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We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data set. This poses two statistical challenges that need to be addressed simultaneously. The first is the assessment of study heterogeneity, with the aim of identifying a subset of studies within which algorithm comparisons can be reliably carried out. The second is the comparison of algorithms using the ensemble of data sets. We address both problems by integrating clustering and model comparison. We formulate a Bayesian model for the array of cross-study validation statistics, which defines clusters of studies with similar properties and provides the basis for meaningful algorithm comparison in the presence of study heterogeneity. We illustrate our approach through simulations involving studies with varying severity of systematic errors, and in the context of medical prognosis for patients diagnosed with cancer, using high-throughput measurements of the transcriptional activity of the tumor's genes.

We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data set. This poses two statistical challenges that need to be addressed simultaneously. The first is the assessment of study heterogeneity, with the aim of identifying a subset of studies within which algorithm comparisons can be reliably carried out. The second is the comparison of algorithms using the ensemble of data sets. We address both problems by integrating clustering and model comparison. We formulate a Bayesian model for the array of cross-study validation statistics, which defines clusters of studies with similar properties and provides the basis for meaningful algorithm comparison in the presence of study heterogeneity. We illustrate our approach through simulations involving studies with varying severity of systematic errors, and in the context of medical prognosis for patients diagnosed with cancer, using high-throughput measurements of the transcriptional activity of the tumor's genes.

We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data set. This poses two statistical challenges that need to be addressed simultaneously. The first is the assessment of study heterogeneity, with the aim of identifying a subset of studies within which algorithm comparisons can be reliably carried out. The second is the comparison of algorithms using the ensemble of data sets. We address both problems by integrating clustering and model comparison. We formulate a Bayesian model for the array of cross-study validation statistics, which defines clusters of studies with similar properties and provides the basis for meaningful algorithm comparison in the presence of study heterogeneity. We illustrate our approach through simulations involving studies with varying severity of systematic errors, and in the context of medical prognosis for patients diagnosed with cancer, using high-throughput measurements of the transcriptional activity of the tumor's genes.

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non-parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non-parametric approach.

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.

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.

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.

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.

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.

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

We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work addresses analysis of stellar reflex motion data, where a planet is detected by observing the "wobble" of its host star as it responds to the gravitational tug of the orbiting planet. Newtonian mechanics specifies an analytical model for the resulting time series, but it is strongly nonlinear, yielding complex, multimodal likelihood functions; it is even more complex when multiple planets are present. The parameter spaces range in size from few-dimensional to dozens of dimensions, depending on the number of planets in the system, and the type of motion measured (line-of-sight velocity, or position on the sky). Since orbits are periodic, Bayesian generalizations of periodogram methods facilitate the analysis. This relies on the model being linearly separable, enabling partial analytical marginalization, reducing the dimension of the parameter space. Subsequent analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance sampling to perform the integrals required for both inference (planet detection and orbit measurement), and information-maximizing sequential design (for adaptive scheduling of observations). We present an overview of our current techniques and highlight directions being explored by ongoing research.

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.

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.

In this paper, we consider the so-called Shape Invariant Model which stands for the estimation of a function f0 submitted to a random translation of law g0 in a white noise model. We are interested in such a model when the law of the deformations is unknown. We aim to recover the law of the process P(f0,g0) as well as f0 and g0. We first provide some identifiability result on this model and then adopt a Bayesian point of view. In this view, we find some prior on f and g such that the posterior distribution concentrates around the functions f0 and g0 when n goes to infinity, we then obtain a contraction rate of order a power of log(n)^(-1). We also obtain a lower bound on the model for the estimation of f0 and g0 in a frequentist paradigm which also decreases following a power of log(n)^(-1).

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.

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

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

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In most cases the solution is explored via Monte Carlo sampling or variational methods. Here we work further on the application of variational methods to clustering problems. We introduce generative models based on a hidden group structure and prior distributions. We extend previous attends by Jaynes, and derive the prior distributions based on symmetry arguments. As a case study we address the problems of two-sides clustering real value data and clustering data represented by a hypergraph or bipartite graph. From the variational calculations, and depending on the starting statistical model for the data, we derive a variational Bayes algorithm, a generalized version of the expectation maximization algorithm with a built in penalization for model complexity or bias. We demonstrate the good performance of the variational Bayes algorithm using test examples.

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In most cases the solution is explored via Monte Carlo sampling or variational methods. Here we work further on the application of variational methods to clustering problems. We introduce generative models based on a hidden group structure and prior distributions. We extend previous attends by Jaynes, and derive the prior distributions based on symmetry arguments. As a case study we address the problems of two-sides clustering real value data and clustering data represented by a hypergraph or bipartite graph. From the variational calculations, and depending on the starting statistical model for the data, we derive a variational Bayes algorithm, a generalized version of the expectation maximization algorithm with a built in penalization for model complexity or bias. We demonstrate the good performance of the variational Bayes algorithm using test examples.

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).]

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

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.

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.

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.

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

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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. ...

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 

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

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

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

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.

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.

We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes' theorem together with the principle of maximum entropy to account for the prior information that these parameters should be natural, i.e.O(1) in appropriate units. Marginalization can then be employed to integrate the resulting probability density function (pdf) over the EFT parameters that are not of specific interest in the fit. We also explore marginalization over the order of the EFT calculation, M, and over the variable, R, that encodes the inherent ambiguity in the notion that these parameters are O(1). This results in a very general formula for the pdf of the EFT parameters of interest given a data set, D. We use this formula and the simpler "augmented chi-squared" in a toy problem for which we generate pseudo-data. These Bayesian methods, when used in combination with the "naturalness prior", facilitate reliable extractions of EFT parameters in cases where chi-squared methods are ambiguous at best. We also examine the problem of extracting the nucleon mass in the chiral limit, M_0, and the nucleon sigma term, from pseudo-data on the nucleon mass as a function of the pion mass. We find that Bayesian techniques can provide reliable information on M_0, even if some of the data points used for the extraction lie outside the region of applicability of the EFT.

Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of dimensionality, and a marginal adjustment strategy was recently introduced in the literature to improve the performance of ABC algorithms in high-dimensional problems. The marginal adjustment approach is extended using a Gaussian copula approximation. The method first estimates the bivariate posterior for each pair of parameters separately using a 2-dimensional Gaussian copula, and then combines these estimates together to estimate the joint posterior. The approximation works well in large sample settings when the posterior is approximately normal, but also works well in many cases which are far from that situation due to the nonparametric estimation of the marginal posterior distributions. If each bivariate posterior distribution can be well estimated with a low-dimensional ABC analysis then this Gaussian copula method can extend ABC methods to problems of high dimension. The method also results in an analytic expression for the approximate posterior which is useful for many purposes such as approximation of the likelihood itself. This method is illustrated with several examples.

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

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

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

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.

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

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