Gibbs Sampling Approach Research Articles

Geoacoustic inversion of M-sequence data from experiments in the South Florida Straits

Matched field inversion is applied to low frequency data from experiments in the South Florida Straits to estimate a sediment velocity profile. The acoustic data consist of signal envelopes derived from M-sequences that were transmitted to a vertical hydrophone array over a range of 10 km. The sound speed profile supported a strong waveguide in the deeper parts of the water column. Signal propagation for a source in the waveguide was dominated by waveguide refracted paths, and surface-reflected bottom-reflected paths that interacted eight to ten times with the bottom. The very long range, shallow water geometry presents a significant challenge for an inversion based on matched field processing. However, examination of the spatial coherence of the received signal indicated useful spatial phase information for spectral components with high signal-to-noise ratios. A Gibbs sampling approach was used to test two different geoacoustic models for the site: (a) a constant gradient sediment and (b) a constant velocity sediment over a half space. The inversion showed a preference for slower speeds of around 1550 m/s at the sea floor, increasing to higher values up to 1700 m/s within about 100 m deeper. These values are consistent with ground truth at the site.

Bayesian inference of inbreeding depression in controlled crosses.

This study shows how a Gibbs sampling approach can be used for Bayesian inference of inbreeding depression. The method presented is mainly concerned with organisms that can be both selfed and outcrossed. Tests performed on simulated data with unequal variances and missing observations show that the method works well. Real data from the plant Scabiosa canescens is also analyzed.

Autoregressive models for capture-recapture data: a Bayesian approach.

In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet.

Bayesian Analysis of the Seasonal Moving Average Model: A Gibbs Sampling Approach

Bayesian Analysis of the Seasonal Moving Average Model: A Gibbs Sampling Approach

Comparisons of Estimation Procedures for Nonlinear Multilevel Models

We introduce General Multilevel Models and discuss the estimation procedures that may be used to fit multilevel models. We apply the proposed procedures to three-level binary data generated in a simulation study. We compare the procedures by two criteria, Bias and efficiency. We find that the estimates of the fixed effects and variance components are substantially and significantly biased using Longford's Approximation and Goldstein's Generalized Least Squares approaches by two software packages VARCL and ML3. These estimates are not significantly biased and are very close to real values when we use Markov Chain Monte Carlo (MCMC) using Gibbs sampling or Nonparametric Maximum Likelihood (NPML) approach. The Gaussian Quadrature (GQ) approach, even with small number of mass points results in consistent estimates but computationally problematic. We conclude that the MCMC and the NPML approaches are the recommended procedures to fit multilevel models.

Effects of incoherent and coherent source spectral information in geoacoustic inversion.

This paper examines the effect on matched-field geoacoustic inversion of including source spectral information, as can be available in controlled-source acoustic surveys. Source information can consist of relative or absolute knowledge of the source amplitude and/or phase spectra, and can allow frequency-coherent processing of spatial acoustic-field data. A number of multi-frequency acoustic processors, appropriate for specific types of source information, are defined based on the likelihood function for complex acoustic-field data with Gaussian noise. The information content of the various processors is quantified in terms of marginal probability distributions and highest-probability density intervals for the unknown geoacoustic and geometric parameters, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. The analysis is illustrated for incoherent and coherent processors corresponding to several types of source knowledge ranging from complete information to no information, and the results are considered as a function of the spatial and frequency sampling of the acoustic fields.

Benchmarking Range-Dependent Propagation Modeling in Matched-Field Inversion

This paper considers how the accuracy of range-dependent propagation modeling affects the results of matched-field inversion (MFI) for seabed geoacoustic parameters. In MFI, the forward problem of computing the acoustic fields associated with candidate geoacoustic models is solved a large number of times. Given significant mismatch due to measurement and theory errors, together with the computationally intensive nature of MFI, the appropriate tradeoff between modeling accuracy and computational speed is not obvious. This tradeoff is considered here in terms of the degradation in information content for the geoacoustic parameters that results from inaccurate propagation modeling. The information content is quantified using the marginal posterior probability distributions of the geoacoustic parameters, as computed from a fast Gibbs sampling approach to Bayesian inversion. A synthetic example of this analysis is presented in which the parabolic equation is used to model acoustic fields for a shallow-water, upslope environment, with different levels of modeling accuracy/speed controlled by the range and depth step sizes of the computational grid.

BENCHMARKING RANGE-DEPENDENT PROPAGATION MODELING IN MATCHED-FIELD INVERSION

This paper considers how the accuracy of range-dependent propagation modeling affects the results of matched-field inversion (MFI) for seabed geoacoustic parameters. In MFI, the forward problem of computing the acoustic fields associated with candidate geoacoustic models is solved a large number of times. Given significant mismatch due to measurement and theory errors, together with the computationally intensive nature of MFI, the appropriate tradeoff between modeling accuracy and computational speed is not obvious. This tradeoff is considered here in terms of the degradation in information content for the geoacoustic parameters that results from inaccurate propagation modeling. The information content is quantified using the marginal posterior probability distributions of the geoacoustic parameters, as computed from a fast Gibbs sampling approach to Bayesian inversion. A synthetic example of this analysis is presented in which the parabolic equation is used to model acoustic fields for a shallow-water, upslope environment, with different levels of modeling accuracy/speed controlled by the range and depth step sizes of the computational grid.

Quantifying data information content in geoacoustic inversion

This paper examines the information content in matched-field geoacoustic inverse problems as a function of a variety of experiment factors, with the aim of guiding data collection and processing to achieve the best possible inversion results. The information content of the unknown geoacoustic parameters is quantified in terms of their marginal posterior probability distributions, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. When sampled to convergence, the marginal distributions are found to have simple, smooth shapes that facilitate straightforward comparisons. The approach is general; the specific examples considered here include factors such as the number of sensors in the receiving array, array length, source-receiver range, source frequency, number of frequencies, source bandwidth, and signal-to-noise ratio.

Bayesian Segregation Analysis of Somatic Cell Scores of Ontario Holstein Cattle

Bayesian segregation analysis using a Gibbs sampling approach was applied to four sets of simulated data and one set of field data to detect evidence of major genes affecting the evaluated trait. The substitution effect of a major gene and its allelic frequency were estimated for each set of data. For two datasets simulated with a model with no major gene effect, the resulting estimates of polygenic variance and heritability agreed with the simulated values and tests for the presence of a major gene were not significant. Analyses of two sets of data simulated with a major gene produced posterior distributions that gave significant evidence of major gene effects but underestimated the substitution values of the major gene. The segregation analysis of field data suggested that a major gene significantly affected somatic cell score (SCS) in the population of Ontario Holstein cattle. The estimated heritability of SCS was approximately 0.16. The major gene variance accounted for about 17% of the total genetic variance and the point estimate of the frequency of the allele having a positive effect on SCS was 0.30. However, the precision of these estimates is questionable based on the simulation results. The effect of the major gene may be underestimated.

Monte Carlo Deconvolution of Digital Signals Guided by the Inverse Filter

Digital deconvolution concerns the restoration of an underlying discrete signal from a blurred noisy observation sequence. The problem can be formulated in a Bayesian framework. As is usual in the Bayesian context, the computation of relevant posterior quantities is the major challenge. Previous work made substantial progress toward making this computation feasible, most notably through the Gibbs sampling approach of Chen and Li and the sequential importance sampling approach of Liu and Chen. Yet, there is room for improvement, because both global Monte Carlo strategies can be very slow to reach the target distribution. We propose two new sampling strategies for efficient restoration of digital signals. The key idea is to use inverse filtering to transform the posterior integration into a problem that is substantially more local than the direct formulation, leading to stable Monte Carlo procedures that are very fast to converge. In the final section, we consider extensions to the case of blind deconvolution, where the filter coefficients are unknown and must be estimated as the signal is being restored.

A hierarchical Bayesian model for estimating historical salmon escapement and escapement timing

In this paper, we present an improved methodology for estimating salmon escapements from stream count data. The new method uses a hierarchical Bayesian model that improves estimates in years when data are sparse by "borrowing strength" from counts in other years. We present a model of escapement and of count data, a hierarchical Bayesian statistical framework, a Gibbs sampling approach for evaluation of the posterior distributions of the quantities of interest, and criteria for determining when the model and inference are adequate. We then apply the hierarchical Bayesian model to estimating historical escapement and escapement timing for pink salmon (Oncorhynchus gorbuscha) returns to Kadashan Creek in Southeast Alaska.

Gibbs sampling-based segregation analysis of asthma-associated quantitative traits in a population-based sample of nuclear families.

Asthma is a common, complex human disease. Elevated serum immunoglobulin E (IgE) levels, elevated blood eosinophil counts, and increased airway responsiveness are physiological traits that are characteristic of asthma. Few studies have investigated major gene effects for these traits in a population-based sample. Further, it is not known if any putative major genes may be common to two or more of these traits. We investigated the existence and nature of major genes modulating asthma-associated quantitative traits in an Australian population-based sample of 210 Caucasian nuclear families. The sharing of these major genes was also investigated. Segregation analysis was based upon a Markov Chain Monte Carlo (Gibbs sampling) approach as implemented in the program BUGS v0.6. All models included adjustment for age, height, tobacco smoke exposure, and gender. The segregation of total IgE levels, blood eosinophil counts, and dose-response slope (DRS) of methacholine challenge were all consistent with major loci at which a recessive allele acted to increase or decrease the phenotype. The respective estimated frequencies of the recessive alleles were 68% (total IgE), 10% (blood eosinophil count), and 27% (DRS). Extensive modelling suggested that the major loci controlling total serum IgE levels, blood eosinophil counts, and airway responsiveness represent different genes. These data provide evidence, for the first time, of the existence of at least 3 distinct genetic pathways involving major gene effects on physiological traits closely associated with asthma. These results have implications for gene discovery programs.

State-Space Models with Regime-Switching: Classical and Gibbs Sampling Approaches with Applications

Both state-space models and Markov switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. One approach, in the classical framework, approximates the likelihood function; the other, in the Bayesian framework, uses Gibbs-sampling to simulate posterior distributions from data. The authors present numerous applications of these approaches in detail: decomposition of time series into trend and cycle, a new index of coincident economic indicators, approaches to modeling monetary policy uncertainty, Friedman's plucking model of recessions, the detection of turning points in the business cycle and the question of whether booms and recessions are duration-dependent, state-space models with heteroskedastic disturbances, fads and crashes in financial markets, long-run real exchange rates, and mean reversion in asset returns.

A Gibbs sampling approach to matched-field source localization and deconvolution

In narrow-band source localization the source spectrum is typically unknown. Matched-field techniques employ normalization schemes to remove the uncertainty for the unknown amplitude at the source, whereas consideration of phase differences between replicas and true field addresses the unknown phase issue. In this work we implement a matched-field technique that simultaneously estimates source location and source spectrum. The estimation is performed using an efficient Gibbs sampling scheme. Results of the Gibbs sampling estimation approach are compared to those of the linear (Bartlett) processor under several noise levels. The comparison reveals that the simultaneous process of deconvolution and localization has superior performance to that of the linear localization process. Moreover, improvement in localization is obtained without a significant increase in computational requirements. In addition to the improved performance, the proposed method has the advantage of providing more information than conventional matched-field localization, since it also estimates the source spectrum which is often of great interest. [Work supported by ONR.]

Random effects in censored ordinal regression: latent structure and Bayesian approach.

This paper discusses random effects in censored ordinal regression and presents a Gibbs sampling approach to fit the regression model. A latent structure and its corresponding Bayesian formulation are introduced to effectively deal with heterogeneous and censored ordinal observations. This work is motivated by the need to analyze interval-censored ordinal data from multiple studies in toxicological risk assessment. Application of our methodology to the data offers further support to the conclusions developed earlier using GEE methods yet provides additional insight into the uncertainty levels of the risk estimates.

Bayesian Interval Estimation of Multiple Correlations with Missing Data: A Gibbs Sampling Approach

A Bayesian method for obtaining an interval estimate of the population squared multiple correlation from an incomplete multivariate normal data set is described. The method is applicable to data sets where values are missing on any combination of the dependent and independent variables. Further, the missing data need not be missing in a completely random fashion. The estimates are constructed using a Markov Chain Monte Carlo procedure known as Gibbs Sampling. The important issues of the convergence properties of the Gibbs sampler, the effect of the choice of a reference prior, and the empirical coverage probabilities of the estimates are considered in detail. Investigations using simulated data suggest that the proposed method can yield accurate interval estimates of the population squared multiple correlation.

Reviews

Economic RecordVolume 76, Issue 232 p. 105-109 Reviews First published: 22 October 2007 https://doi.org/10.1111/j.1475-4932.2000.tb00007.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Reviews in this articles: State Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications, by Chang-Jin Kim and Charles R. Nelson Public Finance and Public Choice: Two Contrasting Visions of the State, by James M. Buchanan and Richard A. Musgrave Charting Twentieth-Century Monetary Policy: Herbert Hoover and Benjamin Strong, 1917–1927. Contributions in Economics and Economic History, Number 210, Silvano A. Wueschner Monetary Policy and the Great Inflation in the United States: The Federal Reserve and the Failure of Macroeconomic Policy, 1965–79, by Thomas Mayer Volume76, Issue232March 2000Pages 105-109 RelatedInformation

A Gibbs-sampler approach to estimate the number of faults in a system using capture-recapture sampling [software reliability

A new recapture debugging model is suggested to estimate the number of faults in a system, /spl nu/, and the failure intensity of each fault, /spl phi/. The Gibbs sampler and the Metropolis algorithm are used in this inference procedure. A numerical illustration suggests a notable improvement on the estimation of /spl nu/ and /spl phi/ compared with that of a removal debugging model.

Conditional Heteroscedasticity in Qualitative Response Models of Time Series: A Gibbs-Sampling Approach to the Bank Prime Rate

Conditional Heteroscedasticity in Qualitative Response Models of Time Series: A Gibbs-Sampling Approach to the Bank Prime Rate