Markov Chain Monte Carlo Procedure Research Articles

Spatio-temporal dynamic model and parallelized ensemble Kalman filter for precipitation data

This paper presents a spatiotemporal dynamic model which allows Bayesian inference of precipitation states in some Venezuelan meteorological stations. One of the limitations that are reported in digital databases is the reliability of the records and the lack of information for certain days, weeks, or months. To complete the missing data, the Gibbs algorithm, a Markov Chain Monte Carlo (MCMC) procedure, was used. A feature of precipitation series is that their distribution contains discrete and continuous components implying complicated dynamics. A model is proposed based on a discrete representation of a stochastic integro-difference equation. Given the difficulty of obtaining explicit analytical expressions for the predictive posterior distribution, approximations were obtained using a sequential Monte Carlo algorithm called the parallelized ensemble Kalman filter. The proposed method permits the completion of the missing data in the series where required and secondly allows the splitting of a large database into smaller ones for separate evaluation and eventual combination of the individual results. The objective is to reduce the dimension and computational cost in order to obtain models that are able to describe the reality in real time. It was shown that the obtained models are able to predict spatially and temporally the states of rainfall for at least three to four days quickly, efficiently and accurately. Three methods of statistical validation were used to evaluate the performance of the model and showed no significant discrepancies. Speedup and efficiency factors were calculated to compare the speed of calculation using the parallelized ensemble Kalman filter algorithm with the speed of the sequential version. The improvement in speed for four pthread executions was greatest.

Markov Chain Monte Carlo-Based Separation of Paired Carrier Multiple Access Signals

Paired carrier multiple access (PCMA) signal is one of the most common single-channel mixtures. It is still a great challenge to recover the component signals from non-cooperative received PCMA signals due to the high complexity of existing single-channel blind source separation algorithms. Hence, a Markov chain Monte Carlo (MCMC) procedure, called the QR Decomposition with M algorithm-based Gibbs sampler, is employed to realize the separation of PCMA signals. The method is robust against modulation parameter estimation error, since a data-aided adaptive filter that can update the channel response is embedded into the QRD-M-based Gibbs sampler. Simulation results show that the MCMC estimator efficiently achieves approximately joint likelihood sequence estimation.

Inference of reaction rate parameters based on summary statistics from experiments

We present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate parameters of the rate coefficient of the H2/O2-mechanism chain branching reaction H+O2→OH+O. Available published data is summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Padé and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss–Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all result in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen–air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

Bayesian estimation for a mixture of simplex distributions with an unknown number of components: HDI analysis in Brazil

ABSTRACTVariables taking value in , such as rates or proportions, are frequently analyzed by researchers, for instance, political and social data, as well as the Human Development Index (HDI). However, sometimes this type of data cannot be modeled adequately using a unique distribution. In this case, we can use a mixture of distributions, which is a powerful and flexible probabilistic tool. This manuscript deals with a mixture of simplex distributions to model proportional data. A fully Bayesian approach is proposed for inference which includes a reversible-jump Markov Chain Monte Carlo procedure. The usefulness of the proposed approach is confirmed by using of the simulated mixture data from several different scenarios and by using the methodology to analyze municipal HDI data of cities (or towns) in the Northeast region and São Paulo state in Brazil. The analysis shows that among the cities in the Northeast, some appear to have a similar HDI to other cities in São Paulo state.

A Dominance Variant Under the Multi-Unidimensional Pairwise-Preference Framework: Model Formulation and Markov Chain Monte Carlo Estimation.

Forced-choice questionnaires have been proposed as a way to control some response biases associated with traditional questionnaire formats (e.g., Likert-type scales). Whereas classical scoring methods have issues of ipsativity, item response theory (IRT) methods have been claimed to accurately account for the latent trait structure of these instruments. In this article, the authors propose the multi-unidimensional pairwise preference two-parameter logistic (MUPP-2PL) model, a variant within Stark, Chernyshenko, and Drasgow's MUPP framework for items that are assumed to fit a dominance model. They also introduce a Markov Chain Monte Carlo (MCMC) procedure for estimating the model's parameters. The authors present the results of a simulation study, which shows appropriate goodness of recovery in all studied conditions. A comparison of the newly proposed model with a Brown and Maydeu's Thurstonian IRT model led us to the conclusion that both models are theoretically very similar and that the Bayesian estimation procedure of the MUPP-2PL may provide a slightly better recovery of the latent space correlations and a more reliable assessment of the latent trait estimation errors. An application of the model to a real data set shows convergence between the two estimation procedures. However, there is also evidence that the MCMC may be advantageous regarding the item parameters and the latent trait correlations.

Prior specification of neighbourhood and interaction structure in binary Markov random fields

We formulate a prior distribution for the energy function of stationary binary Markov random fields (MRFs) defined on a rectangular lattice. In the prior we assign distributions to all parts of the energy function. In particular we define priors for the neighbourhood structure of the MRF, what interactions to include in the model, and for potential values. We define a reversible jump Markov chain Monte Carlo (RJMCMC) procedure to simulate from the corresponding posterior distribution when conditioned to an observed scene. Thereby we are able to learn both the neighbourhood structure and the parametric form of the MRF from the observed scene. We circumvent evaluations of the intractable normalising constant of the MRF when running the RJMCMC algorithm by adopting a previously defined approximate auxiliary variable algorithm. We demonstrate the usefulness of our prior in two simulation examples and one real data example.

Multivariate Wishart Stochastic Volatility and Changes in Regime

This paper generalizes the basic Wishart multivariate stochastic volatility model of Philipov and Glickman (2006) and Asai and McAleer (2009) to encompass regime switching behavior. The latent state variable is driven by a first-order Markov process. The model allows for state-dependent (co)variance and correlation levels and state-dependent volatility spillover effects. Parameter estimates are obtained using Bayesian Markov Chain Monte Carlo procedures and filtered estimates of the latent variances and covariances are generated by particle filter techniques. The model is applied to five European stock index return series. The results show that the proposed regime-switching specification substantially improves the in-sample fit and the VaR forecasting performance relative to the basic model.

Multivariate Wishart stochastic volatility and changes in regime

This paper generalizes the basic Wishart multivariate stochastic volatility model of Philipov and Glickman (J Bus Econ Stat 24:313–328, 2006) and Asai and McAleer (J Econom 150:182–192, 2009) to encompass regime-switching behavior. The latent state variable is driven by a first-order Markov process. The model allows for state-dependent (co)variance and correlation levels and state-dependent volatility spillover effects. Parameter estimates are obtained using Bayesian Markov Chain Monte Carlo procedures and filtered estimates of the latent variances and covariances are generated by particle filter techniques. The model is applied to five European stock index return series. The results show that the proposed regime-switching specification substantially improves the fit to persistent covariance dynamics relative to the basic model.

QTL mapping and breeding value estimation through pedigree-based analysis of fruit size and weight in four diverse peach breeding programs

The narrow genetic base of peach (Prunus persica L. Batsch) challenges efforts to accurately dissect the genetic architecture of complex traits. Standardized phenotypic assessment of pedigree-linked breeding germplasm and new molecular strategies and analytical approaches developed and conducted during the RosBREED project for enabling marker-assisted breeding (MAB) in Rosaceae crops has overcome several aspects of this challenge. The genetic underpinnings of fruit size (fruit equatorial diameter (FD)) and weight (fresh weight (FW)), two most important components of yield, were investigated using the pedigree-based analysis (PBA) approach under a Bayesian framework which has emerged as an alternative strategy to study the genetics of quantitative traits within diverse breeding germplasm across breeding programs. In this study, a complex pedigree with the common founder “Orange Cling” was identified and FD and FW data from 2011 and 2012 analyzed. A genetic model including genetic additive and dominance effects was considered, and its robustness was evaluated by using various prior and initial values in the Markov chain Monte Carlo procedure. Five QTLs were identified which accounted for up to 29 and 17 % of the phenotypic variation for FD and FW, respectively. Additionally, genomic breeding values were obtained for both traits, with accuracies >85 %. This approach serves as a model study for performing PBA across diverse pedigrees. By incorporating multiple breeding programs, the method and results presented support and highlight the ability of this strategy to identify genomic resources as targets for DNA marker development and subsequent MAB within each program.

MagAO IMAGING OF LONG-PERIOD OBJECTS (MILO). I. A BENCHMARK M DWARF COMPANION EXCITING A MASSIVE PLANET AROUND THE SUN-LIKE STAR HD 7449*

ABSTRACT We present high-contrast Magellan adaptive optics images of HD 7449, a Sun-like star with one planet and a long-term radial velocity (RV) trend. We unambiguously detect the source of the long-term trend from 0.6–2.15 μm at a separation of ∼0.″54. We use the object’s colors and spectral energy distribution to show that it is most likely an M4–M5 dwarf (mass ∼0.1–0.2 M ⊙ ?> ) at the same distance as the primary and is therefore likely bound. We also present new RVs measured with the Magellan/MIKE and Planet Finder Spectrograph spectrometers and compile these with archival data from CORALIE and HARPS. We use a new Markov chain Monte Carlo procedure to constrain both the mass ( > 0.17 ?> M ⊙ ?> at 99% confidence) and semimajor axis (∼18 AU) of the M dwarf companion (HD 7449B). We also refine the parameters of the known massive planet (HD 7449Ab), finding that its minimum mass is 1.09 − 0.19 + 0.52 ?> M J , its semimajor axis is 2.33 − 0.02 + 0.01 ?> AU, and its eccentricity is 0.8 − 0.06 + 0.08 ?> . We use N-body simulations to constrain the eccentricity of HD 7449B to ≲0.5. The M dwarf may be inducing Kozai oscillations on the planet, explaining its high eccentricity. If this is the case and its orbit was initially circular, the mass of the planet would need to be ≲1.5 M J . This demonstrates that strong constraints on known planets can be made using direct observations of otherwise undetectable long-period companions.

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.

Binary contingency table method for analysing gene mutation in cancer genome

Somatic mutations are considered to initiate several disorders such as cancer and neurological disease. Hence, a number of computational methods have been developed to find loci subject to frequent mutations in cancer cells. Since normal cells turn into cancer cells through the accumulation of gene mutations, the elucidation of interactive relationships among loci has great potential to reveal the cause of cancer progression; however, only a few methods have been proposed for measuring statistical significance of pairs of loci that are co-mutated or exclusively mutated. In this study, we proposed a novel statistical method to find such significantly interactive pairs of loci by employing the framework of binary contingency tables. Using Markov chain Monte Carlo procedure, the statistical significance is evaluated by sampling null matrices whose marginal sums are equal to those of the input matrix. We applied the proposed method to mutation data of colon cancer patients and successfully obtained significant pairs of loci.

Incorporating stochasticity in the study of exploited fish population dynamics: Implications for the study of post-recruitment harvest strategies

Previous work has shown that an effective method of maintaining spawning stock biomass (SSB), the biomass of fish that are reproductively mature, within an exploited stock is to regulate harvest so that maximum fishing mortality rates occur after peak spawning during the year. This is known as post-recruitment harvest. The goal of this work is to examine if the advantages of post-recruitment harvest hold when reported stochasticity in the age and time distribution of harvest rates, known as selectivity, is considered. A hybrid dynamical systems model, one in which both continuous-time and discrete-time processes operate simultaneously, was derived, and recursive solutions were found. Results from other studies indicating the benefit of post-recruitment harvest were verified using this hybrid model when selectivity was considered fixed. Simulations were repeated including variance in selectivity using a Markov Chain Monte Carlo (MCMC) procedure. Results show that the benefits of post-recruitment harvest to the preservation of SSB were considerably less advantageous when each age class was assumed to be subject to annual stochastic selectivity. Furthermore, the stochastic scenarios gave estimates of SSB that were lower than their fixed selectivity analogs, indicating that the benefits of theoretical post-recruitment harvest may be diminished to some extent when stochasticity plays a large role in the dynamics.

A Bayesian peaks-over-threshold analysis of floods in the Itajaí-açu River under stationarity and nonstationarity

In this paper we revisit the case study of Silva et al. (Stoch Env Res Risk A. doi:10.1007/s00477-015-1072-y, 2015), the Itajai-acu River at Apiuna (Southern Brazil), with an augmented data set and Bayesian inferential techniques. Nonstationary Poisson-GP models are used to study the joint influence of El Nino-Southern Oscillation (ENSO) and of upstream flood control structures on the flood regime at the study site. The Nino3.4 DJF index and a dimensionless reservoir index are used as covariates. Prior belief about the GP shape parameter is elicited by fitting the GEV distribution to AMS samples from 138 sites in Southern Brazil with 40 or more years of data and deriving the distribution from the estimates of that parameter. Following a data-driven exploratory analysis, a Markov chain Monte Carlo (MCMC) procedure is used to sample from the posterior distribution of parameters. Model evaluation and selection used Bayes factors and two information criteria. Results show evidence that, while upstream dams play a significant, though small, role in reducing flood hazard, the influence of the climate covariate is stronger, and an increase in ENSO amplitude in the last decades has led to the occurrence of higher annual maximum floods. MCMC samples are used to derive the Bayesian predictive distribution of annual flood quantiles and design life levels. Uncertainty analyses based on the posterior distribution of parameters and quantiles are presented.

Mapping Generative Models onto a Network of Digital Spiking Neurons.

Stochastic neural networks such as Restricted Boltzmann Machines (RBMs) have been successfully used in applications ranging from speech recognition to image classification, and are particularly interesting because of their potential for generative tasks. Inference and learning in these algorithms use a Markov Chain Monte Carlo procedure called Gibbs sampling, where a logistic function forms the kernel of this sampler. On the other side of the spectrum, neuromorphic systems have shown great promise for low-power and parallelized cognitive computing, but lack well-suited applications and automation procedures. In this work, we propose a systematic method for bridging the RBM algorithm and digital neuromorphic systems, with a generative pattern completion task as proof of concept. For this, we first propose a method of producing the Gibbs sampler using bio-inspired digital noisy integrate-and-fire neurons. Next, we describe the process of mapping generative RBMs trained offline onto the IBM TrueNorth neurosynaptic processor-a low-power digital neuromorphic VLSI substrate. Mapping these algorithms onto neuromorphic hardware presents unique challenges in network connectivity and weight and bias quantization, which, in turn, require architectural and design strategies for the physical realization. Generative performance is analyzed to validate the neuromorphic requirements and to best select the neuron parameters for the model. Lastly, we describe a design automation procedure which achieves optimal resource usage, accounting for the novel hardware adaptations. This work represents the first implementation of generative RBM inference on a neuromorphic VLSI substrate.

σCDM coupled to radiation: Dark energy and Universe acceleration

Recently, the Chiral Cosmological Model (CCM) coupled to cold dark matter (CDM) has been investigated as [Formula: see text]CDM model to study the observed accelerated expansion of the Universe. Dark sector fields (as Dark Energy content) coupled to cosmic dust were considered as the source of Einstein gravity in Friedmann–Robertson–Walker (FRW) cosmology. Such model had a beginning at the matter-dominated era. The purposes of our present investigation are two-fold: To extend “life” of the [Formula: see text]CDM for earlier times to radiation-dominated era and to take into account variation of the exponential potential [Formula: see text] via variation of the interaction parameter [Formula: see text]. We use Markov Chain Monte Carlo (MCMC) procedure to investigate possible values of initial conditions constrained by the measured amount of the dark matter, dark energy and radiation component today. Our analysis includes dark energy contribution to critical density, the ratio of the kinetic and potential energies, deceleration parameter, effective equation of state (EoS) and evolution of DE EoS with variation of coupling constant [Formula: see text]. A comparison with the [Formula: see text]CDM model was performed. A new feature of the model is the existence of some values of potential coupling constant, leading to a [Formula: see text]CDM solution without transition into accelerated expansion epoch.

A novel hybrid learning algorithm for full Bayesian approach of artificial neural networks

The Bayesian neural networks are useful tools to estimate the functional structure in the nonlinear systems. However, they suffer from some complicated problems such as controlling the model complexity, the training time, the efficient parameter estimation, the random walk, and the stuck in the local optima in the high-dimensional parameter cases. In this paper, to alleviate these mentioned problems, a novel hybrid Bayesian learning procedure is proposed. This approach is based on the full Bayesian learning, and integrates Markov chain Monte Carlo procedures with genetic algorithms and the fuzzy membership functions. In the application sections, to examine the performance of proposed approach, nonlinear time series and regression analysis are handled separately, and it is compared with the traditional training techniques in terms of their estimation and prediction abilities.

Practical and conceptual path sampling issues

In the past 15 years transition path sampling (TPS) has evolved from its basic algorithm to an entire collection of methods and a framework for investigating rare events in complex systems. The methodology is applicable to a wide variety of systems and processes, ranging from transitions in small clusters or molecules to chemical reactions, phase transitions, and conformational changes in biomolecules. The basic idea of TPS is to harvest dynamical unbiased trajectories that connect a reactant with a product, by a Markov Chain Monte Carlo procedure called shooting. This simple importance sampling yields the rate constants, the free energy surface, insight in the mechanism of the rare event of interest, and by using the concept of the committor, also access to the reaction coordinate. In the last decade extensions to TPS have been developed, notably the transition interface sampling (TIS) methods, and its generalization multiple state TIS. Combination with advanced sampling methods such as replica exchange and the Wang-Landau algorithm, among others, improves sampling efficiency. Notwithstanding the success of TPS, there are issues left to discuss, and, despite the method's apparent simplicity, many pitfalls to avoid. This paper discusses several of these issues and pitfalls: the choice of stable states and interface order parameters, the problem of positioning the TPS windows and TIS interfaces, the matter of convergence of the path ensemble, the matter of kinetic traps, and the question whether TPS is able to investigate and sample Markov state models. We also review the reweighting technique used to join path ensembles. Finally we discuss the use of the sampled path ensemble to obtain reaction coordinates.

Bayesian clustering of shapes of curves

Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an efficient Bayesian method to cluster curve data using an elastic shape metric that is based on joint registration and comparison of shapes of curves. The elastic-inner product matrix obtained from the data is modeled using a Wishart distribution whose parameters are assigned carefully chosen prior distributions to allow for automatic inference on the number of clusters. Posterior is sampled through an efficient Markov chain Monte Carlo procedure based on the Chinese restaurant process to infer (1) the posterior distribution on the number of clusters, and (2) clustering configuration of shapes. This method is demonstrated on a variety of synthetic data and real data examples on protein structure analysis, cell shape analysis in microscopy images, and clustering of shapes from MPEG7 database.

A regime-switching Nelson–Siegel term structure model of the macroeconomy

This paper presents a regime-switching Nelson–Siegel term structure model with macro factors and introduces a Markov chain Monte Carlo procedure to estimate the model. We find that regime shifts are important for understanding the interaction between the yield curve and economic activity. We also find that two regimes are closely related to the business cycle and monetary policy. Finally, we find that the proposed regime-switching model with macro factors is competitive in the out-of-sample forecasting of bond yields.