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Bayesian network meta-analysis will be conducted using STATA V.14.0 and WinBUGS V.1.4.3 to compare the efficacy of different acupuncture methods for diabetic peripheral neuropathy (DPN).

Bayesian methods of inference are the appropriate statistical tools for providing interval estimates in practice. The example presented here illustrates the relative ease with which Bayesian models can be implemented using simulation techniques to approximate posterior distributions but also shows that these techniques cannot be automatically applied to arrive at sound inferences. In particular, the example dramatizes three important messages. The first two messages are concrete and easily stated: Although the log normal model is often used to estimate the total on the raw scale (e.g., estimate total oil reserves assuming the logarithm of the values are normally distributed), the log normal model may not provide realistic inferences even when it appears to fit fairly well as judged from probability plots. Extending the log normal family to a larger family, such as the Box-Cox family of power transformations, and selecting a better fitting model by likelihood criteria or probability plots, may lead to less realistic inferences for the population total, even when probability plots indicate an adequate fit. In general, inferences are sensitive to features of the underlying distribution of values in the population that cannot be addressed by the data.

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

High-dimensional Bayesian variable selection problems are often solved using computationally expensive Markov Chain Montle Carlo (MCMC) techniques. Recently, a Bayesian variable selection technique was developed for continuous data using the EM algorithm called EMVS. We extend the EMVS method to binary data by proposing both a logistic and probit extension. To preserve the computational speed of EMVS we also implemented the Stochastic Dual Coordinate Descent (SDCA) algorithm. Further, we conduct two extensive simulation studies to show the computational speed of both methods. These simulation studies reveal the power of both methods to quickly identify the correct sparse model. When these EMVS methods are compared to Stochastic Search Variable Selection (SSVS), the EMVS methods surpass SSVS both in terms of computational speed and correctly identifying significant variables. Finally, we illustrate the effectiveness of both methods on two well-known gene expression datasets. Our results mirror the results of previous examinations of these datasets with far less computational cost.

High-dimensional Bayesian variable selection problems are often solved using computationally expensive Markov Chain Montle Carlo (MCMC) techniques. Recently, a Bayesian variable selection technique was developed for continuous data using the EM algorithm called EMVS. We extend the EMVS method to binary data by proposing both a logistic and probit extension. To preserve the computational speed of EMVS we also implemented the Stochastic Dual Coordinate Descent (SDCA) algorithm. Further, we conduct two extensive simulation studies to show the computational speed of both methods. These simulation studies reveal the power of both methods to quickly identify the correct sparse model. When these EMVS methods are compared to Stochastic Search Variable Selection (SSVS), the EMVS methods surpass SSVS both in terms of computational speed and correctly identifying significant variables. Finally, we illustrate the effectiveness of both methods on two well-known gene expression datasets. Our results mirror the results of previous examinations of these datasets with far less computational cost.

Discussion of "Bayesian Models and Methods in Public Policy and Government Settings" by S. E. Fienberg [arXiv:1108.2177]

Determination of the minimum inhibitory concentration (MIC) of a drug that prevents microbial growth is an important step for managing patients with infections. In this paper we present a novel probabilistic approach that accurately estimates MICs based on a panel of multiple curves reflecting features of bacterial growth. We develop a probabilistic model for determining whether a given dilution of an antimicrobial agent is the MIC given features of the growth curves over time. Because of the potentially large collection of features, we utilize Bayesian model selection to narrow the collection of predictors to the most important variables. In addition to point estimates of MICs, we are able to provide posterior probabilities that each dilution is the MIC based on the observed growth curves. The methods are easily automated and have been incorporated into the Becton--Dickinson PHOENIX automated susceptibility system that rapidly and accurately classifies the resistance of a large number of microorganisms in clinical samples. Over seventy-five studies to date have shown this new method provides improved estimation of MICs over existing approaches.

We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function $f$ of $\theta$. How do we efficiently estimate the posterior expectation of $f(\theta)$ simultaneously for all $h$ in $\mathcal{H}$? The second problem is how do we identify subsets of $\mathcal{H}$ which give rise to reasonable choices of $\nu_h$? We assume that we are able to generate Markov chain samples from the posterior for a finite number of the priors, and we develop a methodology, based on a combination of importance sampling and the use of control variates, for dealing with these two problems. The methodology applies very generally, and we show how it applies in particular to a commonly used model for variable selection in Bayesian linear regression, and give an illustration on the US crime data of Vandaele.

This is a network meta-analysis to investigate the efficacy and safety of acupuncture methods for nonspecific low back pain. We will compare acupuncture methods for nonspecific low back pain by bayesian network meta‑analysis and rank the priority of acupuncture methods to assess the efficacy and safety of diverse acupuncture methods for nonspecific low back pain treatment.

The long term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation, inversion for sound-speed in the water-column, and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for inversion via the extraction of features of the acoustic field and optimization. The potential of analytic approaches is also investigated.

The long term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation, inversion for sound-speed in the water-column, and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for inversion via the extraction of features of the acoustic field and optimization. The potential of analytic approaches is also investigated.

The long term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation, inversion for sound-speed in the water-column, and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for inversion via the extraction of features of the acoustic field and optimization. The potential of analytic approaches is also investigated.

We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub-Kahan bidiagonalization for computing Tikhonov regularized solutions to problems where explicit computation of the square root and inverse of the covariance kernel for the prior covariance matrix is not feasible. This is useful for large-scale problems where covariance kernels are defined on irregular grids or are only available via matrix-vector multiplication, e.g., those from the Mat\'{e}rn class. We show that iterates are equivalent to LSQR iterates applied to a directly regularized Tikhonov problem, after a transformation of variables, and we provide connections to a generalized singular value decomposition filtered solution. Our approach shares many benefits of standard hybrid methods such as avoiding semi-convergence and automatically estimating the regularization parameter. Numerical examples from image processing demonstrate the effectiveness of the described approaches.

A series system is simulated to obtain lower confidence limits on system reliability using Bayesian techniques. A comparison between classical and Bayesian methods is made. Random beta variate generators are developed and used in the simulation. The results of the simulation are tabulated for easy comparison of the Bayesian and classical methods. The values of lower confidence limits that are realized using the Bayesian method decrease as the number of components increase. In most cases, as the number of components increase, the Bayesian method appears to yield lower values of lower confidence limits than the classical method.

Bayesian methods for statistical analysis is a book on statistical methods for analysing a wide variety of data. The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchical models, Markov chain Monte Carlo methods, finite population inference, biased sampling and nonignorable nonresponse. The book contains many exercises, all with worked solutions, including complete computer code. It is suitable for self-study or a semester-long course, with three hours of lectures and one tutorial per week for 13 weeks.

In this paper, we introduce efficient ensemble Markov Chain Monte Carlo (MCMC) sampling methods for Bayesian computations in the univariate stochastic volatility model. We compare the performance of our ensemble MCMC methods with an improved version of a recent sampler of Kastner and Fruwirth-Schnatter (2014). We show that ensemble samplers are more efficient than this state of the art sampler by a factor of about 3.1, on a data set simulated from the stochastic volatility model. This performance gain is achieved without the ensemble MCMC sampler relying on the assumption that the latent process is linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter.

Cognitive radio is an exciting wireless technology that has been introduced for the efficient used of spectrum. Using cognitive radios (CRs), the secondary users (unlicensed users) are allowed to use the spectrum which is originally allocated to primary users (PUs) as far as the active primary users are not using it temporarily. In order to prevent harmful interference to primary users, the SUs need to perform spectrum sensing before transmitting signal over the spectrum. In this paper we use an optimal Bayesian detector for digitally modulated primary user to improve the spectrum utilization, without prior knowledge of transmitted sequence of the primary signals. And further suboptimal detectors in low and high SNR regime. We provide the performance analysis in terms of Detection probability and False alarm probability. Abdul Hameed Ansari | Narode Sweety S."Performance Analysis of Bayesian Methods to for the Spectrum Utilization in Cognitive Radio" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-5 , August 2017, URL: http://www.ijtsrd.com/papers/ijtsrd2385.pdf Article URL: http://www.ijtsrd.com/engineering/electronics-and-communication-engineering/2385/performance-analysis-of-bayesian-methods-to-for-the-spectrum-utilization-in-cognitive-radio/abdul-hameed-ansari

This article is from BMC Proceedings , volume 5 . Abstract Background: Bayesian methods allow prediction of genomic breeding values (GEBVs) using high-density single nucleotide polymorphisms (SNPs) covering the whole genome with effective shrinkage of SNP effects using appropriate priors. In this study we applied a modification of the well-known BayesA and BayesB methods to estimate the proportion of SNPs with zero effects (π) and a common variance for non-zero effects. The method, termed BayesCπ, was used to predict the GEBVs of the last generation of the QTLMAS2010 data. The accuracy of GEBVs from various methods was estimated by the correlation with phenotypes in the last generation. The methods were BayesCPi and BayesB with different π values, both with and without polygenic effects, and best linear unbiased prediction using an animal model with a genomic or numerator relationship matrix. Positions of quantitative trait loci (QTLs) were identified based on the variances of GEBVs for windows of 10 consecutive SNPs. We also proposed a novel approach to set significance thresholds for claiming QTL in this specific case by using pedigree-based simulation of genotypes. All analyses were focused on detecting and evaluating QTL with additive effects. Results: The accuracy of GEBVs was highest for BayesCπ, but the accuracy of BayesB with π equal to 0.99 was similar to that of BayesCπ. The accuracy of BayesB dropped with a decrease in π. Including polygenic effects into the model only had marginal effects on accuracy and bias of predictions. The number of QTL identified was 15 when based on a stringent 10% chromosome-wise threshold and increased to 21 when a 20% chromosome-wise threshold was used. Conclusions: The BayesCπ method without polygenic effects was identified to be the best method for the QTLMAS2010 dataset, because it had highest accuracy and least bias. The significance criterion based on variance of 10-SNP windows allowed detection of more than half of the QTL, with few false positives.

In this final report, a summary of main results is given for research in the following areas: (a) development of techniques for the analysis and decomposition of seasonal time series; (b) modeling and analysis of univariate and multiple time series; (c) robustness in statistical analysis; and (d) a unified theory of statistical inference and criticism.

The long-term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation, inversion for sound-speed in the water-column, and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for inversion via the extraction features of the acoustic field and optimization. The potential of analytic approaches also is investigated. Our specific objectives are as follows: (1) Achieve accurate and computationally efficient inversion for propagation medium parameters and source localization by designing estimation schemes that combine acoustic field and statistical modeling, (2) Develop methods for passive localization and inversion of environmental parameters that select features of propagation that are essential to model for accurate inversion, (3) Implement Bayesian filtering methods that provide dynamic and efficient solutions for the first two objectives, and (4) Develop analytic techniques for sediment sound speed estimation. Continuing efforts from previous years, we worked with Bayesian approaches applied to sound signals for the extraction of acoustic features using a combination of physics and statistical signal processing. One of the topics approached this past year was source localization, bathymetry, and water column sound speed estimation using arrival time estimates for propagation in multipath environments with sequential Monte Carlo methods, tied with a linearization method with novel features. The initial goal is to estimate accurately the arrival times of sound paths in shallow water environments. Then, we propagate these arrival times and their posterior PDFs through a quasilinear model for source location, bathymetry, and water column sound speed profile estimation. Finally, we worked on a new sediment sound speed estimation scheme based on Stickler's inverse problem approach.

The long-term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation, inversion for sound-speed in the water-column, and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for inversion via the extraction features of the acoustic field and optimization. The potential of analytic approaches also is investigated. Our specific objectives are as follows: (1) Achieve accurate and computationally efficient inversion for propagation medium parameters and source localization by designing estimation schemes that combine acoustic field and statistical modeling, (2) Develop methods for passive localization and inversion of environmental parameters that select features of propagation that are essential to model for accurate inversion, (3) Implement Bayesian filtering methods that provide dynamic and efficient solutions for the first two objectives, and (4) Develop analytic techniques for sediment sound speed estimation. Continuing efforts from previous years, we worked with Bayesian approaches applied to sound signals for the extraction of acoustic features using a combination of physics and statistical signal processing. One of the topics approached this past year was source localization, bathymetry, and water column sound speed estimation using arrival time estimates for propagation in multipath environments with sequential Monte Carlo methods, tied with a linearization method with novel features. The initial goal is to estimate accurately the arrival times of sound paths in shallow water environments. Then, we propagate these arrival times and their posterior PDFs through a quasilinear model for source location, bathymetry, and water column sound speed profile estimation. Finally, we worked on a new sediment sound speed estimation scheme based on Stickler's inverse problem approach.

The long-term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation, inversion for sound-speed in the water-column, and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for inversion via the extraction features of the acoustic field and optimization. The potential of analytic approaches also is investigated. Our specific objectives are as follows: (1) Achieve accurate and computationally efficient inversion for propagation medium parameters and source localization by designing estimation schemes that combine acoustic field and statistical modeling, (2) Develop methods for passive localization and inversion of environmental parameters that select features of propagation that are essential to model for accurate inversion, (3) Implement Bayesian filtering methods that provide dynamic and efficient solutions for the first two objectives, and (4) Develop analytic techniques for sediment sound speed estimation. Continuing efforts from previous years, we worked with Bayesian approaches applied to sound signals for the extraction of acoustic features using a combination of physics and statistical signal processing. One of the topics approached this past year was source localization, bathymetry, and water column sound speed estimation using arrival time estimates for propagation in multipath environments with sequential Monte Carlo methods, tied with a linearization method with novel features. The initial goal is to estimate accurately the arrival times of sound paths in shallow water environments. Then, we propagate these arrival times and their posterior PDFs through a quasilinear model for source location, bathymetry, and water column sound speed profile estimation. Finally, we worked on a new sediment sound speed estimation scheme based on Stickler's inverse problem approach.

The development of progress plans for each identified technical performance parameter (TPP) is a critical element of technical performance measurement. The measured values of TPPs are referred to as technical performance measures (TPMs). These terms are used interchangeably; however, TPMs more directly reflect how technical progress and technical risk are measured and evaluated. Progress plans, or planned performance profiles, are crucial to effective risk assessment; however, methods for developing these plans are subjective in nature, have no statistical basis or criteria as a rule, and are not sufficiently addressed in literature. The methodology proposed herein for progress plan development will involve the elicitation of expert judgments to formulate probability distributions that reflect the expected values/estimates used to establish progress plans.

The development of progress plans for each identified technical performance parameter (TPP) is a critical element of technical performance measurement. The measured values of TPPs are referred to as technical performance measures (TPMs). These terms are used interchangeably; however, TPMs more directly reflect how technical progress and technical risk are measured and evaluated. Progress plans, or planned performance profiles, are crucial to effective risk assessment; however, methods for developing these plans are subjective in nature, have no statistical basis or criteria as a rule, and are not sufficiently addressed in literature. The methodology proposed herein for progress plan development will involve the elicitation of expert judgments to formulate probability distributions that reflect the expected values/estimates used to establish progress plans.

The general problem of drawing inferences from uncertain or incomplete evidence has invited a variety of technical approaches, some mathematically rigorous and some largely informal and intuitive. Most current inference systems in artificial intelligence have emphasized intuitive methods because the absence of adequate statistical samples forces a reliance on the subjective judgment of human experts. In this paper, the authors describe a subjective Bayesian inference method that realizes some of the advantages of both formal and informal approaches. Of particular interest are the modifications needed to deal with the inconsistencies usually found in collections of subjective statements.

Cognitive radio is an exciting wireless technology that has been introduced for the efficient used of spectrum. Using cognitive radios (CRs), the secondary users (unlicensed users) are allowed to use the spectrum which is originally allocated to primary users (PUs) as far as the active primary users are not using it temporarily. In order to prevent harmful interference to primary users, the SUs need to perform spectrum sensing before transmitting signal over the spectrum. In this paper we use an optimal Bayesian detector for digitally modulated primary user to improve the spectrum utilization, without prior knowledge of transmitted sequence of the primary signals. And further suboptimal detectors in low and high SNR regime. We provide the performance analysis in terms of Detection probability and False alarm probability. Abdul Hameed Ansari | Narode Sweety S."Performance Analysis of Bayesian Methods to for the Spectrum Utilization in Cognitive Radio" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-5 , August 2017, URL: http://www.ijtsrd.com/papers/ijtsrd2385.pdf Article URL: http://www.ijtsrd.com/engineering/electronics-and-communication-engineering/2385/performance-analysis-of-bayesian-methods-to-for-the-spectrum-utilization-in-cognitive-radio/abdul-hameed-ansari

Minimum mean squared error (MMSE) estimators of signals from samples corrupted by jitter (timing noise) and additive noise are nonlinear, even when the signal prior and additive noise have normal distributions. This paper develops a stochastic algorithm based on Gibbs sampling and slice sampling to approximate the optimal MMSE estimator in this Bayesian formulation. Simulations demonstrate that this nonlinear algorithm can improve significantly upon the linear MMSE estimator, as well as the EM algorithm approximation to the maximum likelihood (ML) estimator used in classical estimation. Effective off-chip post-processing to mitigate jitter enables greater jitter to be tolerated, potentially reducing on-chip ADC power consumption.

Minimum mean squared error (MMSE) estimators of signals from samples corrupted by jitter (timing noise) and additive noise are nonlinear, even when the signal prior and additive noise have normal distributions. This paper develops a stochastic algorithm based on Gibbs sampling and slice sampling to approximate the optimal MMSE estimator in this Bayesian formulation. Simulations demonstrate that this nonlinear algorithm can improve significantly upon the linear MMSE estimator, as well as the EM algorithm approximation to the maximum likelihood (ML) estimator used in classical estimation. Effective off-chip post-processing to mitigate jitter enables greater jitter to be tolerated, potentially reducing on-chip ADC power consumption.

(Jaynes') Method of (Shannon-Kullback's) Relative Entropy Maximization (REM or MaxEnt) can be - at least in the discrete case - according to the Maximum Probability Theorem (MPT) viewed as an asymptotic instance of the Maximum Probability method (MaxProb). A simple bayesian interpretation of MaxProb is given here. MPT carries the interpretation over into REM.

Online survey built via Qualtrics and disseminated via Prolific to gather data relating to the measurement of aggression/aggressive behaviour in the general population

There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves planning in an infinitely large tree. However, it is possible to obtain stochastic lower and upper bounds on the value of each tree node. This enables us to use stochastic branch and bound algorithms to search the tree efficiently. This paper proposes two such algorithms and examines their complexity in this setting.

In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions. Of course, this chapter is only a terse introduction to the problems and solutions related to Bayesian computations. For more complete references, see Robert and Casella (2004, 2009), or Marin and Robert (2007), among others. We also restrain from providing an introduction to Bayesian Statistics per se and for comprehensive coverage, address the reader to Robert (2007), (again) among others.

LONG TERM GOALS: The long term goal of this project is to develop efficient inversion algorithms for successful geoacoustic parameter estimation and source localization, exploiting (fully or partially) the physics of the propagation medium. Algorithms are designed for geoacoustic inversion via the extraction features of the acoustic field. OBJECTIVES: Achieve accurate and computationally efficient geoacoustic inversion and source localization by designing estimation schemes that combine acoustic field modeling and statistical modeling. Develop methods for passive localization and inversion of environmental parameters that select features of propagation that are essential to model for accurate inversion. Implement sequential filtering methods that provide dynamic and efficient solutions for the first two objectives.

Clinical outcome prediction from high-dimensional data is problematic in the common setting where there is only a relatively small number of samples. The imbalance causes data overfitting, and outcome prediction becomes computationally expensive or even impossible. We propose a Bayesian outcome prediction method that can be applied to data of arbitrary dimension d, from 2 outcome classes, and reduces overfitting without any approximations at parameter level. This is achieved by avoiding numerical integration or approximation, and solving the Bayesian integrals analytically. We thereby reduce the dimension of numerical integrals from 2d dimensions to 4, for any d. For large d, this is reduced further to 3, and we obtain a simple outcome prediction formula without integrals in leading order for very large d. We compare our method to the mclustDA method (Fraley and Raftery 2002), using simulated and real data sets. Our method perform as well as or better than mclustDA in low dimensions d. In large dimensions d, mclustDA breaks down due to computational limitations, while our method provides a feasible and computationally efficient alternative.

In this paper we briefly review the main methodological aspects concerned with the application of the Bayesian approach to model choice and model averaging in the context of variable selection in regression models. This includes prior elicitation, summaries of the posterior distribution and computational strategies. We then examine and compare various publicly available {\tt R}-packages for its practical implementation summarizing and explaining the differences between packages and giving recommendations for applied users. We find that all packages reviewed lead to very similar results, but there are potentially important differences in flexibility and efficiency of the packages.

We discuss the Hessian PDF reweighting - a technique intended to estimate the effects that new measurements have on a set of PDFs. The method stems straightforwardly from considering new data in a usual $\chi^2$-fit and it naturally incorporates also non-zero values for the tolerance, $\Delta\chi^2>1$. In comparison to the contemporary Bayesian reweighting techniques, there is no need to generate large ensembles of PDF Monte-Carlo replicas, and the observables need to be evaluated only with the central and the error sets of the original PDFs. In spite of the apparently rather different methodologies, we find that the Hessian and the Bayesian techniques are actually equivalent if the $\Delta\chi^2$ criterion is properly included to the Bayesian likelihood function that is a simple exponential.

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.

Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and real datasets. This comparison includes new global noninformative approaches for Bayesian variable selection built on Zellner's g-priors that are similar to Liang et al. (2008). The interest of those calibration-free proposals is discussed. The numerical experiments we present highlight the appeal of Bayesian regularization methods, when compared with non-Bayesian alternatives. They dominate frequentist methods in the sense that they provide smaller prediction errors while selecting the most relevant variables in a parsimonious way.

Unsupervised learning of linguistic structure is a difficult task. Frequently, standard techniques such as maximum-likelihood estimation yield poor results or are simply inappropriate (as when the class of models under consideration includes models of varying complexity). In this talk, I discuss how Bayesian statistical methods can be applied to the problem of unsupervised language learning to develop principled model-based systems and improve results. I first present some work on word segmentation, showing that maximum-likelihood estimation is inappropriate for this task and discussing a nonparametric Bayesian modeling solution. I then argue, using part-of-speech tagging as an example, that a Bayesian approach provides advantages even when maximum-likelihood (or maximum a posteriori) estimation is possible. I conclude by discussing some of the challenges that remain in pursuing a Bayesian approach to language learning. ©2007 Microsoft Corporation. All rights reserved.

In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique contributions. First, we explore the space using low discrepancy point sets instead of a grid. This allows for accurate estimation of marginals of any shape at a much lower computational cost than a grid based approach and thus makes it possible to extend the computational benefit to a hyper parameter space with higher dimensionality (10 or more). Second, we propose a new, quick and easy method to estimate the marginal using a least squares polynomial and prove the conditions under which this polynomial will converge to the true marginal. Our results are valid for a wide range of point sets including grids, random points and low discrepancy points. Third, we show that further accuracy and efficiency can be gained by taking into consideration the functional decomposition of the integrand and illustrate how this can be done using anchored f-ANOVA on weighted spaces.

Parameter ensembles or sets of random effects constitute one of the cornerstones of modern statistical practice. This is especially the case in Bayesian hierarchical models, where several decision theoretic frameworks can be deployed. The estimation of these parameter ensembles may substantially vary depending on which inferential goals are prioritised by the modeller. Since one may wish to satisfy a range of desiderata, it is therefore of interest to investigate whether some sets of point estimates can simultaneously meet several inferential objectives. In this thesis, we will be especially concerned with identifying ensembles of point estimates that produce good approximations of (i) the true empirical quantiles and empirical quartile ratio (QR) and (ii) provide an accurate classification of the ensemble's elements above and below a given threshold. For this purpose, we review various decision-theoretic frameworks, which have been proposed in the literature in relation to the optimisation of different aspects of the empirical distribution of a parameter ensemble. This includes the constrained Bayes (CB), weighted-rank squared error loss (WRSEL), and triple-goal (GR) ensembles of point estimates. In addition, we also consider the set of maximum likelihood estimates (MLEs) and the ensemble of posterior means --the latter being optimal under the summed squared error loss (SSEL). Firstly, we test the performance of these different sets of point estimates as plug-in estimators for the empirical quantiles and empirical QR under a range of synthetic scenarios encompassing both spatial and non-spatial simulated data sets. Performance evaluation is here conducted using the posterior regret. Secondly, two threshold classification losses (TCLs) --weighted and unweighted-- are formulated and formally optimised. The performance of these decision-theoretic tools is also evaluated on real data sets.

This thesis explores the use of Bayesian statistical postprocessing to rapidly train a highly accurate forecast from a 1 km resolution gridded WRF model forecast over a 100 km by 100 km area. These methods leverage three modeled forecast variables—10 m winds, sea-level pressure, and terrain elevation—in conjunction with downstream observations and prior model runs to identify model inaccuracies. Using only three days of data, a Bayesian corrected forecast is produced and analyzed for accuracy and improvement over the original model run relative to real-world observations. Over 90% of the resulting forecasts saw improvement over the raw model forecasts in root mean squared error, and over 87% of the forecasts saw improvement in mean error over the raw model forecasts. Extreme circumstances saw improvements in accuracy of over 9 knots while overall improvements were reliably seen both in accuracy and precision among Bayesian corrected forecasts. These findings are significant as they suggest that Bayesian statistical postprocessing methods work and should be both employable at rapid rates, and result in more accurate forecasts.

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to Bayesian model selection problems. The new algorithm is tested through a change-point identification example. The numerical results indicate that the new algorithm can outperform SAMC and reversible jump MCMC significantly for the model selection problems. The new algorithm represents a general form of the stochastic approximation Markov chain Monte Carlo algorithm. It allows multiple samples to be generated at each iteration, and a bias term to be included in the parameter updating step. A rigorous proof for the convergence of the general algorithm is established under verifiable conditions. This paper also provides a framework on how to improve efficiency of Monte Carlo simulations by incorporating some nonparametric techniques.

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to Bayesian model selection problems. The new algorithm is tested through a change-point identification example. The numerical results indicate that the new algorithm can outperform SAMC and reversible jump MCMC significantly for the model selection problems. The new algorithm represents a general form of the stochastic approximation Markov chain Monte Carlo algorithm. It allows multiple samples to be generated at each iteration, and a bias term to be included in the parameter updating step. A rigorous proof for the convergence of the general algorithm is established under verifiable conditions. This paper also provides a framework on how to improve efficiency of Monte Carlo simulations by incorporating some nonparametric techniques.

The feasibility and effectiveness of a Bayesian method for estimating regressions in m groups is studied by application of the method to data from the Basic Research Service of The American College Testing Program. Evidence supports the belief that in many testing applications the collateral information obtained from each subset of m-1 colleges will be useful for the estimation of the regression in the m-th college. Specifically, on cross-validation in a second sample, the Bayesian predictions had a smaller mean squared error in each of 22 colleges, the reduction averaging 9.7%, when compared with the least squares predictions when four predictor variables were used on a quarter sample in the 22 colleges where initial within-college sample sizes ranged from 26 to 184. Furthermore, even when based on the full sample within each college, the least squares predictions had an average cross-validated mean squared error only barely less than the Bayesian predictions based on the quarter sample. The most apparent benefit of the Bayesian method is that it permits regression to be done in subpopulations where sample sizes are small and where the regressions are different in the subpopulations. In the present study, a decrease of more than 10% in mean squared error was obtained using this approach. (Author)

Norman Fenton's 45 minute The James Hutton Institute Seminar, Aberdeen 27 September 2023

This research develops a new Bayesian technique for the detection of scattering primitives in synthetic aperture radar (SAR) phase history data received from a sensor platform. The primary goal of this research is the estimation of size, position, and orientation parameters defined by the ?canonical? shape primitives of Jackson. Previous Bayesian methods for this problem have focused on the traditional maximum a posteriori (MAP) estimate based on the posterior density. A new concept, the probability mass interval, is developed. In this technique the posterior density is partitioned into intervals, which are then integrated to form a probability mass over that interval using the Gaussian quadrature numerical integration techniques. The posterior density is therefore discretized in such a way that the location of local peaks are preserved. A formal treatment is given to the effect of locally integrating the posterior density in the context of parameter estimation. It is shown that the operation of choosing the interval with the highest probability mass is equivalent to an optimum Bayesian estimator that places zero cost on a ?range? of parameters. The range is user-controlled, and is akin to the idea of parameter resolution. Additionally the peak-preserving property allows the user to begin with coarse intervals and ?zoom? in as they see fit. Associated with these estimates is a measure of quality called the credible interval (or credible set). The credible interval (set) is a region of parameter space where the ?true? parameter is located with a user-defined probability. Narrow credible intervals are associated with high-quality estimates while wide credible intervals are associated with poor estimates. The techniques are implemented in state-of-the-art graphics processor unit (GPU) hardware, which allows the numerical integration to be performed in a reasonable time. A typical estimator requires several hundred million computations and the GPU implementa

To understand their data better, astronomers need to use statistical tools that are more advanced than traditional ``freshman lab'' statistics. As an illustration, the problem of combining apparently incompatible measurements of a quantity is presented from both the traditional, and a more sophisticated Bayesian, perspective. Explicit formulas are given for both treatments. Results are shown for the value of the Hubble Constant, and a 95% confidence interval of 66 < H0 < 82 (km/s/Mpc) is obtained.

This systematic review and Bayesian network meta-analysis will compare the effects of different advanced methods of resistance training (i.e., flywheel training, accentuated eccentric loading, accommodating resistance, potentiation complexes, rest redistribution schemes, supersets, and dropsets) on strength, power, hypertrophy, jump, and sprint adaptations within healthy adults.

We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data $\delta$. Particular attention is given to bounds on the overall work required to achieve a prescribed error level $\varepsilon$. Specifically, we first bound the computational complexity of "plain" MCMC, based on combining MCMC sampling with linear complexity multilevel solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) "surrogate" representation of the forward response map of the PDE over the entire parameter space, and, second, a novel Multi-Level Markov Chain Monte Carlo (MLMCMC) strategy which utilizes sampling from a multilevel discretization of the posterior and of the forward PDE. For both of these strategies we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular we provide sufficient conditions on the regularity of the unknown coefficients of the PDE, and on the approximation methods used, in order for the accelerations of MCMC resulting from these strategies to lead to complexity reductions over "plain" MCMC algorithms for Bayesian inversion of PDEs.}

1Thaw

By Edward Thomas

LibriVox volunteers bring you 11 recordings of <em>Thaw</em> by Edward Thomas. This was the weekly poetry project for March 1st, 2009.

LibriVox volunteers bring you 13 recordings of <em>When First I Came Here</em> by Edward Thomas. This was the weekly poetry project for July 19th, 2009.

LibriVox volunteers bring you 7 recordings of Adlestrop by Edward Thomas. This was the Weekly Poetry project for September 20th, 2009.

William Griffith Thomas was a pastor, teacher and co-founder of the Dallas Theological Seminary. This book contains nine devotional commentaries on prayers from Paul's letters to the churches at Thessalonica, Colossi and Ephesus. Thomas is theologically conservative. His commentaries both look at the meaning of the text and apply it to the heart. Summary by MaryAnn.

Edith Matilda Thomas (August 12, 1854 – September 13, 1925) was an American poet who "was one of the first poets to capture successfully the excitement of the modern city." This poem taken from the The Little Book of Modern Verse. 1917.; Jessie B. Rittenhouse, ed. (1869–1948) - Summary by Wikipedia

6What The Pine Trees Said

By Edith M. Thomas

Edith Matilda Thomas was an American poet who "was one of the first poets to capture successfully the excitement of the modern city. (Wikipedia)

7Charley's Aunt

By Brandon Thomas

The girlfriends are coming to visit the chaps at college, but of course they can't stay unless there is a proper chaperone. So what could be more reasonable that getting a friend from the Drama Club to dress up and pretend to be Charley's Aunt? Simple and sure to work! What could go wrong? Howsabout the real aunt arriving? This play has been revived and adapted numerous times including as films, a Broadway musical, and even an opera. (NOTE: the script contains an almost overwhelming number of stage directions by the author telling each actor what emotion to show, where to move, and even how to create some of the visual effects. Because the directions give a good idea of the on-stage pandemonium one would see at a production of this farce, I have chosen to leave the directions in this audio performance.) - Summary by ToddHW <BR><BR>Cast list:<BR> STEPHEN SPETTIGUE, Solicitor, Oxford: <a href="https://librivox.org/reader/12500">Foon</a><br> COLONEL SIR FRANCIS CHESNEY, BART., Late Indian Service: <a href="https://librivox.org/reader/8425">Larry Wilson</a><br> JACK CHESNEY, Graduate at St. Olde's College, Oxford: <a href="https://librivox.org/reader/12431">Tom Daley</a><br> CHARLEY WYKEHAM, Graduate at St. Olde's College, Oxford: <a href="https://librivox.org/reader/11905">Wolfgang Bas</a><br> LORD FANCOURT BABBERLEY, Graduate at St. Olde's College, Oxford: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> BRASSETT, A College Scout: <a href="https://librivox.org/reader/6754">ToddHW</a><br> DONNA-LUCIA D'ALVADOREZ, From Brazil: <a href="https://librivox.org/reader/10179">Sonia</a><br> AMY SPETTIGUE, Spettigue's Niece: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> KITTY VERDUN, Spettigue's Ward: <a href="https://librivox.org/reader/6281">Beth Thomas</a><br> ELA DELAHAY: <a href="https://librivox.org/reader/11790">TJ Burns</a><br> Stage Directions: <a href="https://librivox.org/reader/11084">Devorah Allen</a><br> Edited by: <a href="https://librivox.org/reader/6754">ToddHW</a>

8Poems by Edward Thomas

By Edward Thomas

Born in 1878, Thomas published his first book when he was 18. Having married while still at university, he supported his family by writing articles and books, some in the form of what we might call slow travel writing, compiled on walks throughout England and Wales. He came to poetry late, encouraged by Robert Frost, and wrote 144 poems between 1914, and 1917 when he was killed, two years after enlisting, and shortly after arriving in France. <br><br> His poetic life coincided with WW1, and though not a war poet, his is the poetry of loss, of life as it would never be again. What is powerful to the English imagination is his depiction of the fragility of the English countryside. This is inseparable from his deep understanding of the longings and regrets of those who would die. Transience and mortality are at the heart of his work. This is true in one of the country’s favourite poems, to be found on this recording: Adlestrop. He is important to other poets in that, at his best, his poetry is quietly, sometimes coldly, conversational, with a slow beat that takes us with him as he thinks through from line to line, and wraps us in his vision of life and the natural world. (Summary by Judith Brennan)

Jātaka tales are ancient Indian folktales that form a part of Buddhist teaching, telling stories of the Buddha’s past lives. Akin to Aesop’s fables, some strikingly similar, they urge the listener to moral behavior and often, more than that, point a way to real insight. - Summary by Scotty Smith

Two fifteen-year-old boys---the younger of whom may have been fourteen---decide to hunt and trap away from home in the north woods of Maine. A true recounting of their adventures can be found here, though the years that passed before the tale was written down may have added a slight bit of exaggeration. Then again, they set out in the winter of 1875 and all that's written could very well be the complete and honest truth! The listener may wish to listen first to Section 18 of this recording---Notes on Maine Animals---as familiarity with these will enhance an understanding of the memoir.

An explanation of the concept of industrial democracy and its relation to capitalism. (Summary by progressingamerica)

12George Sand

By Bertha Thomas

A Victorian Novelist herself, Bertha Thomas presents a biography of the Life of George Sand - Summary by Christine Rottger

A superior Victorian Romance. Full from bow to stern with secret romance, jealousies and confrontations of culture and cultures. This authors' work contain an abundance of charm and engaging dialogue. - Summary by Christine Rottger

This collection celebrates the marigold in verse from the 17th through the 20th centuries. - Summary by Newgatenovelist

In terms of population, in terms of development and in terms of wealth, Victoria boomed in the 1850s and 1860s due to the Gold Rush. Undeniably, the colony had money to burn. Surprise port visits by the Russian corvette Bogatyr and the Confederate warship Shenandoah in the 1860s awakened in Victoria a deep sense of vulnerability, and Victorians set their minds to a new domestic project – a decades long pursuit of security. That effort would ultimately give rise to extensive coastal fortifications, militia and artillery formations both voluntary and professional, sea mines, and a small but not inconsequential naval flotilla whose backbone would be the formidable ironclad H.M.V.S. Cerberus. Not that these efforts were confined to Victoria alone. The not-infrequently perilous straits of the Mother Country as it navigated the treacherous shoals of European politics and global empire provided ample reasons for insomnia. To varying degrees the other states too had constituted forces, and most made a start at acquiring ‘warships’—an assemblage tending more to the ‘dinky’ side than that term might otherwise suggest. But where naval matters were concerned New South Wales made something of a false start, while Queensland and South Australia simply started late. Whether this is because the issue didn’t resonate as much in the other colonies, or whether Victoria simply had larger resources to sink into an inherently (economically) unproductive project is not immediately obvious. Efforts _were_ made in all the colonies, however and joint defence and a federal fleet would be a not insignificant impetus towards Federation. The Australian colonies would largely abandon armaments acquisition with the depression of the 1890s, but the arrival of Theodore Roosevelt’s Great White Fleet in 1908 exercised popular imagination, and the recently federated Commonwealth of Australia set about acquiring a new navy. This new Royal Australian Navy, lead by the battle-cruiser HMAS Australia, steamed into Sydney Harbour for the first time in late 1913. This new institution would be tested far more strenuously than the naval forces of the unfederated colonies ever were. My appreciation to the [url=” https://www.cerberus.com.au/index.html]”Friends of the Cerberus[/url] for their extensive online resources. - Summary by Alister