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Recently, based on negentropy of squared envelope (SE) and of squared envelope spectrum (SES), extensions of spectral kurtosis, the infograms including the SE infogram and the SES infogram, were proposed to detect impulsive and cyclostationary transients. Moreover, they have abilities to detect transients in the cases, where impulsive noises exist or relaxation times of repetitive transients are lower than their repetition rate. Nevertheless, the infograms are fast filtering algorithms and cannot achieve optimal filtering for bearing fault feature identification. This paper aims to extend the infograms to novel Bayesian inference based optimal wavelet filtering for bearing fault feature identification. The innovations of this paper are summarized as follows. Firstly, a state space model of wavelet parameters is presented. Here, wavelet parameters are the states of the state space model. Monotonically increasing guess negentropy measurements are constructed. Secondly, either the SE infogram or the SES infogram is employed to initialize the state space model. Then, considering Gaussian disturbance on wavelet parameters, wavelet parameters are assumed to follow a joint Gaussian distribution. Thirdly, spherical cubature integration based Bayesian inference is introduced to iteratively establish posterior wavelet parameters distributions. At last, optimal wavelet parameters are determined from the posterior wavelet parameters distributions so as to conduct optimal wavelet filtering. Two instance studies including simulated and experimental bearing fault data were investigated to illustrate how the proposed Bayesian inference method works. The results show that the proposed Bayesian inference method is convergent and provides more fault signatures than the infogram. [ABSTRACT FROM AUTHOR]

Quantitative analysis of magnetic resonance imaging (MRI) scans of the brain requires accurate automated segmentation of anatomical structures. A desirable feature for such segmentation methods is to be robust against changes in acquisition platform and imaging protocol. In this paper we validate the performance of a segmentation algorithm designed to meet these requirements, building upon generative parametric models previously used in tissue classification. The method is tested on four different datasets acquired with different scanners, field strengths and pulse sequences, demonstrating comparable accuracy to state-of-the-art methods on T1-weighted scans while being one to two orders of magnitude faster. The proposed algorithm is also shown to be robust against small training datasets, and readily handles images with different MRI contrast as well as multi-contrast data. [ABSTRACT FROM AUTHOR]

The multiframe super-resolution (SR) technique aims to obtain a high-resolution (HR) image by using a set of observed low-resolution (LR) images. In the reconstruction process, artifacts may be possibly produced due to the noise, especially in presence of stronger noise. In order to suppress artifacts while preserving discontinuities of images, in this paper a multiframe SR method is proposed by involving the reconstruction properties of the half-quadratic prior model together with the quadratic prior model using a convex combination. Moreover, by analyzing local features of the underlined HR image, these two prior models are combined by using an automatically calculated weight function, making both smooth and discontinuous pixels handled properly. A variational Bayesian inference (VBF) based algorithm is designed to efficiently and effectively seek the solution of the proposed method. With the VBF framework, motion parameters and hyper-parameters are all determined automatically, leading to an unsupervised SR method. The efficiency of the hybrid prior model is demonstrated theoretically and practically, which shows that our SR method can obtain better results from LR images even with stronger noise. Extensive experiments on several visual data have demonstrated the efficacy and superior performance of the proposed algorithm, which can not only preserve image details but also suppress artifacts. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a statistically motivated framework for performing real-time dialogue state updates and policy learning in a spoken dialogue system. The framework is based on the partially observable Markov decision process (POMDP), which provides a well-founded, statistical model of spoken dialogue management. However, exact belief state updates in a POMDP model are computationally intractable so approximate methods must be used. This paper presents a tractable method based on the loopy belief propagation algorithm. Various simplifications are made, which improve the efficiency significantly compared to the original algorithm as well as compared to other POMDP-based dialogue state updating approaches. A second contribution of this paper is a method for learning in spoken dialogue systems which uses a component-based policy with the episodic Natural Actor Critic algorithm. The framework proposed in this paper was tested on both simulations and in a user trial. Both indicated that using Bayesian updates of the dialogue state significantly outperforms traditional definitions of the dialogue state. Policy learning worked effectively and the learned policy outperformed all others on simulations. In user trials the learned policy was also competitive, although its optimality was less conclusive. Overall, the Bayesian update of dialogue state framework was shown to be a feasible and effective approach to building real-world POMDP-based dialogue systems. [Copyright &y& Elsevier]

This paper investigates a new probabilistic strategy for Bayesian model updating using incomplete modal data. Direct mode matching between the measured and the predicted modal quantities is not required in the updating process, which is realized through model reduction. A Markov chain Monte Carlo technique with adaptive random-walk steps is proposed to draw the samples for model parameter uncertainty quantification. The iterated improved reduced system technique is employed to update the prediction error as well as to calculate the likelihood function in the sampling process. Since modal quantities are used in the model updating, modal identification is first carried out to extract the natural frequencies and mode shapes through the acceleration measurements of the structural system. The proposed algorithm is finally validated by both numerical and experimental examples: a 10-storey building with synthetic data and a 8-storey building with shaking table test data. Results illustrate that the proposed algorithm is effective and robust for parameter uncertainty quantification in probabilistic model updating of buildings. [ABSTRACT FROM AUTHOR]

We address the problem of Bayesian variable selection for high-dimensional linear regression. We consider a generative model that uses a spike-and-slab-like prior distribution obtained by multiplying a deterministic binary vector, which traduces the sparsity of the problem, with a random Gaussian parameter vector. The originality of the work is to consider inference through relaxing the model and using a type-II log-likelihood maximization based on an EM algorithm. Model selection is performed afterwards relying on Occam’s razor and on a path of models found by the EM algorithm. Numerical comparisons between our method, called spinyReg, and state-of-the-art high-dimensional variable selection algorithms (such as lasso, adaptive lasso, stability selection or spike-and-slab procedures) are reported. Competitive variable selection results and predictive performances are achieved on both simulated and real benchmark data sets. An original regression data set involving the prediction of the number of visitors of the Orsay museum in Paris using bike-sharing system data is also introduced, illustrating the efficiency of the proposed approach. The R package spinyReg implementing the method proposed in this paper is available on CRAN. [ABSTRACT FROM AUTHOR]

In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consists of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model. [ABSTRACT FROM AUTHOR]

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations. [ABSTRACT FROM AUTHOR]

Abstract: The focus of this paper is Bayesian modal parameter recursive estimation based on an interacting Kalman filter algorithm with decoupled distributions for frequency and damping. Interacting Kalman filter is a combination of two widely used Bayesian estimation methods: the particle filter and the Kalman filter. Some sensitivity analysis techniques are also proposed in order to deduce a recursive estimate of modal parameters from the estimates of the damping/stiffness coefficients. [Copyright &y& Elsevier]

Abstract: Extraction and separation of functionally different event-related potentials (ERPs) from electroencephalography (EEG) is a long-standing problem in cognitive neuroscience. In this paper, we propose a Bayesian spatio-temporal model for estimating ERP components from multichannel EEG recorded under multiple experimental conditions. The model isolates the spatially and temporally overlapping ERP components by utilizing their phase-locking structure and the inter-condition non-stationarity structure of their amplitudes and latencies. Critically, unlike in previous multilinear algorithms, the non-phase-locked background EEGs are modeled as spatially correlated and non-isotropic signals. A variational algorithm was developed for approximate Bayesian inference of the proposed model, with the effective number of ERP components automatically determined as a part of the algorithm. The utility of the algorithm is demonstrated with applications to synthetic data and the EEG data collected from 13 subjects during a face inversion experiment. The results show that our algorithm more accurately and reliably estimates the spatio-temporal patterns, amplitudes, and latencies of the underlying ERP components in comparison with several state-of-the-art algorithms. [Copyright &y& Elsevier]

Abstract: This paper introduces a damage diagnosis algorithm for civil structures that uses a sequential change point detection method. The general change point detection method uses the known pre- and post-damage feature distributions to perform a sequential hypothesis test. In practice, however, the post-damage distribution is unlikely to be known a priori, unless we are looking for a known specific type of damage. Therefore, we introduce an additional algorithm that estimates and updates this distribution as data are collected using the maximum likelihood and the Bayesian methods. We also applied an approximate method to reduce the computation load and memory requirement associated with the estimation. The algorithm is validated using a set of experimental data collected from a four-story steel special moment-resisting frame and multiple sets of simulated data. Various features of different dimensions have been explored, and the algorithm was able to identify damage, particularly when it uses multidimensional damage sensitive features and lower false alarm rates, with a known post-damage feature distribution. For unknown feature distribution cases, the post-damage distribution was consistently estimated and the detection delays were only a few time steps longer than the delays from the general method that assumes we know the post-damage feature distribution. We confirmed that the Bayesian method is particularly efficient in declaring damage with minimal memory requirement, but the maximum likelihood method provides an insightful heuristic approach. [Copyright &y& Elsevier]

Abstract: Analyses of non-normal data and longitudinal data to study changes in variables measured repeatedly over time have received considerable attention in social and psychological research. This paper proposes a dynamic two-level nonlinear structural equation model with covariates for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables. To cope with the non-normal continuous data, the corresponding residual errors at both first-level and second-level models are modeled through a Bayesian semiparametric modeling on the basis of a truncated and centered Dirichlet process with stick-breaking priors. The first-level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that vary with time; while the second level is defined for individuals to assess their characteristics that are invariant with time. An algorithm based on the blocked Gibbs sampler is implemented for estimation of parameters. An efficient model comparison statistic, namely the -measure, is also introduced. Results of a simulation study indicate that the performance of the Bayesian semiparametric estimation is satisfactory. The proposed methodologies are applied to a real longitudinal study concerning cocaine use. [Copyright &y& Elsevier]

Abstract: Multivariate classification algorithms are powerful tools for predicting cognitive or pathophysiological states from neuroimaging data. Assessing the utility of a classifier in application domains such as cognitive neuroscience, brain–computer interfaces, or clinical diagnostics necessitates inference on classification performance at more than one level, i.e., both in individual subjects and in the population from which these subjects were sampled. Such inference requires models that explicitly account for both fixed-effects (within-subjects) and random-effects (between-subjects) variance components. While models of this sort are standard in mass-univariate analyses of fMRI data, they have not yet received much attention in multivariate classification studies of neuroimaging data, presumably because of the high computational costs they entail. This paper extends a recently developed hierarchical model for mixed-effects inference in multivariate classification studies and introduces an efficient variational Bayes approach to inference. Using both synthetic and empirical fMRI data, we show that this approach is equally simple to use as, yet more powerful than, a conventional t-test on subject-specific sample accuracies, and computationally much more efficient than previous sampling algorithms and permutation tests. Our approach is independent of the type of underlying classifier and thus widely applicable. The present framework may help establish mixed-effects inference as a future standard for classification group analyses. [Copyright &y& Elsevier]

Abstract: Resting state functional connectivity MRI (rs-fcMRI) is a popular technique used to gauge the functional relatedness between regions in the brain for typical and special populations. Most of the work to date determines this relationship by using Pearson's correlation on BOLD fMRI timeseries. However, it has been recognized that there are at least two key limitations to this method. First, it is not possible to resolve the direct and indirect connections/influences. Second, the direction of information flow between the regions cannot be differentiated. In the current paper, we follow-up on recent work by Smith et al. (2011), and apply PC algorithm to both simulated data and empirical data to determine whether these two factors can be discerned with group average, as opposed to single subject, functional connectivity data. When applied on simulated individual subjects, the algorithm performs well determining indirect and direct connection but fails in determining directionality. However, when applied at group level, PC algorithm gives strong results for both indirect and direct connections and the direction of information flow. Applying the algorithm on empirical data, using a diffusion-weighted imaging (DWI) structural connectivity matrix as the baseline, the PC algorithm outperformed the direct correlations. We conclude that, under certain conditions, the PC algorithm leads to an improved estimate of brain network structure compared to the traditional connectivity analysis based on correlations. [Copyright &y& Elsevier]

Abstract: Bayesian inference methods are used extensively in the analysis of Generalized Linear Mixed Models (GLMMs), but it may be difficult to handle the posterior distributions analytically. In this paper, we establish the asymptotic normality of the joint posterior distribution of the parameters and the random effects in a GLMM by using Stein’s Identity. We also show that while incorrect assumptions on the random effects can lead to substantial bias in the estimates of the parameters, the assumed model for the random effects, under some regularity conditions, does not affect the asymptotic normality of the joint posterior distribution. This motivates the use of the approximate normal distributions for sensitivity analysis of the random effects distribution. We additionally illustrate that the approximate normal distribution performs reasonably using both real and simulated data. This creates a primary alternative to Markov Chain Monte Carlo (MCMC) sampling and avoids a wide range of problems for MCMC algorithms in terms of convergence and computational time. [Copyright &y& Elsevier]

Abstract: Acoustic emissions (AE) are stress waves initiated by sudden strain releases within a solid body. These can be caused by internal mechanisms such as crack opening or propagation, crushing, or rubbing of crack surfaces. One application for the AE technique in the field of Structural Engineering is Structural Health Monitoring (SHM). With piezo-electric sensors mounted to the surface of the structure, stress waves can be detected, recorded, and stored for later analysis. An important step in quantitative AE analysis is the estimation of the stress wave source locations. Commonly, source location results are presented in a rather deterministic manner as spatial and temporal points, excluding information about uncertainties and errors. Due to variability in the material properties and uncertainty in the mathematical model, measures of uncertainty are needed beyond best-fit point solutions for source locations. This paper introduces a novel holistic framework for the development of a probabilistic source location algorithm. Bayesian analysis methods with Markov Chain Monte Carlo (MCMC) simulation are employed where all source location parameters are described with posterior probability density functions (PDFs). The proposed methodology is applied to an example employing data collected from a realistic section of a reinforced concrete bridge column. The selected approach is general and has the advantage that it can be extended and refined efficiently. Results are discussed and future steps to improve the algorithm are suggested. [Copyright &y& Elsevier]

Abstract: Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large small problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik’s -insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. [Copyright &y& Elsevier]

Abstract: In this paper, we present an extensive performance evaluation of a novel source localization algorithm, Champagne. It is derived in an empirical Bayesian framework that yields sparse solutions to the inverse problem. It is robust to correlated sources and learns the statistics of non-stimulus-evoked activity to suppress the effect of noise and interfering brain activity. We tested Champagne on both simulated and real M/EEG data. The source locations used for the simulated data were chosen to test the performance on challenging source configurations. In simulations, we found that Champagne outperforms the benchmark algorithms in terms of both the accuracy of the source localizations and the correct estimation of source time courses. We also demonstrate that Champagne is more robust to correlated brain activity present in real MEG data and is able to resolve many distinct and functionally relevant brain areas with real MEG and EEG data. [Copyright &y& Elsevier]

Abstract: A critical problem in accurately estimating uncertainty in model predictions is the lack of details in the literature on the correlation (or full joint distribution) of uncertain model parameters. In this paper we describe a framework and a class of algorithms for analyzing such “missing data” problems in the setting of Bayesian statistics. The analysis focuses on the family of posterior distributions consistent with given statistics (e.g. nominal values, confidence intervals). The combining of consistent distributions is addressed via techniques from the opinion pooling literature. The developed approach allows subsequent propagation of uncertainty in model inputs consistent with reported statistics, in the absence of data. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of finite element model (FEM) updating in the context of model selection. The FEM updating problem arises from the need to update the initial FE model that does not match the measured real system outputs. This inverse system identification-problem is made even more complex by the uncertainties in modeling some of the structural parameters. Such uncertainty often results in a number of competing forms of FE models being proposed which leads to lack of consensus in the field. A model can be formulated in a number of ways; by the number, the location and the form of the updating parameters. We propose the use of a Bayesian evidence statistic to help decide on the best model from any given set of models. This statistic uses the recently developed stochastic nested sampling algorithm whose by-product is the posterior samples of the updated model parameters. Two examples of real structures are each modeled by a number of competing finite element models. The individual model evidences are compared using the Bayes factor, which is the ratio of evidences. Jeffrey''s scale is then used to determine the significance of the model differences obtained through the Bayes factor. [Copyright &y& Elsevier]

Abstract: In this paper we describe a method that can be used for Minimum Bayes Risk (MBR) decoding for speech recognition. Our algorithm can take as input either a single lattice, or multiple lattices for system combination. It has similar functionality to the widely used Consensus method, but has a clearer theoretical basis and appears to give better results both for MBR decoding and system combination. Many different approximations have been described to solve the MBR decoding problem, which is very difficult from an optimization point of view. Our proposed method solves the problem through a novel forward–backward recursion on the lattice, not requiring time markings. We prove that our algorithm iteratively improves a bound on the Bayes risk. [Copyright &y& Elsevier]

Abstract: Multichannel electroencephalography (EEG) offers a non-invasive tool to explore spatio-temporal dynamics of brain activity. With EEG recordings consisting of multiple trials, traditional signal processing approaches that ignore inter-trial variability in the data may fail to accurately estimate the underlying spatio-temporal brain patterns. Moreover, precise characterization of such inter-trial variability per se can be of high scientific value in establishing the relationship between brain activity and behavior. In this paper, a statistical modeling framework is introduced for learning spatio-temporal decompositions of multiple-trial EEG data recorded under two contrasting experimental conditions. By modeling the variance of source signals as random variables varying across trials, the proposed two-stage hierarchical Bayesian model is able to capture inter-trial amplitude variability in the data in a sparse way where a parsimonious representation of the data can be obtained. A variational Bayesian (VB) algorithm is developed for statistical inference of the hierarchical model. The efficacy of the proposed modeling framework is validated with the analysis of both synthetic and real EEG data. In the simulation study we show that even at low signal-to-noise ratios our approach is able to recover with high precision the underlying spatio-temporal patterns and the dynamics of source amplitude across trials; on two brain–computer interface (BCI) data sets we show that our VB algorithm can extract physiologically meaningful spatio-temporal patterns and make more accurate predictions than other two widely used algorithms: the common spatial patterns (CSP) algorithm and the Infomax algorithm for independent component analysis (ICA). The results demonstrate that our statistical modeling framework can serve as a powerful tool for extracting brain patterns, characterizing trial-to-trial brain dynamics, and decoding brain states by exploiting useful structures in the data. [Copyright &y& Elsevier]

Abstract: We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen’s theorem for correlated probability, classification of random sets by likelihood ratio tests, decomposition of complexity and independence, and Bayesian statistics for individual random sequences. Formerly Lambalgen’s theorem for correlated probability is shown under a uniform computability assumption in [H. Takahashi Inform. Compt. 2008]. In this paper we show the theorem without the assumption. [ABSTRACT FROM AUTHOR]

Abstract: The single-particle reconstruction problem of electron cryo-microscopy (cryo-EM) is to find the three-dimensional structure of a macromolecule given its two-dimensional noisy projection images at unknown random directions. Ab initio estimates of the 3D structure are often obtained by the “Angular Reconstitution” method, in which a coordinate system is established from three projections, and the orientation of the particle giving rise to each image is deduced from common lines among the images. However, a reliable detection of common lines is difficult due to the low signal-to-noise ratio of the images. In this paper we describe a global self-correcting voting procedure in which all projection images participate to decide the identity of the consistent common lines. The algorithm determines which common line pairs were detected correctly and which are spurious. We show that the voting procedure succeeds at relatively low detection rates and that its performance improves as the number of projection images increases. We demonstrate the algorithm for both simulative and experimental images of the 50S ribosomal subunit. [Copyright &y& Elsevier]

Abstract: This paper introduces DANGLE, a new algorithm that employs Bayesian inference to estimate the likelihood of all possible values of the backbone dihedral angles ϕ and ψ for each residue in a query protein, based on observed chemical shifts and the conformational preferences of each amino acid type. The method provides robust estimates of ϕ and ψ within realistic boundary ranges, an indication of the degeneracy in the relationship between shift measurements and conformation at each site, and faithful secondary structure state assignments. When a simple degeneracy-based filtering procedure is applied, DANGLE offers an ideal compromise between accuracy and coverage when compared with other shift-based dihedral angle prediction methods. In addition, per residue analysis of shift/structure degeneracy has potential to be a useful new approach for studying the properties of unfolded proteins, with sufficient sensitivity to identify regions of residual structure in the acid denatured state of apomyoglobin. [Copyright &y& Elsevier]

Abstract: The synchronous brain activity measured via MEG (or EEG) can be interpreted as arising from a collection (possibly large) of current dipoles or sources located throughout the cortex. Estimating the number, location, and time course of these sources remains a challenging task, one that is significantly compounded by the effects of source correlations and unknown orientations and by the presence of interference from spontaneous brain activity, sensor noise, and other artifacts. This paper derives an empirical Bayesian method for addressing each of these issues in a principled fashion. The resulting algorithm guarantees descent of a cost function uniquely designed to handle unknown orientations and arbitrary correlations. Robust interference suppression is also easily incorporated. In a restricted setting, the proposed method is shown to produce theoretically zero reconstruction error estimating multiple dipoles even in the presence of strong correlations and unknown orientations, unlike a variety of existing Bayesian localization methods or common signal processing techniques such as beamforming and sLORETA. Empirical results on both simulated and real data sets verify the efficacy of this approach. [Copyright &y& Elsevier]

Abstract: Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis–Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time. [Copyright &y& Elsevier]

This paper derives and evaluates an algorithm for estimating normal covariances. A particular concern is the performance of the estimator when the dimension of the space exceeds the number of observations. The algorithm is simple, tolerably well founded, and seems to be more accurate for its purpose than the alternatives. Other topics discussed are the joint estimation of variances in one and many dimensions; the loss function appropriate to a variance estimator; and its connection with a certain Bayesian prescription. [Copyright &y& Elsevier]

An inductive inference problem will often be structured so that the target variable (hypotheses) are logically distant from the observable events (data). In this situation it may be difficult or impossible to assess the probabilistic connection between them, but it may be possible to decompose the problem through the use of intermediate or explanatory variables. That is, it will often be possible to assess the likelihood of the observed data given some intermediate variable, and the likelihood of that intermediate variable given another, and so on, until the hypotheses of interest are reached. Inferences which incorporate one or more intermediate variables are called hierarchical, cascaded, or multistage inferences. The present paper presents a normative model for the solution of the general hierarchical inference problem. The formulation begins with a formal description of the hierarchical inference tree, including a discussion of various simplifying conditional independence assumptions. The solution is first derived for three special case models of differing structure, and then the algorithm for the general solution is given for two cases: one in which the conditional independence assumptions have been made and one in which they have not. [ABSTRACT FROM AUTHOR]