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## A Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application; Análisis bayesiano en presencia de covariables para datos de sobrevivencia multivariados: un ejemplo de aplicación

SANTOS, Carlos Aparecido; ACHCAR, Jorge Alberto
Tipo: Artigo de Revista Científica
ENG
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In this paper, we introduce a Bayesian analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different ""frailties"" or latent variables are considered to capture the correlation among the survival times for the same individual. We assume Weibull or generalized Gamma distributions considering right censored lifetime data. We develop the Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods.; En este artículo, se introduce un análisis bayesiano para datos multivariados de sobrevivencia en presencia de un vector de covariables y observaciones censuradas. Diferentes "fragilidades" o variables latentes son consideradas para capturar la correlación entre los tiempos de sobrevivencia para un mismo individuo. Asumimos distribuciones Weibull o Gamma generalizadas considerando datos de tiempo de vida a derecha. Desarrollamos el análisis bayesiano usando métodos Markov Chain Monte Carlo (MCMC).

## Modelagem espaço-temporal para dados de incidência de doenças em plantas.; Spatiotemporal modelling of plant disease incidence.

Lima, Renato Ribeiro de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
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## Uma abordagem Bayesiana para o mapeamento de QTLs utilizando o método MCMC com saltos reversíveis; A Bayesian approach to detect quantitative trait loci using reversible-jump MCMC

Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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A utilização de metodologias Bayesianas tem se tornado freqüuente nas aplicações em Genética, em particular em mapeamento de QTLs usando marcadores moleculares. Mapear um QTL implica em identificar sua posição no genoma, bem como seus efeitos genéticos. A abordagem Bayesiana combina, através do Teorema de Bayes, a verossimilhança dos dados fenotípicos com distribuições a priori atribuídas a todos os parâmetros desconhecidos (número, localização e efeito do QTL) induzindo distribuições a posteriori a respeito dessas quantidades. Métodos de mapeamento Bayesiano podem tratar o número desconhecido de QTLs como uma variável aleatória, resultando em complicações na obtençãao da amostra aleatória da distribuição conjunta a posteriori, uma vez que a dimensão do espaço do modelo pode variar. O Método MCMC com Saltos Reversíveis (MCMC-SR), proposto por Green(1995), é excelente para explorar distribuições a posteriori nesse contexto. O método proposto foi avaliado usando dados simulados no WinQTLCart, onde o maior objetivo foi avaliar diferentes prioris atribuídas para o número de QTLs.; The use of Bayesian methodology in genetical applications has grown increasingly popular, in particular in the analysis of quantitative trait loci (QTL) for studies using molecular markers. In such analyses the aim is mapping QTLs...

## Uso dos métodos clássico e bayesiano para os modelos não-lineares heterocedásticos simétricos; Use of the classical and bayesian methods for nonlinear heterocedastic symmetric models

Macêra, Márcia Aparecida Centanin
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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Os modelos normais de regressão têm sido utilizados durante muitos anos para a análise de dados. Mesmo nos casos em que a normalidade não podia ser suposta, tentava-se algum tipo de transformação com o intuito de alcançar a normalidade procurada. No entanto, na prática, essas suposições sobre normalidade e linearidade nem sempre são satisfeitas. Como alternativas à técnica clássica, foram desenvolvidas novas classes de modelos de regressão. Nesse contexto, focamos a classe de modelos em que a distribuição assumida para a variável resposta pertence à classe de distribuições simétricas. O objetivo geral desse trabalho é a modelagem desta classe no contexto bayesiano, em particular a modelagem da classe de modelos não-lineares heterocedásticos simétricos. Vale ressaltar que esse trabalho tem ligação com duas linhas de pesquisa, a saber: a inferência estatística abordando aspectos da teoria assintótica e a inferência bayesiana considerando aspectos de modelagem e critérios de seleção de modelos baseados em métodos de simulação de Monte Carlo em Cadeia de Markov (MCMC). Uma primeira etapa consiste em apresentar a classe dos modelos não-lineares heterocedásticos simétricos bem como a inferência clássica dos parâmetros desses modelos. Posteriormente...

## Uso de Métodos Bayesianos para Confiabilidade de Redes; Using Bayesian methods for network reliability

Oliveira, Sandra Cristina de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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Neste trabalho apresentamos uma análise Bayesiana para confiabilidade de sistemas de redes usando métodos de simulação de Monte Carlo via Cadeias de Markov. Assumimos diferentes densidades a priori para as confiabilidades dos componentes individuais, com o objetivo de obtermos sumários de interesse. A metodologia é exemplificada condiderando um sistema de rede com sete componentes e um caso especial de sistema complexo composto por nove componentes. Consideramos ainda confiabilidade de redes tipo k-out--of-m com alguns exemplos numéricos; In this work we present a Bayesian approach for network reliability systems using Marov Chain Monte Carlo methods. We assume different prior densities for the individual component reliabilities th to get the posterior summaries of interest. The methodology is exemplified considering a network system with seven components and a special case of complex system with nine components. We also consider k-out-of-m system reliabiility with some numerical examples

## New volatility models under a Bayesian perspective: a case study

Cuervo,Edilberto Cepeda; Achcar,Jorge Alberto; Barossi-Filho,Milton
Tipo: Artigo de Revista Científica Formato: text/html
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In this paper, we present a brief description of ARCH, GARCH and EGARCH models. Usually, their parameter estimates are obtained using maximum likelihood methods. Considering new methodological processes to model the volatilities of time series, we need to use other inference approach to get estimates for the parameters of the models, since we can encouter great difficulties in obtaining the maximum likelihood estimates due to the complexity of the likelihood function. In this way, we obtain the inferences for the volatilities of time series under a Bayesian approach, especially using popular simulation algorithms such as the Markov Chain Monte Carlo (MCMC) methods. As an application to illustrate the proposed methodology, we analyze a financial time series of the Gillette Company ranging from January, 1999 to May, 2003.

## Comment on "Bayesian evidence: can we beat MultiNest using traditional MCMC methods", by Rutger van Haasteren (arXiv:0911.2150)

Feroz, F.; Hobson, M. P.; Trotta, R.
Tipo: Artigo de Revista Científica
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In arXiv:0911.2150, Rutger van Haasteren seeks to criticize the nested sampling algorithm for Bayesian data analysis in general and its MultiNest implementation in particular. He introduces a new method for evidence evaluation based on the idea of Voronoi tessellation and requiring samples from the posterior distribution obtained through MCMC based methods. He compares its accuracy and efficiency with MultiNest, concluding that it outperforms MultiNest in several cases. This comparison is completely unfair since the proposed method can not perform the complete Bayesian data analysis including posterior exploration and evidence evaluation on its own while MultiNest allows one to perform Bayesian data analysis end to end. Furthermore, their criticism of nested sampling (and in turn MultiNest) is based on a few conceptual misunderstandings of the algorithm. Here we seek to set the record straight.; Comment: 5 pages, 1 figure, added arXiv numbers to the references

## Non-asymptotic Error Bounds for Sequential MCMC Methods in Multimodal Settings

Schweizer, Nikolaus
Tipo: Artigo de Revista Científica
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We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing properties of the MCMC dynamics, namely, local spectral gaps and local hyperboundedness, and on the amount of probability mass shifted between effectively disconnected components of the state space.

## LISA Data Analysis using MCMC methods

Cornish, Neil J.; Crowder, Jeff
Tipo: Artigo de Revista Científica
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The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50,000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analyses and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we super-cool the chains to extract maximum likelihood estimates...

## Efficient Bayesian inference for stochastic volatility models with ensemble MCMC methods

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

## CosmoHammer: Cosmological parameter estimation with the MCMC Hammer

Akeret, Joël; Seehars, Sebastian; Amara, Adam; Refregier, Alexandre; Csillaghy, André
Tipo: Artigo de Revista Científica
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We study the benefits and limits of parallelised Markov chain Monte Carlo (MCMC) sampling in cosmology. MCMC methods are widely used for the estimation of cosmological parameters from a given set of observations and are typically based on the Metropolis-Hastings algorithm. Some of the required calculations can however be computationally intensive, meaning that a single long chain can take several hours or days to calculate. In practice, this can be limiting, since the MCMC process needs to be performed many times to test the impact of possible systematics and to understand the robustness of the measurements being made. To achieve greater speed through parallelisation, MCMC algorithms need to have short auto-correlation times and minimal overheads caused by tuning and burn-in. The resulting scalability is hence influenced by two factors, the MCMC overheads and the parallelisation costs. In order to efficiently distribute the MCMC sampling over thousands of cores on modern cloud computing infrastructure, we developed a Python framework called CosmoHammer which embeds emcee, an implementation by Foreman-Mackey et al. (2012) of the affine invariant ensemble sampler by Goodman and Weare (2010). We test the performance of CosmoHammer for cosmological parameter estimation from cosmic microwave background data. While Metropolis-Hastings is dominated by overheads...

## Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC Methods

Gilavert, Clément; Moussaoui, Saïd; Idier, Jérôme
Tipo: Artigo de Revista Científica
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The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost. The connection between this algorithm and some existing strategies is discussed and its efficiency is illustrated on a linear inverse problem of image resolution enhancement.; Comment: 20 pages, 10 figures, under review for journal publication

## Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion

Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M.
Tipo: Artigo de Revista Científica
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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...

## MCMC methods for Gaussian process models using fast approximations for the likelihood

Tipo: Artigo de Revista Científica
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Gaussian Process (GP) models are a powerful and flexible tool for non-parametric regression and classification. Computation for GP models is intensive, since computing the posterior density, $\pi$, for covariance function parameters requires computation of the covariance matrix, C, a $pn^2$ operation, where p is the number of covariates and n is the number of training cases, and then inversion of C, an $n^3$ operation. We introduce MCMC methods based on the "temporary mapping and caching" framework, using a fast approximation, $\pi^*$, as the distribution needed to construct the temporary space. We propose two implementations under this scheme: "mapping to a discretizing chain", and "mapping with tempered transitions", both of which are exactly correct MCMC methods for sampling $\pi$, even though their transitions are constructed using an approximation. These methods are equivalent when their tuning parameters are set at the simplest values, but differ in general. We compare how well these methods work when using several approximations, finding on synthetic datasets that a $\pi^*$ based on the "Subset of Data" (SOD) method is almost always more efficient than standard MCMC using only $\pi$. On some datasets, a more sophisticated $\pi^*$ based on the "Nystr\"om-Cholesky" method works better than SOD.

## Markov Chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy

King, Julian A.; Mortlock, Daniel J.; Webb, John K.; Murphy, Michael T.
Tipo: Artigo de Revista Científica
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Recent attempts to constrain cosmological variation in the fine structure constant, alpha, using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for (Delta alpha)/(alpha), the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable.; Comment: IAU 2009 JD9 conference proceedings. 6 pages, 2 figures. MmSAI, vol. 80 in press Paolo Molaro & Elisabeth Vangioni eds

## Bayesian evidence: can we beat MultiNest using traditional MCMC methods?

van Haasteren, Rutger
Tipo: Artigo de Revista Científica
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Markov Chain Monte Carlo (MCMC) methods have revolutionised Bayesian data analysis over the years by making the direct computation of posterior probability densities feasible on modern workstations. However, the calculation of the prior predictive, the Bayesian evidence, has proved to be notoriously difficult with standard techniques. In this work a method is presented that lets one calculate the Bayesian evidence using nothing but the results from standard MCMC algorithms, like Metropolis-Hastings. This new method is compared to other methods like MultiNest, and greatly outperforms the latter in several cases. One of the toy problems considered in this work is the analysis of mock pulsar timing data, as encountered in pulsar timing array projects. This method is expected to be useful as well in other problems in astrophysics, cosmology and particle physics.; Comment: 9 pages, 8 figures, submitted to mnras

## MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster

Cotter, S. L.; Roberts, G. O.; Stuart, A. M.; White, D.
Tipo: Artigo de Revista Científica
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Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement. Gaussian processes or random fields are fields whose marginal distributions, when evaluated at any finite set of $N$ points, are $\mathbb{R}^N$-valued Gaussians. The algorithmic approach that we describe is applicable not only when the desired probability measure has density with respect to a Gaussian process or Gaussian random field reference measure, but also to some useful non-Gaussian reference measures constructed through random truncation. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modelling strategy. These Gaussian-based reference measures are a very flexible modelling tool...

## MCMC Methods for Entropy Optimization and Nonlinear Network Coding

Tipo: Book Section; PeerReviewed Formato: application/pdf
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Although determining the space of entropic vectors for n random variables, denoted by Γ^*_n, is crucial for solving a large class of network information theory problems, there has been scant progress in explicitly characterizing Γ^*_n for n ≥ 4. In this paper, we present a certain characterization of quasi-uniform distributions that allows one to numerically stake out the entropic region via a random walk to any desired accuracy. When coupled with Monte Carlo Markov Chain (MCMC) methods, one may “bias” the random walk so as to maximize certain functions of the entropy vector. As an example, we look at maximizing the violation of the Ingleton inequality for four random variables and report a violation well in excess of what has been previously available in the literature. Inspired by the MCMC method, we also propose a framework for designing optimal nonlinear network codes via performing a random walk over certain truth tables. We show that the method can be decentralized and demonstrate its efficacy by applying it to the Vamos network and a certain storage problem from [1].

## Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

O'Neill, Philip D; Balding, David; Becker, Niels; Eerola, Mervi; Mollison, Denis
Fonte: Blackwell Publishing Ltd Publicador: Blackwell Publishing Ltd
Tipo: Artigo de Revista Científica
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The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.

## Iterative Multiuser Detection based on Monte Carlo Probabilistic Data Association

Shi, Zhenning; Reed, Mark
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
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Multiple-Access Interference (MAI) has been considered as a major performance-limiting factor in the next-generation CDMA systems. Multiuser detection (MUD) methods have been proposed to mitigate the MAI from the co-channel users by incoporating the cross-correlation properties between users. Recently, two classes of emerging techniques, probabilistic data association (PDA) and Markov Chain Monte Carlo (MCMC) methods, have been applied to the multiuser detection. In this paper, we present a new method, named Monte Carlo PDA (MC-PDA), that incorporates the concepts of both to give a more reliable inference of the CDMA symbols by appropriately modelling and updating the MAI. The methodology is general and can be applied to other communication channels.