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## Construção de redes usando estatística clássica e Bayesiana - uma comparação; Building complex networks through classical and Bayesian statistics - a comparison

Thomas, Lina Dornelas
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
66.3%
Nesta pesquisa, estudamos e comparamos duas maneiras de se construir redes. O principal objetivo do nosso estudo é encontrar uma forma efetiva de se construir redes, especialmente quando temos menos observações do que variáveis. A construção das redes é realizada através da estimação do coeficiente de correlação parcial com base na estatística clássica (inverse method) e na Bayesiana (priori conjugada Normal - Wishart invertida). No presente trabalho, para resolver o problema de se ter menos observações do que variáveis, propomos uma nova metodologia, a qual chamamos correlação parcial local, que consiste em selecionar, para cada par de variáveis, as demais variáveis que apresentam maior coeficiente de correlação com o par. Aplicamos essas metodologias em dados simulados e as comparamos traçando curvas ROC. O resultado mais atrativo foi que, mesmo com custo computacional alto, usar inferência Bayesiana é melhor quando temos menos observações do que variáveis. Em outros casos, ambas abordagens apresentam resultados satisfatórios.; This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We construct networks estimating the partial correlation coefficient on Classic Statistics (Inverse Method) and on Bayesian Statistics (Normal - Invese Wishart conjugate prior). In this current work...

## Estudo sobre a aplicação de estatística bayesiana e método de máxima entropia em análise de dados; Study on application of bayesian statistics and method of maximun entropy in data analysis

Eder Arnedo Perassa
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
66.2%
Neste trabalho são estudados os métodos de estatística bayesiana e máxima entropia na análise de dados. É feita uma revisão dos conceitos básicos e procedimentos que podem ser usados para in-ferência de distribuições de probabilidade. Os métodos são aplicados em algumas áreas de interesse, com especial atenção para os casos em que há pouca informação sobre o conjunto de dados. São apresentados algoritmos para a aplicação de tais métodos, bem como alguns exemplos detalhados em que espera-se servirem de auxílio aos interessados em aplicações em casos mais comuns de análise de dados; In this work, we study the methods of Bayesian Statistics and Maximum Entropy in data analysis. We present a review of basic concepts and procedures that can be used for inference of probability distributions. The methods are applied in some interesting fields, with special attention to the cases where there?s few information on set of data, which can be found in physics experiments such as high energies physics, astrophysics, among others. Algorithms are presented for the implementation of such methods, as well as some detailed examples where it is expected to help interested in applications in most common cases of data analysis

## On the use of the bayesian approach for the calibration, evaluation and comparison of process-based forest models

Minunno, Francesco
Relevância na Pesquisa
56.32%
Doutoramento em Engenharia Florestal e dos Recursos Naturais - Instituto Superior de Agronomia; Forest ecosystems have been experiencing fast and abrupt changes in the environmental conditions, that can increase their vulnerability to extreme events such as drought, heat waves, storms, fire. Process-based models can draw inferences about future environmental dynamics, but the reliability and robustness of vegetation models are conditional on their structure and their parametrisation. The main objective of the PhD was to implement and apply modern computational techniques, mainly based on Bayesian statistics, in the context of forest modelling. A variety of case studies was presented, spanning from growth predictions models to soil respiration models and process-based models. The great potential of the Bayesian method for reducing uncertainty in parameters and outputs and model evaluation was shown. Furthermore, a new methodology based on a combination of a Bayesian framework and a global sensitivity analysis was developed, with the aim of identifying strengths and weaknesses of process-based models and to test modifications in model structure. Finally, part of the PhD research focused on reducing the computational load to take full advantage of Bayesian statistics. It was shown how parameter screening impacts model performances and a new methodology for parameter screening...

## Use of Bayesian statistics in drug development: Advantages and challenges

Gupta, Sandeep K
Fonte: Medknow Publications & Media Pvt Ltd Publicador: Medknow Publications & Media Pvt Ltd
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.38%
Mainly, two statistical methodologies are applicable to the design and analysis of clinical trials: frequentist and Bayesian. Most traditional clinical trial designs are based on frequentist statistics. In frequentist statistics prior information is utilized formally only in the design of a clinical trial but not in the analysis of the data. On the other hand, Bayesian statistics provide a formal mathematical method for combining prior information with current information at the design stage, during the conduct of the trial, and at the analysis stage. It is easier to implement adaptive trial designs using Bayesian methods than frequentist methods. The Bayesian approach can also be applied for post-marketing surveillance purposes and in meta-analysis. The basic tenets of good trial design are same for both Bayesian and frequentist trials. It has been recommended that the type of analysis to be used (Bayesian or frequentist) should be chosen beforehand. Switching to an analysis method that produces a more favorable outcome after observing the data is not recommended.

## Bayesian statistics: Relevant for the brain?

Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.29%
Analyzing data from experiments involves variables that we neuroscientists are uncertain about. Efficiently calculating with such variables usually requires Bayesian statistics. As it is crucial when analyzing complex data, it seems natural that the brain would “use” such statistics to analyze data from the world. And indeed, recent studies in the areas of perception, action, and cognition suggest that Bayesian behavior is widespread, in many modalities and species. Consequently, many models have suggested that the brain is built on simple Bayesian principles. While the brain’s code is probably not actually simple, I believe that Bayesian principles will facilitate the construction of faithful models of the brain.

## Philosophy and the practice of Bayesian statistics

Gelman, Andrew; Shalizi, Cosma Rohilla
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.34%
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.

## On the application of Bayesian statistics to protein structure calculation from nuclear magnetic resonance data

Mechelke, Martin
Fonte: Universität Tübingen Publicador: Universität Tübingen
Tipo: Dissertação
Português
Relevância na Pesquisa
66.29%
In the present work, we use concepts of Bayesian statistics to infer the three-dimensional structures of proteins from experimental data. We thus build upon the method of inferential structure determination (ISD) as introduced by Rieping et al. (2005). In line with their probabilistic approach, we factor the probability of a three-dimensional protein structure given the experimental data, into a prior distribution that captures the protein-likeness of a structure and the likelihood that describes how likely the experimental data were generated from a given three-dimensional structure. In this Bayesian framework, we attempt to develop structure calculation from NMR experiments into a highly accurate, objective and parameter-free process. We start by focusing on integrating new types of data, as ISD currently does not entail a mechanism to incorporate chemical shifts in the calculation process. To alleviate this shortcoming, we propose a hidden Markov Model that captures the relationship between protein structures and chemical shifts. Based on our probabilistic model, we are able to predict the secondary structure and dihedral angles of a protein from chemical shifts. Another means to high quality structures involves improving the potential functions that form the core of ISD’s prior distributions. Although potential functions are designed to approximate physical forces...

## A Bayesian/MCMC Approach to Galaxy Modelling: NGC 6503

PUGLIELLI, DAVID
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado Formato: 9284903 bytes; application/pdf
Português
Relevância na Pesquisa
56.19%
We use Bayesian statistics and Markov chain Monte Carlo (MCMC) techniques to construct dynamical models for the spiral galaxy NGC 6503. The constraints include surface brightness profiles which display a Freeman Type II structure; HI and ionized gas rotation curves; the stellar rotation, which is nearly coincident with the ionized gas curve; and the line of sight stellar dispersion, which displays a $\sigma-$drop at the centre. The galaxy models consist of a S\'{e}rsic bulge, an exponential disc with an optional inner truncation and a cosmologically motivated dark halo. The Bayesian/MCMC technique yields the joint posterior probability distribution function for the input parameters, allowing constraints on model parameters such as the halo cusp strength, structural parameters for the disc and bulge, and mass-to-light ratios. We examine several interpretations of the data: the Type II surface brightness profile may be due to dust extinction, to an inner truncated disc or to a ring of bright stars; and we test separate fits to the gas and stellar rotation curves to determine if the gas traces the gravitational potential. We test each of these scenarios for bar stability, ruling out dust extinction. We also find that the gas cannot trace the gravitational potential...

## Bayesian Statistics at Work: the Troublesome Extraction of the CKM Phase alpha

Charles, J.; Hocker, A.; Lacker, H.; Diberder, F. R. Le; T'Jampens, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.26%
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the isospin analysis of B-->PP (P = pi or rho) decays in heavy-flavor physics is chosen to illustrate the effect of the naive "objective" choice of flat priors in a multi-dimensional parameter space in presence of mirror solutions. It is demonstrated that the posterior distribution for the parameter of interest, the phase alpha, strongly depends on the choice of the parameterization in which the priors are uniform, and on the validity range in which the (un-normalizable) priors are truncated. We prove that the most probable values found by the Bayesian treatment do not coincide with the explicit analytical solution, in contrast to the frequentist approach. It is also shown in the appendix that the alpha-->0 limit cannot be consistently treated in the Bayesian paradigm, because the latter violates the physical symmetries of the problem.; Comment: 17 pages, 10 figures

## Significance in gamma-ray astronomy - the Li & Ma problem in Bayesian statistics

Gillessen, S.; Harney, H. L.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.29%
The significance of having detected an astrophysical gamma ray source is usually calculated by means of a formula derived by Li & Ma in 1983. We solve the same problem in terms of Bayesian statistics, which provides a logically more satisfactory framework. We do not use any subjective elements in the present version of Bayesian statistics. We show that for large count numbers and a weak source the Li & Ma formula agrees with the Bayesian result. For other cases the two results differ, both due to the mathematically different treatment and the fact that only Bayesian inference can take into account prior knowldege.; Comment: 12 pages, 3 figures, accepted for publication in A&A

## Bayesian computational methods

Robert, Christian P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.32%
In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions. Of course, this chapter is only a terse introduction to the problems and solutions related to Bayesian computations. For more complete references, see Robert and Casella (2004, 2009), or Marin and Robert (2007), among others. We also restrain from providing an introduction to Bayesian Statistics per se and for comprehensive coverage, address the reader to Robert (2007), (again) among others.; Comment: This is a revised version of a chapter written for the Handbook of Computational Statistics, edited by J. Gentle, W. Hardle and Y. Mori in 2003, in preparation for the second edition

## Building complex networks through classical and Bayesian statistics - a comparison

Thomas, Lina D.; Fossaluza, Victor; Yambartsev, Anatoly
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.32%
This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We construct networks estimating the partial correlation coefficient on Classic Statistics (Inverse Method) and on Bayesian Statistics (Normal - Inverse Wishart conjugate prior). In this current work, in order to solve the problem of having less observations than variables, we propose a new methodology called local partial correlation, which consists of selecting, for each pair of variables, the other variables most correlated to the pair.We applied these methods on simulated data and compared them through ROC curves. The most attractive result is that, even though it has high computational costs, to use Bayesian inference on trees is better when we have less observations than variables. In other cases, both approaches present satisfactory results.; Comment: 9 pages, 5 figures, conference Brazilian Meeting on Bayesian Statistics 2012

## Bayesian reasoning in cosmology

Mielczarek, Jakub; Szydlowski, Marek; Tambor, Pawel
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.3%
We discuss epistemological and methodological aspects of the Bayesian approach in astrophysics and cosmology. The introduction to the Bayesian framework is given for a further discussion concerning the Bayesian inference in physics. The interplay between the modern cosmology, Bayesian statistics, and philosophy of science is presented. We consider paradoxes of confirmation, like Goodman's paradox, appearing in the Bayesian theory of confirmation. As in Goodman's paradox the Bayesian inference is susceptible to some epistemic limitations in the logic of induction. However Goodman's paradox applied to cosmological hypotheses seems to be resolved due to the evolutionary character of cosmology and accumulation new empirical evidences. We argue that the Bayesian framework is useful in the context of falsificability of quantum cosmological models, as well as contemporary dark energy and dark matter problem.; Comment: RevTeX4, 14 pages, 6 figures; v2 new title, improvements and corrections, more on Bayesian inference with example in cosmology

## The two envelopes paradox in non-Bayesian and Bayesian statistics

Ishikawa, Shiro
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
56.38%
The purpose of this paper is to clarify the (non-Bayesian and Bayesian) two-envelope problems in terms of quantum language (or, measurement theory), which was recently proposed as a linguistic turn of quantum mechanics (with the Copenhagen interpretation). The two envelopes paradox is only a kind of high school student's probability puzzle, and it may be exaggerated to say that this is an unsolved problem. However, since we are convinced that quantum language is just statistics of the future, we believe that there is no clear answer without the description by quantum language. In this sense, the readers are to find that quantum language provides the final answer (i.e., the easiest and deepest understanding) to the two envelope-problems in both non-Bayesian and Bayesian statistics. Also, we add the discussion about St. Petersburg two-envelope paradox.; Comment: 17 pages

## "Not only defended but also applied": The perceived absurdity of Bayesian inference

Gelman, Andrew; Robert, Christian P.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.3%
The missionary zeal of many Bayesians of old has been matched, in the other direction, by a view among some theoreticians that Bayesian methods are absurd-not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on probability theory and continuing with more recent cases such as the perceived Bayesian nature of the so-called doomsday argument. We analyze in this note the intellectual background behind various misconceptions about Bayesian statistics, without aiming at a complete historical coverage of the reasons for this dismissal.; Comment: 10 pages, to appear in The American Statistician (with discussion)

## Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

Abe, Sumiyoshi
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
56.12%
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely-separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown in particular how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.; Comment: 17 pages, 1 figure. Published version

## Philosophy and the practice of Bayesian statistics

Gelman, Andrew; Shalizi, Cosma Rohilla
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
56.4%
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.; Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3: Further typo fixes. v4: Revised in response to referees

## Bayesian Synthesis: Combining subjective analyses, with an application to ozone data

Yu, Qingzhao; MacEachern, Steven N.; Peruggia, Mario
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.36%
Bayesian model averaging enables one to combine the disparate predictions of a number of models in a coherent fashion, leading to superior predictive performance. The improvement in performance arises from averaging models that make different predictions. In this work, we tap into perhaps the biggest driver of different predictions---different analysts---in order to gain the full benefits of model averaging. In a standard implementation of our method, several data analysts work independently on portions of a data set, eliciting separate models which are eventually updated and combined through a specific weighting method. We call this modeling procedure Bayesian Synthesis. The methodology helps to alleviate concerns about the sizable gap between the foundational underpinnings of the Bayesian paradigm and the practice of Bayesian statistics. In experimental work we show that human modeling has predictive performance superior to that of many automatic modeling techniques, including AIC, BIC, Smoothing Splines, CART, Bagged CART, Bayes CART, BMA and LARS, and only slightly inferior to that of BART. We also show that Bayesian Synthesis further improves predictive performance. Additionally, we examine the predictive performance of a simple average across analysts...

## A Bayesian Surrogate Model for Rapid Time Series Analysis and Application to Exoplanet Observations

Ford, Eric B.; Moorhead, Althea V.; Veras, Dimitri
Tipo: Artigo de Revista Científica