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While perception tasks such as visual object recognition and text understanding play an important role in human intelligence, the subsequent tasks that involve inference, reasoning and planning require an even higher level of intelligence. The past few years have seen major advances in many perception tasks using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. To achieve integrated intelligence that involves both perception and inference, it is naturally desirable to tightly integrate deep learning and Bayesian models within a principled probabilistic framework, which we call Bayesian deep learning. In this unified framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in return, the feedback from the inference process is able to enhance the perception of text or images. This paper proposes a general framework for Bayesian deep learning and reviews its recent applications on recommender systems, topic models, and control. In this paper, we also discuss the relationship and differences between Bayesian deep learning and other related topics like Bayesian treatment of neural networks.

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.

After a derivation of the quantum Bayes theorem, and a discussion of the reconstruction of the unknown state of identical spin systems by repeated measurements, the main part of this paper treats the problem of determining the unknown phase difference of two coherent sources by photon measurements. While the approach of this paper is based on computing correlations of actual measurements (photon detections), it is possible to derive indirectly a probability distribution for the phase difference. In this approach, the quantum phase is not an observable, but a parameter of an unknown quantum state. Photon measurements determine a probability distribution for the phase difference. The approach used in this paper takes into account both photon statistics and the finite efficiency of the detectors.

After a derivation of the quantum Bayes theorem, and a discussion of the reconstruction of the unknown state of identical spin systems by repeated measurements, the main part of this paper treats the problem of determining the unknown phase difference of two coherent sources by photon measurements. While the approach of this paper is based on computing correlations of actual measurements (photon detections), it is possible to derive indirectly a probability distribution for the phase difference. In this approach, the quantum phase is not an observable, but a parameter of an unknown quantum state. Photon measurements determine a probability distribution for the phase difference. The approach used in this paper takes into account both photon statistics and the finite efficiency of the detectors.

We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave background. Our strategy relies on Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to perform the necessary high-dimensional integrals. We describe the Metropolis-Hastings algorithm in detail and discuss the results of our test on simulated data.

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.

Fienberg convincingly demonstrates that Bayesian models and methods represent a powerful approach to squeezing illumination from data in public policy settings. However, no school of inference is without its weaknesses, and, in the face of the ambiguities, uncertainties, and poorly posed questions of the real world, perhaps we should not expect to find a formally correct inferential strategy which can be universally applied, whatever the nature of the question: we should not expect to be able to identify a "norm" approach. An analogy is made between George Box's "no models are right, but some are useful," and inferential systems [arXiv:1108.2177].

Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example, measurements from current, state-of-the-art technology. For most of the samples, only the outcome $Y$ and surrogate covariates, $\mathbf {W}$, are available. These surrogates may be data from prior studies using older technologies. Owing to the dimension of the problem and the large fraction of missing information, a critical issue is appropriate shrinkage of model parameters for an optimal bias-variance trade-off. We discuss a variety of fully Bayesian and Empirical Bayes algorithms which account for uncertainty in the missing data and adaptively shrink parameter estimates for superior prediction. These methods are evaluated via a comprehensive simulation study. In addition, we apply our methods to a lung cancer data set, predicting survival time ($Y$) using qRT-PCR ($\mathbf {X}$) and microarray ($\mathbf {W}$) measurements.

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.

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.

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.

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level starts from elementary notions, without assuming any previous knowledge of statistical methods, and then progresses to more advanced, research-level topics. After an introduction to the importance of statistical inference for the physical sciences, elementary notions of probability theory and inference are introduced and explained. Bayesian methods are then presented, starting from the meaning of Bayes Theorem and its use as inferential engine, including a discussion on priors and posterior distributions. Numerical methods for generating samples from arbitrary posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then covered. The last section deals with the topic of Bayesian model selection and how it is used to assess the performance of models, and contrasts it with the classical p-value approach. A series of exercises of various levels of difficulty are designed to further the understanding of the theoretical material, including fully worked out solutions for most of them.

This comment emphasizes the importance of model checking and model fitting when making inferences about finite population quantities. It also suggests the value of using unit level models when making inferences for small subpopulations, that is, "small area" analyses [arXiv:1108.2356].

Explains how Bayesian networks can tackle the limitations of pure data-driven statistical machine learning methods when applied to observational data. This is the lecture I was due to present at the NHS Health and Care Analytics Conference, 5 July 2023. For the back story on this see: https://wherearethenumbers.substack.com/p/an-update-on-my-nhs-conference-cancellation

Explains how Bayesian networks can tackle the limitations of pure data-driven statistical machine learning methods when applied to observational data. This is the lecture I was due to present at the NHS Health and Care Analytics Conference, 5 July 2023. For the back story on this see: https://wherearethenumbers.substack.com/p/an-update-on-my-nhs-conference-cancellation

Bayesian inference has become increasingly important in statistical machine learning. Exact Bayesian calculations are often not feasible in practice, however. A number of approximate Bayesian methods have been proposed to make such calculations practical, among them the variational Bayesian (VB) approach. The VB approach, while useful, can nevertheless suffer from slow convergence to the approximate solution. To address this problem, we propose Parameter-eXpanded Variational Bayesian (PX-VB) methods to speed up VB. The new algorithm is inspired by parameter-expanded expectation maximization (PX-EM) and parameterexpanded data augmentation (PX-DA). Similar to PX-EM and -DA, PX-VB expands a model with auxiliary variables to reduce the coupling between variables in the original model. We analyze the convergence rates of VB and PX-VB and demonstrate the superior convergence rates of PX-VB in variational probit regression and automatic relevance determination.

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.

Single-Case Experimental Designs (SCEDs) have lately been recognized as a valuable alternative tolarge group studies. SCEDs form a great tool for the evaluation of treatment effectiveness in heterogeneous and low-incidence conditions, which are common in the field of communication disorders. Mediation analysis is indispensable in treatment research because it informs researchers about the mechanism through which the intervention leads to changes (e.g., communication skills) in the outcome of interest (e.g., developmental outcomes). Despite the increasing popularity of both SCEDs and mediation analysis, there are currently no methods for estimating mediated effects for a single individual. This paper describes how Bayesian piecewise regression analysis can be used for mediation analysis in SCEDs. A Playskin LiftTM dataset from one infant born preterm who is at risk for cognitive developmental delays is used to illustrate two approaches to mediation analysis in SCEDs: Bayesian computation of the mediated effect and Bayesian informative hypothesis testing. Annotated R code is provided so researchers can easily fit the proposed models to their own SCED data set. Advantages and limitations of the method are discussed. [This is the online version of an article published in "Evidence-Based Communication Assessment and Intervention" (ISSN 1748-9539).]

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.

Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics for comparing the performance of Bayesian optimization methods and propose a ranking mechanism for summarizing performance within various genres or strata of test functions. These test functions serve to mimic the complexity of hyperparameter optimization problems, the most prominent application of Bayesian optimization, but with a closed form which allows for rapid evaluation and more predictable behavior. This offers a flexible and efficient way to investigate functions with specific properties of interest, such as oscillatory behavior or an optimum on the domain boundary.

This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies rather than variable dimension techniques like reversible jump MCMC, including: crude Monte Carlo, maximum likelihood based importance sampling, bridge and harmonic mean sampling, as well as Chib's method based on the exploitation of a functional equality. We demonstrate in this survey how these different methods can be efficiently implemented for testing the significance of a predictive variable in a probit model. Finally, we compare their performances on a real dataset.

The relation between hybrid CLs and bayesian methods used for limit setting is discussed. It is shown that the two methods are equivalent in the single channel case even when the background yield is not perfectly known. Only counting experiments are considered in this document.

The relation between hybrid CLs and bayesian methods used for limit setting is discussed. It is shown that the two methods are equivalent in the single channel case even when the background yield is not perfectly known. Only counting experiments are considered in this document.

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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)

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.

The four-planet system around GJ 581 has received attention because it has been claimed that there are possibly two additional low-mass companions as well - one of them being a planet in the middle of the stellar habitable zone. We re-analyse the available HARPS and HIRES Doppler data in an attempt to determine the false positive rate of our Bayesian data analysis techniques and to count the number of Keplerian signals in the GJ 581 data. We apply the common Lomb-Scargle periodograms and posterior sampling techniques in the Bayesian framework to estimate the number of signals in the radial velocities. We also analyse the HARPS velocities sequentially after each full observing period to compare the sensitivities and false positive rates of the two signal detection techniques. By relaxing the assumption that the radial velocity noise is white, we also demonstrate the consequences that noise correlations have on the obtained results and the significances of the signals. According to our analyses, the number of Keplerian signals favoured by the publicly available HARPS and HIRES radial velocity data of GJ 581 is four. This result relies on the sensitivity of the Bayesian statistical analysis techniques but also depends on the assumed noise model. We also show that the radial velocity noise is actually not white and that this feature has to be accounted for when analysing radial velocities in a search for low-amplitude signals corresponding to low-mass planets. ...

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 article is from International Journal of Health Geographics , volume 12 . Abstract Background: There is a rising public and political demand for prospective cancer cluster monitoring. But there is little empirical evidence on the performance of established cluster detection tests under conditions of small and heterogeneous sample sizes and varying spatial scales, such as are the case for most existing population-based cancer registries. Therefore this simulation study aims to evaluate different cluster detection methods, implemented in the open soure environment R, in their ability to identify clusters of lung cancer using real-life data from an epidemiological cancer registry in Germany. Methods: Risk surfaces were constructed with two different spatial cluster types, representing a relative risk of RR = 2.0 or of RR = 4.0, in relation to the overall background incidence of lung cancer, separately for men and women. Lung cancer cases were sampled from this risk surface as geocodes using an inhomogeneous Poisson process. The realisations of the cancer cases were analysed within small spatial (census tracts, N = 1983) and within aggregated large spatial scales (communities, N = 78). Subsequently, they were submitted to the cluster detection methods. The test accuracy for cluster location was determined in terms of detection rates (DR), false-positive (FP) rates and positive predictive values. The Bayesian smoothing models were evaluated using ROC curves. Results: With moderate risk increase (RR = 2.0), local cluster tests showed better DR (for both spatial aggregation scales > 0.90) and lower FP rates (both 

This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for confidence regions are reported.

Model selection is important in any statistical analysis, and the primary goal is to find the preferred (or most parsimonious) model, based on certain criteria, from a set of candidate models given data. Several recent publications have employed the deviance information criterion (DIC) to do model selection among different forms of multilevel item response theory models (MLIRT). The majority of the practitioners use WinBUGS for implementing MCMC algorithms for MLIRT models, and the default version of DIC provided by WinBUGS focused on the measurement-level parameters only. The results herein show that this version of DIC is inappropriate. This study introduces five variants of DIC as a model selection index for MLIRT models with dichotomous outcomes. Considering a multilevel IRT model with three levels, five forms of DIC are formed: first-level conditional DIC computed from the measurement model only, which is the index given by many software packages such as WinBUGS; second-level marginalized DIC and second-level joint DIC computed from the second-level model; and top-level marginalized DIC and top-level joint DIC computed from the entire model. We evaluate the performance of the five model selection indices via simulation studies. The manipulated factors include the number of groups, the number of second-level covariates, the number of top-level covariates, and the types of measurement models (one-parameter vs. two-parameter). Considering the computational viability and interpretability, the second-level joint DIC is recommended for MLIRT models under our simulated conditions. [This article was published in "Journal of Educational Measurement" (EJ1208645).]

Learning the network structure of a large graph is computationally demanding, and dynamically monitoring the network over time for any changes in structure threatens to be more challenging still. This paper presents a two-stage method for anomaly detection in dynamic graphs: the first stage uses simple, conjugate Bayesian models for discrete time counting processes to track the pairwise links of all nodes in the graph to assess normality of behavior; the second stage applies standard network inference tools on a greatly reduced subset of potentially anomalous nodes. The utility of the method is demonstrated on simulated and real data sets.

This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian inversion is proposed and efficiently constructed using a scalable randomized SVD algorithm. Useful optimality results are established for the associated posterior error covariance matrix and posterior mean approximations, which are further investigated in a numerical experiment consisting of a large-scale atmospheric tracer transport source-inversion problem. This method proves to be a robust and efficient approach to dimension reduction, as well as a natural framework to analyze the information content of the inversion. Possible extensions of this approach to the non-linear framework in the context of operational numerical weather forecast data assimilation systems based on the incremental 4D-Var technique are also discussed, and a detailed implementation of a new Randomized Incremental Optimal Technique (RIOT) for 4D-Var algorithms leveraging our theoretical results is proposed.

In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the complexity of the link function between unknown field and measurements can make it difficult to draw inference from the associated posterior. We prove that for this inverse problem a basic SMC method has a Monte Carlo rate of convergence with constants which are independent of the dimension of the discretization of the problem; indeed convergence of the SMC method is established in a function space setting. We also develop an enhancement of the sequential Monte Carlo (SMC) methods for inverse problems which were introduced in \cite{kantas}; the enhancement is designed to deal with the additional complexity of this elliptic inverse problem. The efficacy of the methodology, and its desirable theoretical properties, are demonstrated on numerical examples in both two and three dimensions.

In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the complexity of the link function between unknown field and measurements can make it difficult to draw inference from the associated posterior. We prove that for this inverse problem a basic SMC method has a Monte Carlo rate of convergence with constants which are independent of the dimension of the discretization of the problem; indeed convergence of the SMC method is established in a function space setting. We also develop an enhancement of the sequential Monte Carlo (SMC) methods for inverse problems which were introduced in \cite{kantas}; the enhancement is designed to deal with the additional complexity of this elliptic inverse problem. The efficacy of the methodology, and its desirable theoretical properties, are demonstrated on numerical examples in both two and three dimensions.

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

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

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

It takes years of effort employing the best telescopes and instruments to obtain high-quality stellar photometry, astrometry, and spectroscopy. Stellar evolution models contain the experience of lifetimes of theoretical calculations and testing. Yet most astronomers fit these valuable models to these precious datasets by eye. We show that a principled Bayesian approach to fitting models to stellar data yields substantially more information over a range of stellar astrophysics. We highlight advances in determining the ages of star clusters, mass ratios of binary stars, limitations in the accuracy of stellar models, post-main-sequence mass loss, and the ages of individual white dwarfs. We also outline a number of unsolved problems that would benefit from principled Bayesian analyses.

It takes years of effort employing the best telescopes and instruments to obtain high-quality stellar photometry, astrometry, and spectroscopy. Stellar evolution models contain the experience of lifetimes of theoretical calculations and testing. Yet most astronomers fit these valuable models to these precious datasets by eye. We show that a principled Bayesian approach to fitting models to stellar data yields substantially more information over a range of stellar astrophysics. We highlight advances in determining the ages of star clusters, mass ratios of binary stars, limitations in the accuracy of stellar models, post-main-sequence mass loss, and the ages of individual white dwarfs. We also outline a number of unsolved problems that would benefit from principled Bayesian analyses.

It takes years of effort employing the best telescopes and instruments to obtain high-quality stellar photometry, astrometry, and spectroscopy. Stellar evolution models contain the experience of lifetimes of theoretical calculations and testing. Yet most astronomers fit these valuable models to these precious datasets by eye. We show that a principled Bayesian approach to fitting models to stellar data yields substantially more information over a range of stellar astrophysics. We highlight advances in determining the ages of star clusters, mass ratios of binary stars, limitations in the accuracy of stellar models, post-main-sequence mass loss, and the ages of individual white dwarfs. We also outline a number of unsolved problems that would benefit from principled Bayesian analyses.

In an era of large spectroscopic surveys of stars and big data, sophisticated statistical methods become more and more important in order to infer fundamental stellar parameters such as mass and age. Bayesian techniques are powerful methods because they can match all available observables simultaneously to stellar models while taking prior knowledge properly into account. However, in most cases it is assumed that observables are uncorrelated which is generally not the case. Here, we include correlations in the Bayesian code BONNSAI by incorporating the covariance matrix in the likelihood function. We derive a parametrisation of the covariance matrix that, in addition to classical uncertainties, only requires the specification of a correlation parameter that describes how observables co-vary. Our correlation parameter depends purely on the method with which observables have been determined and can be analytically derived in some cases. This approach therefore has the advantage that correlations can be accounted for even if information for them are not available in specific cases but are known in general. Because the new likelihood model is a better approximation of the data, the reliability and robustness of the inferred parameters are improved. We find that neglecting correlations biases the most likely values of inferred stellar parameters and affects the precision with which these parameters can be determined. For example, we apply our technique to massive OB stars, but emphasise that it is valid for any type of stars. For effective temperatures and surface gravities determined from atmosphere modelling, we find that masses can be underestimated on average by $0.5\sigma$ and mass uncertainties overestimated by a factor of about 2 when neglecting correlations. At the same time, the age precisions are underestimated over a wide range of stellar parameters. [abridged]

According to Hansen, Madow and Tepping [J. Amer. Statist. Assoc. 78 (1983) 776--793], "Probability sampling designs and randomization inference are widely accepted as the standard approach in sample surveys." In this article, reasons are advanced for the wide use of this design-based approach, particularly by federal agencies and other survey organizations conducting complex large scale surveys on topics related to public policy. Impact of Bayesian methods in survey sampling is also discussed in two different directions: nonparametric calibrated Bayesian inferences from large samples and hierarchical Bayes methods for small area estimation based on parametric models.

This article is from BMJ Open , volume 3 . Abstract Objectives: To identify published closed-loop Bayesian mixed treatment comparisons (MTCs) and to summarise characteristics regarding their conduct and reporting. Design: Systematic review. Methods: We searched multiple bibliographic databases (January 2006–31 July 2011) for full-text, English language publications of Bayesian MTCs comparing the effectiveness or safety of ≥3 interventions based on randomised controlled trials and having at least one closed loop. Methodological and reporting characteristics of MTCs were extracted in duplicate and summarised descriptively. Results: We identified 34 Bayesian MTCs spanning 13 clinical areas. Publication of MTCs increased over the 5-year period; with 76.5% published during or after 2009. MTCs included a mean (±SD) of 35.9±30.1 trials (n=33 459±71 233 participants) and 8.5±4.3 interventions (85.7% pharmacological). Non-informative and informative prior distributions were reported to be used in 44.1% and 8.8% of MTCs, respectively, with the remainder failing to specify the prior used. A random-effects model was used to analyse the networks of trials in 58.5% of MTCs, all using WinBUGS; however, code was infrequently provided (20.6%). More than two-thirds of MTCs (76.5%) also conducted traditional meta-analysis. Methods used to evaluate convergence, heterogeneity and inconsistency were infrequently reported, but from those providing detail, methods appeared varied. MTCs most often used a binary effect measure (85.3%) and ranking of interventions based on probability was common (61.8%), although rarely displayed in a figure (8.8% of MTCs). MTCs were published in 24 different journals with a mean impact factor of 9.20±8.71. While 70.8% of journals imposed limits on word counts and 45.8% limits on the number of tables/figures, online supplements/appendices were allowed in 79.2% of journals. Publication of closed-loop Bayesian MTCs is increasing in frequency, but details regarding their methodology are often poorly described. Efforts in clarifying the appropriate methods and reporting of Bayesian MTCs should be of priority.

This article is from BMJ Open , volume 3 . Abstract Objectives: To identify published closed-loop Bayesian mixed treatment comparisons (MTCs) and to summarise characteristics regarding their conduct and reporting. Design: Systematic review. Methods: We searched multiple bibliographic databases (January 2006–31 July 2011) for full-text, English language publications of Bayesian MTCs comparing the effectiveness or safety of ≥3 interventions based on randomised controlled trials and having at least one closed loop. Methodological and reporting characteristics of MTCs were extracted in duplicate and summarised descriptively. Results: We identified 34 Bayesian MTCs spanning 13 clinical areas. Publication of MTCs increased over the 5-year period; with 76.5% published during or after 2009. MTCs included a mean (±SD) of 35.9±30.1 trials (n=33 459±71 233 participants) and 8.5±4.3 interventions (85.7% pharmacological). Non-informative and informative prior distributions were reported to be used in 44.1% and 8.8% of MTCs, respectively, with the remainder failing to specify the prior used. A random-effects model was used to analyse the networks of trials in 58.5% of MTCs, all using WinBUGS; however, code was infrequently provided (20.6%). More than two-thirds of MTCs (76.5%) also conducted traditional meta-analysis. Methods used to evaluate convergence, heterogeneity and inconsistency were infrequently reported, but from those providing detail, methods appeared varied. MTCs most often used a binary effect measure (85.3%) and ranking of interventions based on probability was common (61.8%), although rarely displayed in a figure (8.8% of MTCs). MTCs were published in 24 different journals with a mean impact factor of 9.20±8.71. While 70.8% of journals imposed limits on word counts and 45.8% limits on the number of tables/figures, online supplements/appendices were allowed in 79.2% of journals. Publication of closed-loop Bayesian MTCs is increasing in frequency, but details regarding their methodology are often poorly described. Efforts in clarifying the appropriate methods and reporting of Bayesian MTCs should be of priority.

The objectives of this scoping review are to: 1. Identify Stroke trials that used Bayesian Statistics. 2. Determine the Motivation for adopting Bayesian statistics. 3. Examine how the technical choices around the construction of the Prior and Posterior distributions illustrated the motivations for using Bayesian statistics.

We compare classical and Bayesian methods for fitting the poisson distribution to the number of hurricanes making landfall on sections of the US coastline.

We compare classical and Bayesian methods for fitting the poisson distribution to the number of hurricanes making landfall on sections of the US coastline.

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