Highest Probability Density Interval Research Articles

Phylogeography of the temperate grassland plant Tephroseris kirilowii (Asteraceae) inferred from multiplexed inter-simple sequence repeat genotyping by sequencing (MIG-seq) data.

A group of temperate grassland plant species termed the "Mansen elements" occurs in Japan and is widely distributed in the grasslands of continental East Asia. It has been hypothesized that these species are continental grassland relicts in Japan that stretch back to a colder age, but their migration history has not been elucidated. To assess the migration history of the Mansen elements, we performed phylogeographic analyses of Tephroseris kirilowii, a member of this group, using single-nucleotide polymorphisms (SNPs) obtained from multiplexed inter-simple sequence repeat genotyping by sequencing (MIG-seq). It was estimated that the Japanese populations of T. kirilowii were divided from those of continental East Asia at 25.2 thousand years ago (ka) with 95% highest probability density interval (HPD) of 15.3-40.0ka and that Japanese clades first diverged at 20.2ka with 95% HPD of 10.4-30.1ka. As the climatically suitable range during the last glacial maximum (LGM) estimated using ecological niche modeling (ENM) was limited in Japan and there was a slight genetic differentiation among Japanese populations, a post-glacial expansion of T. kirilowii in the Japanese Archipelago was indicated.

Stress–Strength Inference on the Multicomponent Model Based on Generalized Exponential Distributions under Type-I Hybrid Censoring

The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation methods of the maximum likelihood and Bayesian are utilized to infer the system reliability. For the Bayesian estimation method, informative and non-informative priors combined with three loss functions are considered. Because the computational difficulty on working posteriors, the Markov chain Monte Carlo method is adopted to obtain the approximation of the reliability estimator posterior. In addition, the bootstrap method and highest probability density interval are used to obtain the reliability confidence intervals. The simulation study shows that the Bayes estimator with informative prior is superior to other competitors. Finally, two real examples are given to illustrate the proposed estimation methods.

Association of Infarct Topography and Outcome After Endovascular Thrombectomy in Patients With Acute Ischemic Stroke.

The care of patients with large vessel occlusion (LVO) stroke has been revolutionized by endovascular thrombectomy (EVT). While EVT has a large effect size, most patients treated with EVT remain disabled or die within 90 days. A better understanding of outcomes may influence EVT selection criteria, novel therapies, and prognostication. We sought to identify associations between outcomes and brain regions involved in ischemic lesions. For this cohort study, consecutive patients with LVO who were treated with EVT and underwent post-EVT MRI were identified from a tertiary referral center (2011-2019). Acute ischemic lesions were manually segmented from diffusion-weighted imaging and spatially normalized. Individual lesions were parcellated (atlas-defined 94 cortical regions, 14 subcortical nuclei, 20 white matter tracts) and reduced to 10 essential lesion patterns with the use of unsupervised dimensionality reduction techniques. Ninety-day modified Rankin Scale (mRS) score (>2) was modeled via bayesian regression, taking the 10 lesion patterns as inputs and controlling for lesion size, age, sex, acute NIH Stroke Scale (NIHSS) score, alteplase, prior stroke, intracerebral hemorrhage, and good reperfusion (Thrombolysis in Cerebral Infarction 2b-3). In comparative analyses, 90-day mRS score was modeled considering covariates only, and compartment-wise relevances for acute stroke severity and 90-day mRS score were evaluated. There were 151 patients with LVO identified (age 68 ± 15 years, 52% female). The median NIHSS score was 16 (interquartile range 13-20); 56% had mRS score >2. Lesion locations predictive of 90-day mRS score involved bilateral but left hemispherically more pronounced precentral and postcentral gyri, insular and opercular cortex, and left putamen and caudate (area under the curve 0.91, highest probability density interval [HPDI] covering 90% certainty 0.90-0.92). The lesion location model outperformed the simpler model relying on covariates only (bayesian model comparison of 97% weight to the model with vs 3% weight to the model without lesion location). While lesions affecting subcortical nuclei had the highest relevance for stroke severity (posterior distribution mean 0.75, 90% HPDI 0.256-1.31), lesions affecting white matter tracts had the highest relevance for 90-day mRS score (0.656, 90% HPDI 0.0864-1.12). These data describe the significance for outcomes of specific brain regions involved in ischemic lesions on MRI after EVT. Future work in additional datasets is needed to confirm these granular findings.

Dose Reduction of Preoperative Radiotherapy in Myxoid Liposarcoma

Currently, preoperative radiotherapy for all soft-tissue sarcomas is identical at a 50-Gy dose level, which can be associated with morbidity, particularly wound complications. The observed clinical radiosensitivity of the myxoid liposarcoma subtype might offer the possibility to reduce morbidity. To assess whether a dose reduction of preoperative radiotherapy for myxoid liposarcoma would result in comparable oncological outcome with less morbidity. The Dose Reduction of Preoperative Radiotherapy in Myxoid Liposarcomas (DOREMY) trial is a prospective, single-group, phase 2 nonrandomized controlled trial being conducted in 9 tertiary sarcoma centers in Europe and the US. Participants include adults with nonmetastatic, biopsy-proven and translocation-confirmed myxoid liposarcoma of the extremity or trunk who were enrolled between November 24, 2010, and August 1, 2019. Data analyses, using both per-protocol and intention-to-treat approaches, were conducted from November 24, 2010, to January 31, 2020. The experimental preoperative radiotherapy regimen consisted of 36 Gy in once-daily 2-Gy fractions, with subsequent definitive surgical resection after an interval of 4 or more weeks. As a short-term evaluable surrogate for local control, the primary end point was centrally reviewed pathologic treatment response. The experimental regimen was regarded as a success when 70% or more of the resection specimens showed extensive treatment response, defined as 50% or greater of the tumor volume containing treatment effects. Morbidity outcomes consisted of wound complications and late toxic effects. Among the 79 eligible patients, 44 (56%) were men and the median (interquartile range) age was 45 (39-56) years. Two patients did not undergo surgical resection because of intercurrent metastatic disease. Extensive pathological treatment response was observed in 70 of 77 patients (91%; posterior mean, 90.4%; 95% highest probability density interval, 83.8%-96.4%). The local control rate was 100%. The rate of wound complication requiring intervention was 17%, and the rate of grade 2 or higher toxic effects was 14%. The findings of the DOREMY nonrandomized clinical trial suggest that deintensification of preoperative radiotherapy dose is effective and oncologically safe and is associated with less morbidity than historical controls, although differences in radiotherapy techniques and follow-up should be considered. A 36-Gy dose delivered in once-daily 2-Gy fractions is proposed as a dose-fractionation approach for myxoid liposarcoma, given that phase 3 trials are logistically impossible to execute in rare cancers. ClinicalTrials.gov Identifier: NCT02106312.

Bayesian Estimation of the Shape Parameters of Mcdonald Generalized Beta-Binomial Distribution

The paper explores and establishes a unique Bayesian framework for estimating three shape parameters of the McDonald generalized beta-binomial distribution. The mixture distribution is used in modelling overdispersed binomial data. Foundations of the framework have been enriched by knowledge of Bayesian statistics and Markov Chain Monte Carlo methods. A Metropolis within Gibbs Monte Carlo method to sample from the unknown posterior form of the distribution was used. The shape parameters (α, β and γ) were assigned flat gamma priors to ensure equal probabilities for all the values. McDonald generalized beta-binomial variables were simulated with fixed shape parameters set at (α,β,γ)=(0.5,0.5,0.5) respectively and samples generated were used to estimate the parameters, to evaluate if the method recovers estimates close to the true parameter values. Standard errors were also computed for the simulated data and real data. Further, credible regions and highest probability density intervals (HPD) were computed and their corresponding lengths. To evaluate the marginal posterior samples for every shape parameter generated trace plots presented, their respective correlation plots were also presented and the histograms to show the distributions assumed by every parameter. Bayesian framework provides a direct and flexible method of computation for a mixture distribution whose complexity may pose challenges of integration when using the classical methods of estimation.

Committee neural network and weighted multiple regression to predict the energetic values of poultry feedstuffs

Abstract: The objective of this work was to compare the committee neural network (CNN) and weighted multiple linear regression (WMLR) models, in order to estimate the nitrogen-corrected apparent metabolizable energy (AMEn) of poultry feedstuffs. The prediction equation was adjusted by using a WMLR model and the meta-analysis principle. The models were compared by considering the correct prediction percentages, based on the classic prediction intervals and on the highest-probability density intervals, and by using a comparison test for proportions. The accuracy of the models was evaluated based on the values of the mean squared error, coefficient of determination, mean absolute deviation, mean absolute percentage error, and bias. Data from metabolic trials were used to compare the selected models. The committee neural network is the model that showed the highest accuracy of prediction, being recommended as the most accurate model to predict AMEn values for energetic concentrate feedstuffs used by the poultry feed industry.

Implementation Research on Shared Decision Making in Primary Care: Inventory of Intracluster Correlation Coefficients.

Background. Cluster randomized trials are important sources of information on evidence-based practices in primary care. However, there are few sources of intracluster correlation coefficients (ICCs) for designing such trials. We inventoried ICC estimates for shared decision-making (SDM) measures in primary care. Methods. Data sources were studies led by the Canada Research Chair in Shared Decision Making and Knowledge Transition. Eligible studies were conducted in primary care, included at least 2 hierarchical levels, included SDM measures for individual units nested under any type of cluster (area, clinic, or provider), and were approved by an ethics committee. We classified measures into decision antecedents, decision processes, and decision outcomes. We used Bayesian random-effect models to estimate mode ICCs and the 95% highest probability density interval (HPDI). We summarized estimates by calculating median and interquartile range (IQR). Results. Six of 14 studies were included. There were 97 ICC estimates for 17 measures. ICC estimates ranged from 0 to 0.5 (median, 0.03; IRQ, 0-0.07). They were higher for process measures (median, 0.03; IQR, 0-0.07) than for antecedent measures (0.02; 0-0.07) or outcome measures (0.02; 0-0.06), for which, respectively, "decisional conflict" (mode, 0.48; 95% HPDI, 0.39-0.57), "reluctance to disclose uncertainty to patients" (0.5; 0.11-0.89), and "quality of the decision" (0.45; 0.14-0.84) had the highest ICCs. ICCs for provider-level clustering (median, 0.06; IQR, 0-0.13) were higher than for other levels. Limitations. This convenience sample of studies may not reflect all potential ICC ranges for primary care SDM measures. Conclusions. Our inventory of ICC estimates for SDM measures in primary care will improve the ease and accuracy of power calculations in cluster randomized trials and inspire its further expansion in SDM contexts.

The U&I study: study protocol for a feasibility randomised controlled trial of a pre-cognitive behavioural therapy digital \u2018informed choice\u2019 intervention to improve attitudes towards uptake and implementation of CBT for psychosis

BackgroundAt least 40% of people with psychosis have persistent distressing symptoms despite optimal medication treatment. Cognitive behaviour therapy for psychosis (CBTp) is the only NICE-recommended individual therapy for psychosis, with effects on symptoms, distress and quality of life. Yet <10% of service-users receive it and 94% of trusts struggle to provide it. Of those offered it, 22–43% refuse or do not attend. We have developed a new pre-CBTp informed choice intervention to address knowledge and attitudes that influence uptake and implementation and now want to test it in a feasibility trial.MethodsThe design is a two-arm, feasibility randomised controlled trial (RCT), with 1:1 randomisation, stratified by participant group and site. Participants are 40 psychosis patients and 40 clinicians, who are ambivalent towards uptake or implementation of CBTp. Sites are community and inpatient services in Sussex and London. The intervention is a pre-CBT digital psychoeducation intervention designed to address identified knowledge and attitudinal barriers to uptake and implementation of CBTp, incorporating behaviour change mechanisms, and supported by animated introductory, patient and clinician stories. The comparator is the NHS choices website for CBT. The primary aim is to assess clinical feasibility (recruitment, randomisation, acceptability, use, delivery, outcome measurement, retention). A secondary aim is a preliminary evaluation of efficacy. Outcomes will be assessed at baseline, post intervention, and one-month follow-up (blind to treatment arm). The primary efficacy outcome is likelihood of offering/taking up CBTp. Secondary outcomes include knowledge and attitudes towards CBTp, illness perceptions, empowerment, psychological wellbeing (patients only) and CBTp implementation (clinicians only). Use of the intervention and CBT behaviours during the follow-up period will be recorded and captured in a feedback questionnaire. Use, acceptability and experience of outcome assessment will be explored in qualitative interviews with participants (n = 6 per group). The efficacy evaluation will report descriptive data, key model parameters and 95% highest probability density intervals in a Bayesian growth model.DiscussionThis is the first feasibility trial of a digital ‘informed choice’ decision aid for the implementation of CBTp. If the trial proves feasible and demonstrates preliminary evidence of efficacy, a large multi-site trial will be warranted.Trial registrationISRCTN registry, ISRCTN53107879. Registered prospectively on 2 August 2017.

Tracing hepatitis B virus (HBV) genotype B5 (formerly B6) evolutionary history in the circumpolar Arctic through phylogeographic modelling.

BackgroundIndigenous populations of the circumpolar Arctic are considered to be endemically infected (>2% prevalence) with hepatitis B virus (HBV), with subgenotype B5 (formerly B6) unique to these populations. The distinctive properties of HBV/B5, including high nucleotide diversity yet no significant liver disease, suggest virus adaptation through long-term host-pathogen association.MethodsTo investigate the origin and evolutionary spread of HBV/B5 into the circumpolar Arctic, fifty-seven partial and full genome sequences from Alaska, Canada and Greenland, having known location and sampling dates spanning 40 years, were phylogeographically investigated by Bayesian analysis (BEAST 2) using a reversible-jump-based substitution model and a clock rate estimated at 4.1 × 10−5 substitutions/site/year.ResultsFollowing an initial divergence from an Asian viral ancestor approximately 1954 years before present (YBP; 95% highest probability density interval [1188, 2901]), HBV/B5 coalescence occurred almost 1000 years later. Surprisingly, the HBV/B5 ancestor appears to locate first to Greenland in a rapid coastal route progression based on the landscape aware geographic model, with subsequent B5 evolution and spread westward. Bayesian skyline plot analysis demonstrated an HBV/B5 population expansion occurring approximately 400 YBP, coinciding with the disruption of the Neo-Eskimo Thule culture into more heterogeneous and regionally distinct Inuit populations throughout the North American Arctic.DiscussionHBV/B5 origin and spread appears to occur coincident with the movement of Neo-Eskimo (Inuit) populations within the past 1000 years, further supporting the hypothesis of HBV/host co-expansion, and illustrating the concept of host-pathogen adaptation and balance.

Rapid replacement of prevailing genotype of human respiratory syncytial virus by genotype ON1 in Beijing, 2012–2014

Human respiratory syncytial virus (HRSV) is the most common viral pathogen causing lower respiratory infections in infants and young children worldwide. HRSV ON1 genotype in subgroup A with a characteristic of a 72 nucleotide duplication in the second highly variable region of attachment glycoprotein gene, has been reported in some countries since it was first detected in clinical samples collected in Canada in 2010. In this study, 557 HRSV antigen-positive nasopharyngeal aspirates were randomly selected during 2012/2013 to 2013/2014 HRSV seasons in Beijing for subgroup typing and for ON1 genotype screening by using a PCR based method developed for easily identifying genotype ON1 out of strains of subtype A. It was found that subgroup B was dominant in the 2012/2013 season and sudden shift of subgroup dominance from B to A and rapid replacement of previously prevailing NA1 genotype by ON1 genotype occurred in the 2013/2014 season. Reversible amino acid replacement in the G protein gene was found in a new branch of ON1 genotype. The evolutionary rate of the 351 global ON1 sequences was estimated to 7.34×10−3 nucleotide substitutions per site per year (95% highest probability density intervals, HPD, 5.71×10−3 to 9.04×10−3), with the time of most recent common ancestor dating back to June 2009.

The evolutionary history and spatiotemporal dynamics of the fever, thrombocytopenia and leukocytopenia syndrome virus (FTLSV) in China.

BackgroundIn 2007, a novel bunyavirus was found in Henan Province, China and named fever, thrombocytopenia and leukocytopenia syndrome virus (FTLSV); since then, FTLSV has been found in ticks and animals in many Chinese provinces. Human-to-human transmission has been documented, indicating that FTLSV should be considered a potential public health threat. Determining the historical spread of FTLSV could help curtail its spread and prevent future movement of this virus.Method/Principal FindingsTo examine the pattern of FTLSV evolution and the origin of outbreak strains, as well to examine the rate of evolution, the genome of 12 FTLSV strains were sequenced and a phylogenetic and Bayesian phylogeographic analysis of all available FTLSV sequences in China were performed. Analysis based on the FTLSV L segment suggests that the virus likely originated somewhere in Huaiyangshan circa 1790 (95% highest probability density interval: 1756–1817) and began spreading around 1806 (95% highest probability density interval: 1773–1834). Analysis also indicates that when FTLSV arrived in Jiangsu province from Huaiyangshan, Jiangsu Province became another source for the spread of the disease. Bayesian factor test analysis identified three major transmission routes: Huaiyangshan to Jiangsu, Jiangsu to Liaoning, and Jiangsu to Shandong. The speed of FTLSV movement has increased in recent decades, likely facilitated by modern human activity and ecosystem changes. In addition, evidence of RNA segment reassortment was found in FTLSV; purifying selection appears to have been the dominant force in the evolution of this virus.ConclusionResults presented in the manuscript suggest that the Huaiyangshan area is likely be the origin of FTLSV in China and identified probable viral migration routes. These results provide new insights into the origin and spread of FTLSV in China, and provide a foundation for future virological surveillance and control.

Neural network committee to predict the AMEn of poultry feedstuffs

A committee of neural networks is the aggregation of two or more neural networks for making overall predictions that are supposedly more accurate than those obtained by the individual networks. The objective of this paper was to assign some uncertainty over the predictions of neural networks, using a network committee to estimate the nitrogen-corrected metabolizable energy (AMEn) values of the energetic and protein concentrate feedstuffs for broilers. The dataset used to implement each expert network contains 568 experimental results. Another dataset with 48 bioassay results was used as test data. From several implemented multilayer perceptrons, the networks that presented the best generalization performance were selected to constitute the committee. The percentage of correct predictions was used as the criterion to compare committees that contained different numbers of networks. The highest probability density intervals were obtained for each feedstuff in the test data in this comparison. The estimator that ensured more accurate predictions was selected. The highest accuracy for predicting the AMEn values of concentrate feedstuffs for broilers was achieved by a committee with 1,000 networks with the use of the mode of the empirical distribution obtained from 1,000 estimated values of the AMEn. The accuracy of the models was evaluated based on their values of error measures between the observed and predicted values, in which the mode of the empirical distribution presented lower values of mean squared error (MSE = 45,285.43), mean absolute deviation (MAD = 177.66) and mean absolute percentage error (MAPE = 5.97 %) compared to the mean and the median.

Genetic analysis of twinning rate and milk yield using a threshold‐linear model in Japanese Holsteins

The objective of this study was to estimate genetic parameters and breeding values for the twinning rate of the first three parities (T1, T2 and T3) and 305-day milk yield in first lactation (MY), using a four-trait threshold-linear animal model in Japanese Holsteins. Data contained 1 323 946 cows calving between 1990 and 2007. Twinning was treated as a binary character: 'single' or 'twin or more'. Reported T1, T2 and T3 were 0.70%, 2.87%, and 3.73%, respectively. Individual 305-day milk yield was computed using a multiple trait prediction for cows with at least eight test-day records. (Co)variance components were estimated via Gibbs sampling for randomly sampled subsets. Posterior means of heritabilities for T1, T2 and T3 were 0.11, 0.16 and 0.14, respectively. Genetic correlations between parities were 0.92 or greater. Genetic correlations of MY with twinning rate were not 'significant' (i.e. their 95% highest probability density intervals contained zeros). Multiple births at different parities were considered as the same genetic trait. The average evaluations of T1 (T2) for sires born before 1991 was 0.48% (2.25%) compared with a mean of 0.76% (3.37%) for sires born after 1992. A recent increase in the reported twinning rate reflects the positive genetic trend for sires in Japanese Holsteins.

Low Diversity in the Mitogenome of Sperm Whales Revealed by Next-Generation Sequencing

Large population sizes and global distributions generally associate with high mitochondrial DNA control region (CR) diversity. The sperm whale (Physeter macrocephalus) is an exception, showing low CR diversity relative to other cetaceans; however, diversity levels throughout the remainder of the sperm whale mitogenome are unknown. We sequenced 20 mitogenomes from 17 sperm whales representative of worldwide diversity using Next Generation Sequencing (NGS) technologies (Illumina GAIIx, Roche 454 GS Junior). Resequencing of three individuals with both NGS platforms and partial Sanger sequencing showed low discrepancy rates (454-Illumina: 0.0071%; Sanger-Illumina: 0.0034%; and Sanger-454: 0.0023%) confirming suitability of both NGS platforms for investigating low mitogenomic diversity. Using the 17 sperm whale mitogenomes in a phylogenetic reconstruction with 41 other species, including 11 new dolphin mitogenomes, we tested two hypotheses for the low CR diversity. First, the hypothesis that CR-specific constraints have reduced diversity solely in the CR was rejected as diversity was low throughout the mitogenome, not just in the CR (overall diversity π = 0.096%; protein-coding 3rd codon = 0.22%; CR = 0.35%), and CR phylogenetic signal was congruent with protein-coding regions. Second, the hypothesis that slow substitution rates reduced diversity throughout the sperm whale mitogenome was rejected as sperm whales had significantly higher rates of CR evolution and no evidence of slow coding region evolution relative to other cetaceans. The estimated time to most recent common ancestor for sperm whale mitogenomes was 72,800 to 137,400 years ago (95% highest probability density interval), consistent with previous hypotheses of a bottleneck or selective sweep as likely causes of low mitogenome diversity.

Reconstructing the History of Maize Streak Virus Strain A Dispersal To Reveal Diversification Hot Spots and Its Origin in Southern Africa

Maize streak virus strain A (MSV-A), the causal agent of maize streak disease, is today one of the most serious biotic threats to African food security. Determining where MSV-A originated and how it spread transcontinentally could yield valuable insights into its historical emergence as a crop pathogen. Similarly, determining where the major extant MSV-A lineages arose could identify geographical hot spots of MSV evolution. Here, we use model-based phylogeographic analyses of 353 fully sequenced MSV-A isolates to reconstruct a plausible history of MSV-A movements over the past 150 years. We show that since the probable emergence of MSV-A in southern Africa around 1863, the virus spread transcontinentally at an average rate of 32.5 km/year (95% highest probability density interval, 15.6 to 51.6 km/year). Using distinctive patterns of nucleotide variation caused by 20 unique intra-MSV-A recombination events, we tentatively classified the MSV-A isolates into 24 easily discernible lineages. Despite many of these lineages displaying distinct geographical distributions, it is apparent that almost all have emerged within the past 4 decades from either southern or east-central Africa. Collectively, our results suggest that regular analysis of MSV-A genomes within these diversification hot spots could be used to monitor the emergence of future MSV-A lineages that could affect maize cultivation in Africa.

Estimating current injectors in Scotland and their drug-related death rate by sex, region and age-group via Bayesian capture—recapture methods

Using Bayesian capture-recapture methods, we estimate current injectors in Scotland in 2003, and, thereby, injectors' drug-related death rates for the period 2003-2005. Four different data sources are considered [Hepatitis C Virus (HCV) database, hospital admissions, social enquiry reports, and drug misuse database reports by General Practices or Drug Treatment Agencies] which provide covariate information on sex, region (Greater Glasgow versus elsewhere in Scotland) and age group (15-34 years and 35+ years).We quantified Scotland's current injectors in 2003 at 27,400 (95% highest probability density interval: 20,700-32,100) by incorporating underlying model uncertainty in terms of the possible interactions present between data sources and/or covariates. The posterior probability was 72% that Scotland had more current injectors in 2003 than in 2000. Detailed comparison with 2000 gave evidence of importantly changed numbers of current injectors for different covariate classes.In addition, and of particular social interest, is the estimation of injectors' drug-related death rates. Expert information was used to construct upper and lower bounds on the number of drug-related deaths pertaining to injectors, which were then used to provide bounds on injectors' drug-related death rates. Failure to incorporate expert information could result in over-estimation of drug-related death rates for subclasses of injectors.

A Monte Carlo Method for Computing the HPD Interval for Ratio of Two Multivariate Normal Generalized Variances

ABSTRACT In this article, we develop a method for computing a Bayesian HPD (highest probability density) interval for a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval are intractable and thus a Bayesian HPD interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao (1999). Necessary theory involved in the method and computation is provided.

Bayesian geoacoustic inversion for the inversion techniques 2001 workshop

This paper applies a Bayesian formulation to range-dependent geoacoustic inverse problems. Two inversion methods, a hybrid optimization algorithm and a Bayesian sampling algorithm, are applied to some of the 2001 Inversion Techniques Workshop benchmark data. The hybrid inversion combines the local (gradient-based) method of downhill simplex with the global search method of simulated annealing in an adaptive algorithm. The Bayesian inversion algorithm uses a Gibbs sampler to estimate properties of the posterior probability density, such as mean and maximum a posteriori parameter estimates, marginal probability distributions, highest-probability density intervals, and the model covariance matrix. The methods are applied to noise-free and noisy benchmark data from shallow ocean environments with range-dependent geophysical and geometric properties. An under-parameterized approach is applied to determine the optimal model parameterization consistent with the resolving power of the acoustic data. The Bayesian inversion method provides a complete solution including quantitative uncertainty estimates and correlations, while the hybrid inversion method provides parameter estimates in a fraction of the computation time.

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.

Monte Carlo Estimation of Bayesian Credible and HPD Intervals

This article considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective marginal posterior distribution using a Markov chain Monte Carlo (MCMC) sampling algorithm. We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. Necessary theory is developed and illustrative examples—including a simulation study—are given.