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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.

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

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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.

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.

Introduction In genomic selection, genetic values of individuals are predicted using genetic markers that are distributed all across the genome and are in linkage disequilibrium with quantitative trait locus. Different methods have been introduced to predict genomic breeding values. These methods take into account different assumptions. Non-parametric methods, including artificial neural networks, have fewer assumptions than parametric methods, and can apply nonlinear relationships in genomic predictions so, in theory these approaches are more robust against genetic architecture changes and are able to provide better predictions.   Materials and Methods In current study, the prediction ability of Bayesian neural networks with different architectures (1 to 5 neurons in the hidden layer) and parametric methods (GBLUP, Bayes RR, Bayes A, Bayes B, Bayes C Bayes L) in four simulated genetic architectures and four real traits of mouse (six weeks weight, growth slope, body mass index and body length) were compared using the correlation coefficient between predicted and expected values, mean square error of prediction and computation time. All simulated genetic architectures were additive and the gene effects followed a normal distribution. The number of QTLs in the first and third genetic architecture was 50 and it was 500 for second and fourth genetic architecture. The heritability of the first and second genetic architectures was 0.3 and the heritability of the third and the fourth genetic architectures was 0.7. The real data consisted of 1,296 mice which were genotyped with 9,265 SNP markers.   Results and Discussion The highest prediction accuracy of Bayesian neural networks were 0.640 (4 neuron in the hidden layer), 0.664 (4 neuron in the hidden layer), 0.800 (1 neuron in the hidden layer) and 0.810 (1 neuron in the hidden layer), and the highest prediction accuracy of parametric methods were 0.711(Bayes B), 0.685 (Bayes A), 0.903(Bayes B) and 0.836 (Bayes B) respectively for one to four simulated genetic architectures. These results showed the superiority of parametric methods to Bayesian neural networks in terms of prediction accuracy in genetic architectures with additive effects. In additive genetic architectures, the allelic effects of genetic variations are independent. In parametric models, these effects are assumed to be independent, therefore in additive genetic architectures can be expected that parametric methods are able to provide better predictions than nonparametric methods.   The maximum predictive abilities of Bayesian neural networks to predict six weeks weight, growth slope, body mass index and body length were 0.474 (1 neuron in the hidden layer), 0.349 (4 neuron in the hidden layer), 0.154 (1 neuron in the hidden layer) and 0.214 (4 neuron in the hidden layer). The predictive abilities of parametric methods to predict these traits were similar and equal to 0.477, 0.336, 0.170, and 0.221 in average. The results showed that the predictive abilities of Bayesian neural networks and parametric methods were similar on real data as the difference between the best predictive ability of Bayesian neural networks and parametric methods for Six weeks weight, growth slope and body length were less than 1%. The difference was slightly higher for the body mass index and equal to 1.8%. The mean squared error of prediction of Bayesian Neural Networks was slightly less than parametric methods in the simulated genetic architectures. The results indicate a slight superiority of Bayesian neural networks compared to parametric methods in terms of mean squared error of prediction as an indicator of overall fit. The mean square prediction error is an appropriate criterion for evaluating the prediction performance of different methods because it contains both accuracy and bias. Considering table (3) and table (5), it can be concluded that the prediction of the Bayesian neural network are less accurate but more unbiased than the parametric methods. This could be due to more applied penalty in parametric methods compared to Bayesian neural networks, which can lead to an increase in the average mean squared error of prediction. In real data, the mean squared error of prediction of the Bayesian neural networks and parametric methods were similar. The computation time of Bayesian neural networks was increased with an increase in the number of neurons in the hidden layer. The computation time of the parametric methods was the same with the exception of GBLUP. The GBLUP method took more computation time. The computation time of neural the networks with 1 to 2 neurons in the hidden layer were less than GBLUP. Genomic prediction using Bayesian Neural Networks with a greater number of neurons is really challenging, and improving their performance in terms of computational cost is necessary before applying them in genomic selection. Conclusion Although parametric methods had better predictive accuracy and predictive ability due to the additive genetic architecture of the studied traits, it can be concluded that Bayesian neural networks are powerful tools in genomic enabled prediction that can predict genomic breeding values with acceptable accuracy. The genomic prediction ability of the neural networks depends on target traits, the animal species, and neural network architecture. Before using Bayesian neural networks in genomic prediction, it is better to compare the results with parametric methods. It is also necessary to improve the computation time of the Bayesian neural networks with a greater number of neurons in hidden layer before applying them in real application of genomic selection. 

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.

This article is from BMC Bioinformatics , volume 12 . Abstract Background: A Bayesian approach based on a Dirichlet process (DP) prior is useful for inferring genetic population structures because it can infer the number of populations and the assignment of individuals simultaneously. However, the properties of the DP prior method are not well understood, and therefore, the use of this method is relatively uncommon. We characterized the DP prior method to increase its practical use. Results: First, we evaluated the usefulness of the sequentially-allocated merge-split (SAMS) sampler, which is a technique for improving the mixing of Markov chain Monte Carlo algorithms. Although this sampler has been implemented in a preceding program, HWLER, its effectiveness has not been investigated. We showed that this sampler was effective for population structure analysis. Implementation of this sampler was useful with regard to the accuracy of inference and computational time. Second, we examined the effect of a hyperparameter for the prior distribution of allele frequencies and showed that the specification of this parameter was important and could be resolved by considering the parameter as a variable. Third, we compared the DP prior method with other Bayesian clustering methods and showed that the DP prior method was suitable for data sets with unbalanced sample sizes among populations. In contrast, although current popular algorithms for population structure analysis, such as those implemented in STRUCTURE, were suitable for data sets with uniform sample sizes, inferences with these algorithms for unbalanced sample sizes tended to be less accurate than those with the DP prior method. Conclusions: The clustering method based on the DP prior was found to be useful because it can infer the number of populations and simultaneously assign individuals into populations, and it is suitable for data sets with unbalanced sample sizes among populations. Here we presented a novel program, DPART, that implements the SAMS sampler and can consider the hyperparameter for the prior distribution of allele frequencies to be a variable.

The impetus for this study was provided by the interest of the U.S. Army Operational Test and Evaluation Agency (OTEA) to investigate the possible application of Bayesian statistical analysis and decision theory to sample size determination for operational testing. In order to understand some of the procedures discussed later in this study, a basic knowledge of the nature of operational testing as performed by OTEA is necessary. The purpose of operational testing is to provide a source of data from which estimates may be developed as to the military utility, operational effectiveness and operational suitability of new weapon systems. This data is obtained through a sequence of three operational tests; each test in the sequence is completed and the results analyzed prior to beginning the next test. For ease of reference, these tests will be referred to as Operational Test I (OT I), Operational Test II (OT II) and Operational Test III (OT III). Once the data has been collected and the estimates developed an assessment is made of the new system's desirability as compared to systems which are already available.

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.

One of the major test requirements for study of equipment that increases their efficiency is to reduce the number of tests at a given accuracy of statistical information. Based on the Bayesian method, which takes into account a priori data of statistical studies, the algorithm for estimates of the results for statistical tests has been made. This algorithm provides the required accuracy with less number of test

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This is an individual participant data meta-analysis (IPD) or retrospective pooled study. Six unpublished studies from the Computational Psychiatry lab at Melbourne University were previously carried out using variations of the Coin Estimation Task (described below) which modelled participants’ weight of sensory reliance relative to prior expectations. All studies were carried out online and participants were sourced from a mixed online university population and the general population. All studies previously investigated a variety of different research questions to the current study, with the primary outcomes variable of interest being sensory reliance (i.e., slope), as well as subjective prior and likelihood variance. Part of this data is published in (Goodwin et al, 2022). As a part of their exploratory analyses, two studies observed a significant effect of a shifted subjective prior mean to the right of the true prior (true prior = 0.0 screen coordinate) and one study showed a non-significant shift. The present study will attempt to collate all previous data from six researchers to investigate whether an overall effect of spatial asymmetry is observed.

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 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).

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.

Producers and consumers of test scores are increasingly concerned about fraudulent behavior before and during the test. There exist several statistical or psychometric methods for detecting fraudulent behavior on tests. This paper provides a review of the Bayesian approaches among them. Four hitherto-unpublished real data examples are provided to demonstrate the application of Bayesian approaches to detect various types of fraudulent behavior on tests. The examples show that Bayesian methods can be useful in detecting several types of test fraud. [This paper was published in "Measurement: Interdisciplinary Research and Perspectives" (EJ1174692).]

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.

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.

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.

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.

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.

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

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.

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.

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.

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

In this paper, we propose a generalized scale mixture family of distributions, namely the Power Exponential Scale Mixture (PESM) family, to model the sparsity inducing priors currently in use for sparse signal recovery (SSR). We show that the successful and popular methods such as LASSO, Reweighted $\ell_1$ and Reweighted $\ell_2$ methods can be formulated in an unified manner in a maximum a posteriori (MAP) or Type I Bayesian framework using an appropriate member of the PESM family as the sparsity inducing prior. In addition, exploiting the natural hierarchical framework induced by the PESM family, we utilize these priors in a Type II framework and develop the corresponding EM based estimation algorithms. Some insight into the differences between Type I and Type II methods is provided and of particular interest in the algorithmic development is the Type II variant of the popular and successful reweighted $\ell_1$ method. Extensive empirical results are provided and they show that the Type II methods exhibit better support recovery than the corresponding Type I methods.

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 radiation background. We propose the application of Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to estimate the parameters. A complete statistical analysis is presented, with the Metropolis-Hastings algorithm described in detail.

Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learning, with substantial recent developments on adaptive, flexible and scalable Bayesian learning. This article provides a survey of the recent advances in Big learning with Bayesian methods, termed Big Bayesian Learning, including nonparametric Bayesian methods for adaptively inferring model complexity, regularized Bayesian inference for improving the flexibility via posterior regularization, and scalable algorithms and systems based on stochastic subsampling and distributed computing for dealing with large-scale applications.

In this paper, we compare the performance of two methods for estimating Bayesian networks from data containing exogenous variables and random effects. The first method is fully Bayesian in which a prior distribution is placed on the exogenous variables, whereas the second method, which we call the residual approach, accounts for the effects of exogenous variables by using the notion of restricted maximum likelihood. We review the two score-based metrics, then study their performance by measuring the Kullback Leibler divergence, or distance, between the two resulting posterior density functions. The Kullback Leibler divergence provides a natural framework for comparing distributions. The residual approach is considerably simpler to apply in practice and we demonstrate its utility both theoretically and via simulations. In particular, in applications where the exogenous variables are not of primary interest, we show that the potential loss of information about parameters and induced components of correlation, is generally small.

In genetic association analyses, it is often desired to analyze data from multiple potentially-heterogeneous subgroups. The amount of expected heterogeneity can vary from modest (as might typically be expected in a meta-analysis of multiple studies of the same phenotype, for example), to large (e.g. a strong gene-environment interaction, where the environmental exposure defines discrete subgroups). Here, we consider a flexible set of Bayesian models and priors that can capture these different levels of heterogeneity. We provide accurate numerical approaches to compute approximate Bayes Factors for these different models, and also some simple analytic forms which have natural interpretations and, in some cases, close connections with standard frequentist test statistics. These approximations also have the convenient feature that they require only summary-level data from each subgroup (in the simplest case, a point estimate for the genetic effect, and its standard error, from each subgroup). We illustrate the flexibility of these approaches on three examples: an analysis of a potential gene-environment interaction for a recombination phenotype, a large scale meta-analysis of genome-wide association data from the Global Lipids consortium, and a cross-population analysis for expression quantitative trait loci (eQTLs).

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard good-ness-of-fit statistics. Limited-information fit statistics and bootstrapping procedures offer valuable solutions to this problem, but they present an additional concern in their strict reliance on the (potentially misleading) observed data. To address both of these issues, we demonstrate the technique, which yields insightful, useful, and comprehensive evaluations of specific properties of a given model. We illustrate this technique using item response data from a patient-reported psychopathology screening questionnaire, and we provide annotated R code to promote dissemination of this informative method in other prevention science modeling scenarios. [This paper was published in "Prevention Science."]

This thesis examines three methods for calculating the 100(1- α)% lower confidence limits for the reliability of a K-sized series system. Assuming that each component reliability has a Beta distribution, identical posterior parameters A and B are assigned for each component.

Probability theory

This article is from PLoS ONE , volume 9 . Abstract The aim of this study was to evaluate the impact of genotype imputation on the performance of the GBLUP and Bayesian methods for genomic prediction. A total of 10,309 Holstein bulls were genotyped on the BovineSNP50 BeadChip (50 k). Five low density single nucleotide polymorphism (SNP) panels, containing 6,177, 2,480, 1,536, 768 and 384 SNPs, were simulated from the 50 k panel. A fraction of 0%, 33% and 66% of the animals were randomly selected from the training sets to have low density genotypes which were then imputed into 50 k genotypes. A GBLUP and a Bayesian method were used to predict direct genomic values (DGV) for validation animals using imputed or their actual 50 k genotypes. Traits studied included milk yield, fat percentage, protein percentage and somatic cell score (SCS). Results showed that performance of both GBLUP and Bayesian methods was influenced by imputation errors. For traits affected by a few large QTL, the Bayesian method resulted in greater reductions of accuracy due to imputation errors than GBLUP. Including SNPs with largest effects in the low density panel substantially improved the accuracy of genomic prediction for the Bayesian method. Including genotypes imputed from the 6 k panel achieved almost the same accuracy of genomic prediction as that of using the 50 k panel even when 66% of the training population was genotyped on the 6 k panel. These results justified the application of the 6 k panel for genomic prediction. Imputations from lower density panels were more prone to errors and resulted in lower accuracy of genomic prediction. But for animals that have close relationship to the reference set, genotype imputation may still achieve a relatively high accuracy.

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.

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.

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

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.

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.

Introduction Genomic Selection (GS) has been proved to be a powerful tool for estimating genetic values in livestock breeding. Newly developed sequencing technologies have dramatically reduced the cost of genotyping and significantly increased the scale of genotype data that used for GS. The estimation of breeding values in order to select the best animals as parents of the next generation is the main goal of animal breeding programs. Traditional methods of genetic evaluation were performed using a combination of phenotypic and pedigree information to produce estimated breeding values. Most simulation studies of genomic selection (GS) methods have considered genetic architectures in which the number and relative magnitudes of quantitative trait loci (QTL) have varied. Among the Bayesian methods, those using marker-specific shrinkage of effects (e.g., BayesA or BayesB of or the Bayesian LASSO are commonly used in animal breeding applications. The Bayesian methods proposed differ in the way of looking at the variances of parameters. In classical livestock breeding methods, selection for important economic traits using pedigree information with individual phenotypic records was performed and best Linear Prediction of Breeding Values (BLUP) is achieved. In genome selection, genomic breeding values of all individuals can be predicted with high accuracy using a linear model. Various factors can be affecting the accuracy of genomic breeding values. Therefore, the present study aimed to evaluate the accuracy of estimating genomic breeding values in different genetic architectures including different distributions of gene effects, different numbers of QTL, different levels of heritability and different marker densities using GBLUP and Bayesian methods including Bayes A, Bayes B, Bayes C and Bayes LASSO. In addition to comparing the performance of different methods in different genetic architectures, a marker density and QTL numbers were introduced for simulation programs of sheep populations.   Materials and Methods To create a basic population (G0), 100 heads of livestock, including 50 males and 50 females, were considered. The frequency of primary alleles for single-nucleotide polymorphisms in the basal generation was considered to be 0.5. To create the first generation (G1), the parents were randomly selected from the males and females of the G0 generation. Parental gametes were simulated based on the assumption of disconnection imbalance using the Halldan location function method, and then randomly generated gametes were randomly selected and mixed to create a new generation of G1 generation. A genome with a length of 300 cM was simulated and 500, 1000 and 1500 SNPs were equally spaced over the chromosome. Three different numbers of QTL (50, 100 and 150) were considered and QTLs were uniformly distributed over the chromosome. One hundred individuals, including 50 males and 50 females, were simulated for the base population. The first generation structure was followed through to the 50th generation of random mating to make linkage disequilibrium populations. Generation 51 was assumed as a training population and the other generations (52 to 60) as validation populations. Five methods, GBLUP, Bayes A, Bayes B, Bayes C and Bayesian LASSO, were used to estimate genomic breeding values.   Results and Discussion In all five methods, the accuracy of genomic values decreased as the number of QTLs increased from 50 to 150. The reason for this can be attributed to the limited amount of genetic variance distributed over many QTLs. Also predicting accuracy of all five methods increased with increasing marker density. Results showed that increasing marker density at low (0.1) and high (0.5) heritability levels, increased genomic accuracy but increasing at moderate heritability (0.3) traits did not affect the accuracy of genomic evaluation. Accuracy of genomic breeding values in the gamma distribution provides better gene effects to uniform distributions.   Conclusion The results showed that factors such as marker density, QTL numbers, distribution QTL effect and trait heritability were effective in estimating the accuracy of genomic breeding values. In high heritability traits, the higher markers density and lower QTL numbers, leading to increase accuracy of estimating genomic breeding values. In genomic studies, if the trait is affected by a small number of QTLs, estimation of breeding values by Bayes B method can yield a more favorable result. Marker densities did not affect the accuracy of genomic evaluation in traits of moderate heritability, and since most of the economic traits in native species of sheep are moderate heritability, 500 to 1000 markers can be used to estimate breeding values in simulation programs

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).]

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

The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.

We develop single-event risk Prior probability distributions based on historical and heritage data. The Priors can be used to bound single-event effects risk for testing, part selection and design.