combines geospatial measures of children's neighbourhoods with demographic information and child mental health outcomes for all school entrants in Australia's 21 most populous cities and towns. Objective early childhood education and care service location and quality exposures were developed for each study child based on home addresses. Four geographic availability exposures (counts within 3 km) were examined for cross-sectional associations with child mental health outcomes (externalising and internalising difficulties, competence). We estimated associations using multilevel logistic regression (Markov Chain Monte Carlo estimation) adjusting for child demographics and stratifying by urbanicity. ResultsChildren with higher counts of high-quality preschool services within 3 km of home had lower odds of difficulties and higher odds of competence. Overall, exposures were most consistently associated with children's competence. Across all outcomes, the most consistent patterning was observed for children living in the inner city and middle ring. Results varied depending on whether service quality was accounted for in measures of availability. Geographic availability of early childhood services showed patterning by neighbourhood disadvantage and by maternal education. ConclusionWe found some evidence that geographic availability of high-quality preschools was associated with better child mental health outcomes, but results varied by urbanicity. While future research is required to unpack these differences, these findings indicate the importance of accounting for both geographic availability and service quality simultaneously in future research, policy and practice.

Parameter estimation from the Lyα forest in the Fourier space using an information-maximizing neural network

Our aim is to present a robust parameter estimation with simulated forest spectra from Sherwood-Relics simulations suite by using an information-maximizing neural network (IMNN) to extract maximal information from 1D-transmitted flux in the Fourier space. We performed 1D estimations using IMNN for intergalactic medium (IGM) thermal parameters $T_0$ and gamma at $z=2-4$, and cosmological parameters $ and s $ at $z=3-4$. We compared our results with estimates from the power spectrum using the posterior distribution from a Markov Chain Monte Carlo (MCMC). We then checked the robustness of IMNN estimates against deviation in spectral noise levels, continuum uncertainties, and instrumental smoothing effects. Using mock forest sightlines from the publicly available CAMELS project, we also checked the robustness of the trained IMNN on a different simulation. As a proof of concept, we demonstrated a 2D-parameter estimation for $T_0$ and photoionization rates, $ HI We obtain improved estimates of $T_0$ and gamma using IMNN over the standard MCMC approach. These estimates are also more robust against signal-to-noise deviations at $z=2$ and 3. At $z=4$, the sensitivity to noise deviations is on par with MCMC estimates. The IMNN also provides $T_0$ and gamma estimates that are robust against continuum uncertainties by extracting small-scale continuum-independent information from the Fourier domain. In the cases of $ and s $, the IMNN performs on par with MCMC but still offers a significant speed boost in estimating parameters from a new dataset. The improved estimates with IMNN are seen for high instrumental resolution (FWHM=6 At medium or low resolutions, the IMNN performs similarly to MCMC, suggesting an improved extraction of small-scale information with IMNN. We also find that IMNN estimates are robust against the choice of simulation. By performing a 2D-parameter estimation for $T_0$ and $ HI $, we also demonstrate how to take forward this approach observationally in the future.

Bayesian cluster geographically weighted regression for spatial heterogeneous data.

Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. One of these algorithms is geographically weighted regression (GWR) which was proposed in the geography literature to allow relationships in a regression model to vary over space. In contrast to traditional linear regression models, which have constant regression coefficients over space, regression coefficients are estimated locally at spatially referenced data points with GWR. The motivation for the adaption of GWR is the idea that a set of constant regression coefficients cannot adequately capture spatially varying relationships between covariates and an outcome variable. GWR has been applied widely in diverse fields, such as ecology, forestry, epidemiology, neurology and astronomy. While frequentist GWR gives us point estimates and confidence intervals, Bayesian GWR enriches our understanding by including prior knowledge and providing probability distributions for parameters and predictions of interest. This paper pursues three main objectives. First, it introduces covariate effect clustering by integrating a Bayesian geographically weighted regression (BGWR) with a post-processing step that includes Gaussian mixture model and the Dirichlet process mixture model. Second, this paper examines situations in which a particular covariate holds significant importance in one region but not in another in the Bayesian framework. Lastly, it addresses computational challenges in existing BGWR, leading to enhancements in Markov chain Monte Carlo estimation suitable for large spatial datasets. The efficacy of the proposed method is demonstrated using simulated data and is further validated in a case study examining children's development domains in Queensland, Australia, using data provided by Children's Health Queensland and Australia's Early Development Census.

Efficiency comparison of MCMC and Transport Map Bayesian posterior estimation for structural health monitoring

In this paper, an alternative to solving Bayesian inverse problems for structural health monitoring based on a variational formulation with so-called transport maps is examined. The Bayesian inverse formulation is a widely used tool in structural health monitoring applications. While Markov Chain Monte Carlo (MCMC) methods are often implemented in these settings, they come with the problem of using many model evaluations, which in turn can become quite costly. We focus here on recent developments in the field of transport theory, where the problem is formulated as finding a deterministic, invertible mapping between some easy to evaluate reference density and the posterior. The resulting variational formulation can be solved with integration and optimization methods. We develop a general formulation for the application of transport maps to vibration-based structural health monitoring. Further, we study influences of different integration approaches on the efficiency and accuracy of the transport map approach and compare it to the Transitional MCMC algorithm, a widely used method for structural identification. Both methods are applied to a lower-dimensional dynamic model with uni- and multi-modal properties, as well as to a higher-dimensional neural network surrogate system of an airplane structure. We find that transport maps have a significant increase in accuracy and efficiency, when used in the right circumstances.

Can the Phillips curve provide answers to current high inflation rates

Motivated by the weak response of the inflation rate to the tight labor market, the Federal Reserve (Fed) Bank stepped away from its longstanding preemptive policy to fight inflation as the economy approached full employment. This paper aims to reevaluate the relationships of four measures of inflation with the unemployment rate. We accomplish this task by allowing the Phillips curve (PC) slope to vary over time and depend on the magnitude of the unemployment gap. Assessed by both PC convex specification assessment and the Markov chain Monte Carlo (MCMC) estimation method, we confirm the convexity of the PC when the unemployment gap is negative. In addition, we show that the slope of the PC more than doubled when we allow the coefficient on the economic slack to vary over time. Thus, our study shows that PC is still a relevant tool for guiding monetary policy.

Gaussian Process Vector Autoregressions and Macroeconomic Uncertainty

We develop a nonparametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a Gaussian process prior on the functional relationship that determines the conditional mean of the model, hence, the name of Gaussian process vector autoregression (GP-VAR). A flexible stochastic volatility specification is used to provide additional flexibility and control for heteroscedasticity. Markov chain Monte Carlo (MCMC) estimation is carried out through an efficient and scalable algorithm which can handle large models. The GP-VAR is used to analyze the effects of macroeconomic uncertainty, with a particular emphasis on time variation and asymmetries in the transmission mechanisms.

Two-Stage Limited-Information Estimation for Structural Equation Models of Round-Robin Variables

We propose and demonstrate a new two-stage maximum likelihood estimator for parameters of a social relations structural equation model (SR-SEM) using estimated summary statistics (Σ^) as data, as well as uncertainty about Σ^ to obtain robust inferential statistics. The SR-SEM is a generalization of a traditional SEM for round-robin data, which have a dyadic network structure (i.e., each group member responds to or interacts with each other member). Our two-stage estimator is developed using similar logic as previous two-stage estimators for SEM, developed for application to multilevel data and multiple imputations of missing data. We demonstrate out estimator on a publicly available data set from a 2018 publication about social mimicry. We employ Markov chain Monte Carlo estimation of Σ^ in Stage 1, implemented using the R package rstan. In Stage 2, the posterior mean estimates of Σ^ are used as input data to estimate SEM parameters with the R package lavaan. The posterior covariance matrix of estimated Σ^ is also calculated so that lavaan can use it to calculate robust standard errors and test statistics. Results are compared to full-information maximum likelihood (FIML) estimation of SR-SEM parameters using the R package srm. We discuss how differences between estimators highlight the need for future research to establish best practices under realistic conditions (e.g., how to specify empirical Bayes priors in Stage 1), as well as extensions that would make 2-stage estimation particularly advantageous over single-stage FIML.

Estimating and Calibrating Markov Chain Sample Error Variance

Markov chain Monte Carlo (MCMC) methods are a powerful and versatile tool with applications spanning a wide spectrum of fields, including Bayesian inference, computational biology, and physics. One of the key challenges in applying MCMC algorithms is to deal with estimation error. The main result in this article is a closed form, non-asymptotic solution for the sample error variance of a single MCMC  estimate. Importantly, this result assumes that the state-space is finite and discrete. We demonstrate with examples how this result can help estimate and calibrate MCMC estimation error variance in the more general case, when the state-space is continuous and/or unbounded.

Comparison of distance-based spatial weight matrix in modeling Internet signal strengths in Tasikmalaya regency using logistic spatial autoregressive model

To ensure that national development objectives in rural areas are achieved evenly and sustainably, the Government of Indonesia applies the principles of Village Sustainable Development Goals (SDGs), which are derivative programs of SDGs. One of the indicators in measuring the progress and independence of villages in Indonesia is the availability of cellular phone signal access. Cellular phone signals have a vital role because most internet users in Indonesia rely on mobile data connections from cellular operators. However, the signal emitted by a provider tower has a limited range. According to the data of the Developing Villages Index in 2022, Tasikmalaya Regency is one of the regencies with the highest number of villages that have weak signal strength in West Java Province, Indonesia. To examine the effect of distance and height difference between the placement of the nearest provider tower and the location of the Village Office on the internet signal strength category in Tasikmalaya Regency, Logistic Spatial Autoregressive modeling is needed. In this study, the Bayesian Markov-Chain Monte Carlo estimation method was used, because it has advantages in flexibility and computational efficiency. In spatial modeling, there is a spatial weight matrix determined by the researcher’s understanding of the observed phenomenon. The variable observed in this study is signal strength, which has an orientation at a distance. However, there are several types of distance-based spatial weight matrices, such as K-nearest neighbor, radial distance, power distance, and exponential distance. To determine the most suitable distance-based spatial weight matrix in internet signal strength modeling, the four (4) weight matrices were compared based on the goodness of fit measure models, calculated from the confusion matrix. The results of the analysis showed that the radial distance weight matrix with a threshold distance of d = 1.7km is the most suitable use of distance-based spatial weight matrix in internet signal modeling in Tasikmalaya Regency. The weight matrix exerted a positive spatial autocorrelation effect of 57.141%. In addition, the height difference factor between the location of the provider tower with the location of the village office has a greater effect than the horizontal distance.

Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

SummaryModeling and predicting extreme movements in GDP is notoriously difficult, and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large datasets in quantile regression models to forecast the conditional distribution of US GDP growth. To capture possible nonlinearities, we include several nonlinear specifications. The resulting models will be huge dimensional, and we thus rely on a set of shrinkage priors. Since Markov chain Monte Carlo estimation becomes slow in these dimensions, we rely on fast variational Bayes approximations to the posterior distribution of the coefficients and the latent states. We find that our proposed set of models produces precise forecasts. These gains are especially pronounced in the tails. Using Gaussian processes to approximate the nonlinear component of the model further improves the good performance, in particular in the right tail.