Markov Chain Monte Carlo Approach Research Articles

Automatically Structuralize the Curvilinear Glacier Using Phase-Coded Convolution

The morphological structure of glaciers is essential to understand and model their dynamics. In this letter, a novel method based on phase-coded disk (PCD) and phase-coded convolution is presented to automatically delineate the morphological structure of curvilinear glaciers from ice surface velocities. First, a region-growing algorithm is used to identify the glacier image object from an ice surface velocity remote sensing product. Secondly, the phase-coded convolution is applied to derive the image object’s magnitude surface. A Markov chain Monte Carlo (MCMC) approach is then developed to extract the centerlines of glacier tributaries. Finally, the morphological structure and attributes of the glacier image object are numerically derived based on the centerlines. A glacier in Alaska was employed to test the proposed method and conventional hydrologic method. The results proved the effectiveness of the proposed PCD-based method. This study is a trailblazing pilot study that novelly employs computer vision technology to automatically structuralize curvilinear glaciers. The outcomes enable the inspection and monitoring of complex glacier dynamics on a tributary level.

Investigation of the orbital period and mass relations for W UMa-type contact systems

ABSTRACT New relationships between the orbital period and some parameters of W Ursae Majoris (W UMa)-type systems are presented in this study. To investigate the relationships, we calculated the absolute parameters of a sample of 118 systems. For this purpose, we used the parallax values obtained from the Gaia Early Data Release 3 star catalogue for more precise calculations. The other required parameters, including the light-curve solutions and the orbital period, were derived from previous research. For some relationships, we added 86 systems from another study with an orbital period of less than 0.6 d to our sample, allowing us to increase the number of systems to 204. Therefore, the mass (M) values of each component along with all the other absolute parameters were recalculated for these contact systems. We used the Markov chain Monte Carlo approach in order to gain the new orbital period–mass relations (P–M) per component, and added the temperature (T) to the process to acquire the new orbital period–temperature (P–T1) relation. We presented the orbital period behaviour in terms of log(g) by new relations for each component. We have also obtained a model between the orbital period, the mass of the primary component, and temperature (P–M1–T1) using the artificial neural network method. Additionally, we present a model for the relationship between the orbital period and the mass ratio (P–q) by fitting a multilayer perceptron regression model to a sample of the data collected from the literature.

Temperature and Salinity Inverted for a Mediterranean Eddy Captured With Seismic Data, Using a Spatially Iterative Markov Chain Monte Carlo Approach

Ocean submesoscale dynamics are thought to play a key role in both the climate system and ocean productivity, however, subsurface observations at these scales remain rare. Seismic oceanography, an established acoustic imaging method, provides a unique tool for capturing oceanic structure throughout the water column with spatial resolutions of tens of meters. A drawback to the seismic method is that temperature and salinity are not measured directly, limiting the quantitative interpretation of imaged features. The Markov Chain Monte Carlo (MCMC) inversion approach has been used to invert for temperature and salinity from seismic data, with spatially quantified uncertainties. However, the requisite prior model used in previous studies relied upon highly continuous acoustic reflection horizons rarely present in real oceanic environments due to instabilities and turbulence. Here we adapt the MCMC inversion approach with an iteratively updated prior model based on hydrographic data, sidestepping the necessity of continuous reflection horizons. Furthermore, uncertainties introduced by the starting model thermohaline fields as well as those from the MCMC inversion itself are accounted for. The impact on uncertainties of varying the resolution of hydrographic data used to produce the inversion starting model is also investigated. The inversion is applied to a mid-depth Mediterranean water eddy (or meddy) captured with seismic imaging in the Gulf of Cadiz in 2007. The meddy boundary exhibits regions of disrupted seismic reflectivity and rapid horizontal changes of temperature and salinity. Inverted temperature and salinity values typically have uncertainties of 0.16°C and 0.055 psu, respectively, and agree well with direct measurements. Uncertainties of inverted results are found to be highly dependent on the resolution of the hydrographic data used to produce the prior model, particularly in regions where background temperature and salinity vary rapidly, such as at the edge of the meddy. This further advancement of inversion techniques to extract temperature and salinity from seismic data will help expand the use of ocean acoustics for understanding the mesoscale to finescale structure of the interior ocean.

The CARMENES search for exoplanets around M dwarfs

We determined effective temperatures, surface gravities, and metallicities for a sample of 343 M dwarfs observed with CARMENES, the double-channel, high-resolution spectrograph installed at the 3.5 m telescope at Calar Alto Observatory. We employed STEPARSYN, a Bayesian spectral synthesis implementation particularly designed to infer the stellar atmospheric parameters of late-type stars following a Markov chain Monte Carlo approach. We made use of the BT-Settl model atmospheres and the radiative transfer code turbospectrum to compute a grid of synthetic spectra around 75 magnetically insensitive Fe I and Ti I lines plus the TiO γ and ϵ bands. To avoid any potential degeneracy in the parameter space, we imposed Bayesian priors on Teff and logg based on the comprehensive, multi-band photometric data available for the sample. We find that this methodology is suitable down to M7.0 V, where refractory metals such as Ti are expected to condense in the stellar photospheres. The derived Teff, logg, and [Fe/H] range from 3000 to 4200 K, 4.5 to 5.3 dex, and −0.7 to 0.2 dex, respectively. Although our Teff scale is in good agreement with the literature, we report large discrepancies in the [Fe/H] scales, which might arise from the different methodologies and sets of lines considered. However, our [Fe/H] is in agreement with the metallicity distribution of FGK-type stars in the solar neighbourhood and correlates well with the kinematic membership of the targets in the Galactic populations. Lastly, excellent agreement in Teff is found for M dwarfs with interferometric angular diameter measurements, as well as in the [Fe/H] between the components in the wide physical FGK+M and M+M systems included in our sample.

Cosmological constraints of interacting phantom dark energy models

In this paper, we consider three phantom dark energy models, in the context of interaction between the dark components namely cold dark matter (CDM) and dark energy (DE). The first model, known as wdCDM can induce a big rip singularity (BR) while the two remaining induce future abrupt events known as the Little Rip (LR) and Little Sibling of the Big Rip (LSBR). These phantom DE models can be distinguished by their equation of state. We invoke a new phenomenon such as the interaction between CDM and DE given that it could solve or alleviate some of the problems encountered in standard cosmology. We aim to find out the effect of such an interaction on the cosmological parameters of the studied models, as well as, the persistence or the disappearance of the singularity and the abrupt events induced by the models under study. We choose an interaction term proportional to DE density, i.e. Q=λHρd, since the case where Q∝ρm could lead to a large scale instability at early time. We also do not claim at all that Q=λHρd is the ideal choice since it suffers from a negative CDM density in the future. By the use of a Markov Chain Monte Carlo (MCMC) approach, and by assuming a flat FLRW Universe, we constrain the cosmological parameters of each of the three phantom DE models studied. Furthermore, by the aid of the corrected Akaike Information Criterion (AICc) tool, we compare our phantom DE models. Finally, a perturbative analysis of phantom DE models under consideration is performed based on the best fit background parameters.

Rotation Curves in z ∼ 1–2 Star-forming Disks: Comparison of Dark Matter Fractions and Disk Properties for Different Fitting Methods

Abstract We present a follow-up analysis examining the dynamics and structures of 41 massive, large star-forming galaxies at z ∼ 0.67 − 2.45 using both ionized and molecular gas kinematics. We fit the galaxy dynamics with models consisting of a bulge, a thick, turbulent disk, and an NFW dark matter halo, using code that fully forward-models the kinematics, including all observational and instrumental effects. We explore the parameter space using Markov Chain Monte Carlo (MCMC) sampling, including priors based on stellar and gas masses and disk sizes. We fit the full sample using extracted 1D kinematic profiles. For a subset of 14 well-resolved galaxies, we also fit the 2D kinematics. The MCMC approach robustly confirms the results from least-squares fitting presented in Paper I: the sample galaxies tend to be baryon-rich on galactic scales (within one effective radius). The 1D and 2D MCMC results are also in good agreement for the subset, demonstrating that much of the galaxy dynamical information is captured along the major axis. The 2D kinematics are more affected by the presence of noncircular motions, which we illustrate by constructing a toy model with constant inflow for one galaxy that exhibits residual signatures consistent with radial motions. This analysis, together with results from Paper I and other studies, strengthens the finding that massive, star-forming galaxies at z ∼ 1 − 2 are baryon-dominated on galactic scales, with lower dark matter fractions toward higher baryonic surface densities. Finally, we present details of the kinematic fitting code used in this analysis.

The impact of active case finding on transmission dynamics of tuberculosis: A modelling study

BackgroundIn the last decade, active case finding (ACF) strategies for tuberculosis (TB) have been implemented in many diverse settings, with some showing large increases in case detection and reporting at the sub-national level. There have also been several studies which seek to provide evidence for the benefits of ACF to individuals and communities in the broader context. However, there remains no quantification of the impact of ACF with regards to reducing the burden of transmission. We sought to address this knowledge gap and quantify the potential impact of active case finding on reducing transmission of TB at the national scale and further, to determine the intensification of intervention efforts required to bring the reproduction number (R0) below 1 for TB.MethodsWe adopt a dynamic transmission model that incorporates heterogeneity in risk to TB to assess the impact of an ACF programme (IMPACT TB) on reducing TB incidence in Vietnam and Nepal. We fit the models to country-level incidence data using a Bayesian Markov Chain Monte Carlo approach. We assess the impact of ACF using a parameter in our model, which we term the treatment success rate. Using programmatic data, we estimate how much this parameter has increased as a result of IMPACT TB in the implementation districts of Vietnam and Nepal and quantify additional efforts needed to eliminate transmission of TB in these countries by 2035.ResultsExtending the IMPACT TB programme to national coverage would lead to moderate decreases in TB incidence and would not be enough to interrupt transmission by 2035. Decreasing transmission sufficiently to bring the reproduction number (R0) below 1, would require a further intensification of current efforts, even at the sub-national level.ConclusionsActive case finding programmes are effective in reducing TB in the short term. However, interruption of transmission in high-burden countries, like Vietnam and Nepal, will require comprehensive incremental efforts. Complementary measures to reduce progression from infection to disease, and reactivation of latent infection, are needed to meet the WHO End TB incidence targets.

Transdimensional simultaneous inversion of velocity structure and event locations in downhole microseismic monitoring

In downhole microseismic monitoring, the velocity model plays a vital role in accurate mapping of the hydraulic fracturing image. For velocity model uncertainties in the number of layers or interface depths, the conventional velocity calibration method has been shown to effectively locate the perforation shots; however, it introduces nonnegligible location errors for microseismic events, especially for complex geologic formations with inclinations. To improve the event location accuracy, we have exploited the advantages of the reversible jump Markov chain Monte Carlo approach in generating different dimensions of velocity models and adopted a transdimensional Bayesian simultaneous inversion framework for obtaining the effective velocity structure and event locations simultaneously. The transdimensional inversion changes the number of layers during the inversion process and selects the optimal interface depths and velocity values to improve the event location accuracy. The confidence intervals of the simultaneous inversion event locations estimated by Bayesian inference enable us to evaluate the location uncertainties in the horizontal and vertical directions. Two synthetic examples and a field test are presented to illustrate the performance of our methodology, and the event location accuracy is shown to be higher than that obtained using the conventional methods. With less dependence on prior information, our transdimensional simultaneous inversion method can be used to obtain an effective velocity structure for facilitating highly accurate hydraulic fracturing mapping.

Updating Variational Bayes: fast sequential posterior inference

Variational Bayesian (VB) methods produce posterior inference in a time frame considerably smaller than traditional Markov Chain Monte Carlo approaches. Although the VB posterior is an approximation, it has been shown to produce good parameter estimates and predicted values when a rich classes of approximating distributions are considered. In this paper, we propose the use of recursive algorithms to update a sequence of VB posterior approximations in an online, time series setting, with the computation of each posterior update requiring only the data observed since the previous update. We show how importance sampling can be incorporated into online variational inference allowing the user to trade accuracy for a substantial increase in computational speed. The proposed methods and their properties are detailed in two separate simulation studies. Additionally, two empirical illustrations are provided, including one where a Dirichlet Process Mixture model with a novel posterior dependence structure is repeatedly updated in the context of predicting the future behaviour of vehicles on a stretch of the US Highway 101.

Probabilistic modelling of effects of antibiotics and calendar time on transmission of healthcare-associated infection

Healthcare-associated infection and antimicrobial resistance are major concerns. However, the extent to which antibiotic exposure affects transmission and detection of infections such as MRSA is unclear. Additionally, temporal trends are typically reported in terms of changes in incidence, rather than analysing underling transmission processes. We present a data-augmented Markov chain Monte Carlo approach for inferring changing transmission parameters over time, screening test sensitivity, and the effect of antibiotics on detection and transmission. We expand a basic model to allow use of typing information when inferring sources of infections. Using simulated data, we show that the algorithms are accurate, well-calibrated and able to identify antibiotic effects in sufficiently large datasets. We apply the models to study MRSA transmission in an intensive care unit in Oxford, UK with 7924 admissions over 10 years. We find that falls in MRSA incidence over time were associated with decreases in both the number of patients admitted to the ICU colonised with MRSA and in transmission rates. In our inference model, the data were not informative about the effect of antibiotics on risk of transmission or acquisition of MRSA, a consequence of the limited number of possible transmission events in the data. Our approach has potential to be applied to a range of healthcare-associated infections and settings and could be applied to study the impact of other potential risk factors for transmission. Evidence generated could be used to direct infection control interventions.

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

The non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. The estimation of the model is difficult, since the unobservable surplus demand is a time-varying stochastic variable in the return equation, and the market liquidity arises both in the mean term and in the variance term of the return equation in the MM model. A fast and efficient Markov Chain Monte Carlo (MCMC) approach based on an efficient simulation smoother algorithm and an acceptance-rejection Metropolis–Hastings algorithm is designed to estimate the non-linear MM model. Since the simulation smoother algorithm makes use of the band diagonal structure and positive definition of Hessian matrix of the logarithmic density, it can quickly draw the market liquidity. In addition, we discuss the MM model with Student-t heavy tail distribution that can be utilized to address the presence of outliers in typical financial time series. Using the presented modeling method to make analysis of daily income of the S&P 500 index through the point forecast and the density forecast, we find clear support for time-varying volatility, volatility feedback effect, market microstructure theory, and Student-t heavy tails in the financial time series. Through this method, one can use the estimated market liquidity and surplus demand which is much smoother than the strong stochastic return process to assist the transaction decision making in the financial market.

Multi-Year Survey and Bayesian Modeling Approach for Characterizing Arsenic Pollution in Marine Clams Cultivated Along the Tidal Flats of Mid-Eastern China

Marine clam is one of the main sources of arsenic (As), and the tidal flats of Jiangsu Province are considered major culturing areas for clams in mid-eastern China. In view of increasingly severe pollution in this region, concerns have been raised by the consumers with the safety of clams they purchased or may purchase. To address these concerns, we conducted a multi-year survey to determine the levels of As and As species in five major clam species cultivated in eight production areas of this region. Based on the above analysis data, Bayesian statistics used a Markov Chain Monte Carlo approach was applied to predict the toxic As residue distributions in clams produced in this region and their health risks to Chinese adults. It was found that the bioaccumulation ability of total As (tAs) and inorganic As (iAs) was species-specific, while Mactra veneriformis (MV) had the strongest accumulation capacity for toxic iAs (0.22–2.85 mg/kg dw). Up to 6.7% of the tested MV samples exceeding the iAs limit of China Food and Drug Administration. The content of iAs was also found to be related significantly to the harvest seasons, with clam in the spawning period (June) having the lowest iAs concentrations. The non-carcinogenic and carcinogenic health risk from dietary exposure to iAs associated with MV consumption was rather high, which suggested that specific attention should be paid to the safety of clam consumption in this region.

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

ABSTRACTElectrical resistivity tomography is a non‐linear and ill‐posed geophysical inverse problem that is usually solved through gradient‐descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two‐dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high‐dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non‐linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high‐frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un‐reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient‐based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.

Rare and widespread: integrating Bayesian MCMC approaches, Sanger sequencing and Hyb-Seq phylogenomics to reconstruct the origin of the enigmatic Rand Flora genus Camptoloma.

Genera that are widespread, with geographically discontinuous distributions and represented by few species, are intriguing. Is their achieved disjunct distribution recent or ancient in origin? Why are they species-poor? The Rand Flora is a continental-scale pattern in which closely related species appear codistributed in isolated regions over the continental margins of Africa. Genus Camptoloma (Scrophulariaceae) is the most notable example, comprising three species isolated from each other on the northwest, eastern, and southwest Africa. We employed Sanger sequencing of nuclear and plastid markers, together with genomic target sequencing of 2190 low-copy nuclear genes, to infer interspecies relationships and the position of Camptoloma within Scrophulariaceae by using supermatrix and multispecies-coalescent approaches. Lineage divergence times and ancestral ranges were inferred with Bayesian Markov chain Monte Carlo (MCMC) approaches. The population history was estimated with phylogeographic coalescent methods. Camptoloma rotundifolium, restricted to Southern Africa, was shown to be a sister species to the disjunct clade formed by C. canariense, endemic to the Canary Islands, and C. lyperiiflorum, distributed in the Horn of Africa-Southern Arabia. Camptoloma was inferred to be sister to the mostly South African tribes Teedieae and Buddlejeae. Stem divergence was dated in the Late Miocene, while the origin of the extant disjunction was inferred as Early Pliocene. The current disjunct distribution of Camptoloma across Africa was likely the result of fragmentation and extinction and/or population bottlenecking events associated with historical aridification cycles during the Neogene; the pattern of species divergence, from south to north, is consistent with the "climatic refugia" Rand Flora hypothesis.

Upper mantle radial anisotropy under the Indian Ocean from higher mode surface waves and a hierarchical transdismensional approach

SUMMARYWe investigated the likelihood of radial anisotropy in the shallow and deep upper mantle, including the mantle transition zone (MTZ) under the Indian Ocean. Seismic anisotropy can be an indicator of mantle deformation through lattice preferred orientation of anisotropic crystals in the mantle. It has thus the potential to illuminate Earth’s dynamic interior, but previous seismic tomography studies have not achieved consensus on the existence of radial anisotropy below ∼250 km depth. We developed a fully nonlinear transdimensional hierarchical Bayesian Markov Chain Monte Carlo approach to invert fundamental and higher mode surface wave dispersion data and applied it to a subset of a global Love and Rayleigh wave data set. We obtained posterior model parameter distributions for shear wave velocity (VS) and radial anisotropy ξ under the Indian Ocean. These posterior model distributions were used to calculate the probability of having radial anisotropy at different depths. We demonstrated that separate inversions of Love and Rayleigh waves yield models compatible with the results of joint inversions within uncertainties. The obtained pattern of VS anomalies agrees with most previous studies. They display negative anomalies along ridges in the uppermost mantle, but those are stronger than for regularized inversions. The Central Indian Ridge and the Southeastern Indian Ridge present velocity anomalies that extend to ∼200 km depth, whereas the Southwestern Indian Ridge seems to have a shallower origin. Weaker, laterally variable velocity perturbations were found at larger depths. The anisotropy models differ more strongly from regularized inversion results and their uncertainties were rather large. We found that anisotropy models from regularized inversions also depend on the chosen parametrization, which is consistent with the existence of a large model null-space. Apart from a fast horizontally polarized shear wave signal in the top 100 km, likely reflecting the horizontal plate motion due to asthenospheric deformation, no clear relation to surface geology was detected in the anisotropy models. We found that, although the anisotropy model uncertainties are rather large, and lateral variations are present, the data generally prefer at least 1 per cent anisotropy in the MTZ with fast vertically polarized shear waves, within errors. Incorporating group velocity data did not help better constrain deep structure by reducing parameter trade-offs. We also tested the effect of prior constraints on the 410- and 660-km topography and found that the undulations of these discontinuities had little effect on the resulting models in our study region.

Sequential Dynamic Leadership Inference Using Bayesian Monte Carlo Methods

Hierarchy and leadership interactions commonly occur in animal groups, crowds of people, and in vehicle motions. Such interactions are often affected by one or more individuals who possess key domain information (e.g., final destination, environmental constraints, and best routes) or pertinent traits (e.g., better navigation, sensing, and decision making capabilities) compared with the rest of the group. This article presents a framework for the automatic identification of group structure and leadership from noisy sensory observations of tracked groups. Accordingly, a new leader-follower model is developed, which assumes the dynamics of the group to be a multivariate Ornstein-Uhlenbeck process with the designated leader(s) drifting to the destination and followers reverting to the leaders' state. Sequential Monte Carlo approaches, and specifically the sequential Markov chain Monte Carlo approach, are adopted to infer, probabilistically, the evolving leadership structure. A Rao-Blackwellisation scheme is employed such that the kinematic state of the objects in the group is inferred in closed form by Kalman filtering. Experiments show that the proposed techniques can successfully determine the leadership structures in challenging scenarios with a corresponding enhancement in tracking accuracy through direct consideration of the leadership interactions of the group.

Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

AbstractIn geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical inversion are used to condition them on measurement data. Among these techniques, Markov chain Monte Carlo (MCMC) techniques stand out, because they yield asymptotically unbiased conditional realizations. However, standard Markov Chain Monte Carlo (MCMC) methods suffer the curse of dimensionality when refining the discretization. This means that their efficiency decreases rapidly with an increasing number of discretization cells. Several MCMC approaches have been developed such that the MCMC efficiency does not depend on the discretization of the random field. The preconditioned Crank Nicolson Markov Chain Monte Carlo (pCN‐MCMC) and the sequential Gibbs (or block‐Gibbs) sampling are two examples. This paper presents a combination of both approaches with the goal to further reduce the computational costs. Our algorithm, the sequential pCN‐MCMC, will depend on two tuning‐parameters: the correlation parameter of the pCN approach and the block size of the sequential Gibbs approach. The original pCN‐MCMC and the Gibbs sampling algorithm are special cases of our method. We present an algorithm that automatically finds the best tuning‐parameter combination ( and ) during the burn‐in‐phase of the algorithm, thus choosing the best possible hybrid between the two methods. In our test cases, we achieve a speedup factors of 1–5.5 over pCN and of 1–6.5 over Gibbs. Furthermore, we provide the MATLAB implementation of our method as open‐source code.

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system's radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. The DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

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.

Bayesian Estimation of Partially Linear Additive Spatial Autoregressive Models with P-Splines

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.