scholarly journals Optimális neurális hálózat kiválasztása Bayes-becslés segítségével

2021 ◽  
pp. 37-46
Author(s):  
Béla Szekeres ◽  
Milán Kondics
Keyword(s):  
Monte Carlo ◽  
A Posteriori ◽  
Nested Sampling

Ezen munkánkban célunk, hogy neurális hálózatokra alkalmazva a Bayes-becslést az \textit{a posteriori} becslések során a különböző modellek közül kiválasszuk a tanító adatoknak legjobban megfelelőt. Mindehhez egy sokdimenziós integrál kiszámítása szükséges, amely a hagyományos Monte-Carlo módszerekkel is nehéz feladat; erre a célra a {beágyazott mintavételezés (nested sampling)} algoritmust alkalmazzuk, és a számítások járulékos eredményeként kapjuk meg a betanított hálózatot a hiperparaméterek terében is bolyongást végezve. Továbbá rámutatunk arra, hogyan lehet ötvözni a gradiens visszaterjesztéses és a véletlen bolyongásos tanítást hibrid hálózatokat nyerve.

scholarly journals Detecção de locos de características quantitativas (QTL) afetando o crescimento e a carcaça de suínos: um enfoque Bayesiano com o uso de diferentes prioris

2008 ◽  
Vol 37 (2) ◽  
pp. 261-272
Author(s):  
Tarcisio de Moraes Gonçalves ◽  
Ana Luísa Lopes da Costa ◽  
Juliana Salgado Laranjo ◽  
Mary Ana Petersen Rodriguez ◽  
Geovanne Ferreira Rebouças
Keyword(s):  
Monte Carlo ◽  
A Posteriori ◽  
Large White

Foram utilizados 1.129 animais, 298 F1 e 831 F2 para gordura intramuscular (GIM, %) e ganho de peso (GP, g/dia) e 324 F1 e 805 F2 para espessura de toucinho (ET, mm), obtidos por meio do cruzamento de suínos machos da raça Meishan e fêmeas Large White e Landrace. Os animais foram genotipados para marcadores moleculares cobrindo todo o genoma. Foram estudados os cromossomos 1, 2, 4, 5, 6, 7, 13, 14 e19 para ET e GIM e os cromossomos 1, 2, 4, 6, 7, 8, 13, 17 e19 para GP entre 25 e 90 kg de peso vivo (PV). Análises de QTL usando metodologia Bayesiana foram aplicadas mediante o modelo genético estatístico combinando os efeitos Poligênico Infinito (MPI), Poligênico Finito (MPF) e de QTL. Os sumários dos parâmetros estimados foram baseados nas distribuições marginais a posteriori obtidas por Cadeia de Markov, algoritmo de Monte Carlo (MCMC). De modo geral, por meio dos resultados, foi possível evidenciar um QTL para ET, independentemente da priori estudada. Não foi possível detectar QTL para as características GIM e GP com a aplicação desta metodologia, o que pode estar relacionado aos marcadores não-informativos ou à ausência de QTL segregando nos cromossomos estudados. Há vantagens em analisar dados experimentais ajustando modelos genéticos combinados e não considerando unicamente o modelo poligênico ou o oligogênico. As análises ilustraram a utilidade e aplicabilidade do método Bayesiano no qual foram utilizados modelos finitos.

scholarly journals A neural network approach to estimating a posteriori distributions of Bayesian retrieval problems

2018 ◽  
Vol 11 (8) ◽  
pp. 4627-4643 ◽  
Author(s):  
Simon Pfreundschuh ◽  
Patrick Eriksson ◽  
David Duncan ◽  
Bengt Rydberg ◽  
Nina Håkansson ◽  
...  
Keyword(s):  
Neural Network ◽  
Monte Carlo ◽  
Monte Carlo Integration ◽  
A Posteriori ◽  
Retrieval Performance ◽  
Neural Network Approach ◽  
Novel Approach ◽  
Uncertainty Estimates ◽  
Non Gaussian ◽  
Similar Accuracy

Abstract. A neural-network-based method, quantile regression neural networks (QRNNs), is proposed as a novel approach to estimating the a posteriori distribution of Bayesian remote sensing retrievals. The advantage of QRNNs over conventional neural network retrievals is that they learn to predict not only a single retrieval value but also the associated, case-specific uncertainties. In this study, the retrieval performance of QRNNs is characterized and compared to that of other state-of-the-art retrieval methods. A synthetic retrieval scenario is presented and used as a validation case for the application of QRNNs to Bayesian retrieval problems. The QRNN retrieval performance is evaluated against Markov chain Monte Carlo simulation and another Bayesian method based on Monte Carlo integration over a retrieval database. The scenario is also used to investigate how different hyperparameter configurations and training set sizes affect the retrieval performance. In the second part of the study, QRNNs are applied to the retrieval of cloud top pressure from observations by the Moderate Resolution Imaging Spectroradiometer (MODIS). It is shown that QRNNs are not only capable of achieving similar accuracy to standard neural network retrievals but also provide statistically consistent uncertainty estimates for non-Gaussian retrieval errors. The results presented in this work show that QRNNs are able to combine the flexibility and computational efficiency of the machine learning approach with the theoretically sound handling of uncertainties of the Bayesian framework. Together with this article, a Python implementation of QRNNs is released through a public repository to make the method available to the scientific community.

Using nested sampling with Galilean Monte Carlo for model comparison problems in acoustics

2013 ◽  
Vol 133 (5) ◽  
pp. 3575-3575
Author(s):  
Paul Goggans ◽  
Wesley Henderson ◽  
Ning Xiang
Keyword(s):  
Monte Carlo ◽  
Model Comparison ◽  
Nested Sampling

scholarly journals Comparação de diferentes estratégias para a análise de características de crescimento e de carcaça de suínos cruzados: modelos finito e infinitesimal poligênico

2005 ◽  
Vol 34 (5) ◽  
pp. 1531-1539 ◽  
Author(s):  
Tarcísio de Moraes Gonçalves ◽  
Henrique Nunes de Oliveira ◽  
Henk Bovenhuis ◽  
Marco Bink ◽  
Johan Van Arendonk
Keyword(s):  
Monte Carlo ◽  
Reversible Jump ◽  
A Posteriori ◽  
Large White ◽  
Inferencia Bayesiana

Foi utilizada uma análise de segregação com o uso da inferência Bayesiana para estimar componentes de variância e verificar a presença de genes de efeito principal (GEP) influenciando duas características de carcaça: gordura intramuscular (GIM), em %, e espessura de toucinho (ET), em mm; e uma de crescimento, ganho de peso (g/dia) dos 25 aos 90 kg de peso vivo (GP). Para este estudo, foram utilizadas informações de 1.257 animais provenientes de um delineamento de F2, obtidos do cruzamento de suínos machos Meishan e fêmeas Large White e Landrace. No melhoramento genético animal, os modelos poligênicos finitos (MPF) podem ser uma alternativa aos modelos poligênicos infinitesimais (MPI) para avaliação genética de características quantitativas usando pedigrees complexos. MPI, MPF e MPI combinado com MPF foram empiricamente testados para se estimar componentes de variâncias e número de genes no MPF. Para a estimação de médias marginais a posteriori de componentes de variância e de parâmetros, foi utilizada uma metodologia Bayesiana, por meio do uso da Cadeia de Markov, algoritmos de Monte Carlo (MCMC), via Amostrador de Gibbs e Reversible Jump Sampler (Metropolis-Hastings). Em função dos resultados obtidos, pode-se evidenciar quatro GEP, sendo dois para GIM e dois para ET. Para ET, o GEP explicou a maior parte da variação genética, enquanto, para GIM, o GEP reduziu significativamente a variação poligênica. Para a variação do GP, não foi possível determinar a influência do GEP. As herdabilidades estimadas ajustando-se MPI para GIM, ET e GP foram de 0,37; 0,24 e 0,37, respectivamente. Estudos futuros com base neste experimento que usem marcadores moleculares para mapear os genes de efeito principal que afetem, principalmente GIM e ET, poderão lograr êxito.

Conditioning Stochastic Reservoir Models to Well-Test Data

2000 ◽  
Vol 3 (01) ◽  
pp. 74-79 ◽  
Author(s):  
Nanqun He ◽  
Dean S. Oliver ◽  
Albert C. Reynolds
Keyword(s):  
Monte Carlo ◽  
Posteriori Probability ◽  
Production Data ◽  
A Posteriori ◽  
Well Test ◽  
Pressure Data ◽  
Reservoir Properties ◽  
Dynamic Data ◽  
Reservoir Models ◽  
Flow Simulator

Summary Generating realizations of reservoir permeability and porosity fields that are conditional to static and dynamic data are difficult. The constraints imposed by dynamic data are typically nonlinear and the relationship between the observed data and the petrophysical parameters is given by a flow simulator which is expensive to run. In addition, spatial organization of real rock properties is quite complex. Thus, most attempts at conditioning reservoir properties to dynamic data have either approximated the relationship between data and parameters so that complex geologic models could be used, or have used simplified spatial models with actual production data. In this paper, we describe a multistep procedure for efficiently generating realizations of reservoir properties that honor dynamic data from complex stochastic models. First, we generate a realization of the rock properties that is conditioned to static data, but not to the pressure data. Second, we generate a realization of the production data (i.e., add random errors to the production data). Third, we find the property field that is as close as possible to the uncalibrated realization and also honors the realization of the production data. The ensemble of realizations generated by this procedure often provides a good empirical approximation to the posteriori probability density function for reservoir models and can be used for Monte Carlo inference. We apply the above procedure to the problem of conditioning a three-dimensional stochastic model to data from two well tests. The real-field example contains two facies. Permeabilities within each facies were generated using a "cloud transform" that honored the observed scatter in the crossplot of permeability and porosity. We cut a volume, containing both test wells, from the full-field model, then scaled it up to about 9,000 cells before calibrating to pressure data. Although the well-test data were of poor quality, the data provided information to modify the permeabilities within the regions of investigations and on the overall permeability average. Introduction The problem of generating plausible reservoir models that are conditional to dynamic or production-type data has been an active area of research for several years. Existing studies can be classified by the way in which they approach three key aspects of the problem:Complexity of the stochastic geologic or petrophysical model.Method of computing pressure response from a reservoir model.Attention to the problem of sampling realizations from the a posteriori probability density function. Most researchers have worked with simple models (e.g., characterized by a variogram), an effective well-test permeability instead of a flow simulator, and largely ignored the problem of sampling. Other, more sophisticated examples include the use of a complex stochastic geologic model (channels), and simulated annealing to sample from the a posteriori probability distribution function (PDF), but an effective well-test permeability instead of pressure data (and a simulator) for conditioning.1 The works by Oliver2 and by Chu et al.3 provide other examples. In these cases, a flow simulator was used for conditioning but the geology was relatively simple and realizations were generated using a linearization approximation around the maximum a posteriori model. Landa4 treated the problem of conditioning two-dimensional channels, but chose a simple model that could be described by a few parameters. A large part of our effort has gone into ensuring that the ensemble of realizations that we generated would be representative of the uncertainty in the reservoir properties. In order to do this rigorously, we have used the actual pressure data but have had to limit ourselves to Gaussian random fields and to fairly small synthetic models. We recently applied Markov chain Monte Carlo (MCMC) methods5 to generate an ensemble of realizations because we believe they provide the best framework for ensuring that we obtain a representative set of realizations suitable for making economic decisions. The principal advantage of MCMC is that it provides a method for sampling realizations from complicated probability distributions such as the distributions of reservoirs conditional to production data. The method consists of a proposal of a new realization, and a decision as to whether to accept the proposed realization, or to again accept the current realization. The "chain" refers to the sequence of accepted realizations and "Monte Carlo" refers to the stochastic aspect in the proposal acceptance steps. Unfortunately, it appears to be impractical to use MCMC methods for generating realizations that are conditional to production data. If realizations are proposed from a relatively simple probability density function (e.g., multivariate Gaussian), then most realizations are rejected and the method is inefficient. Alternatively, if realizations are proposed from a PDF that is complicated but close to the desired PDF, the Metropolis-Hastings criterion, which involves the ratio of the probability of proposing the proposed realization to the probability of proposing the current realization, is difficult to evaluate. Oliver et al.6 proposed a methodology for incorporating production data that followed the second approach but ignored the Metropolis-Hastings criterion, instead accepting every realization. We showed that the method is rigorously valid for conditioning Gaussian random fields to linear data (i.e., weighted averages of model variables) and is easily adapted to more complex geostatistical models and types of data. Although the method is then not rigorously correct, we have shown that the distribution of realizations is good for simple, but highly nonlinear problems. The realizations generated using this methodology still honor all the data—the ensemble of realizations is, however, not a perfect representation of the true distribution even as the number of realizations becomes very large.

scholarly journals A neural network approach to estimate a posteriori distributions of Bayesian retrieval problems

2018 ◽  
Author(s):  
Simon Pfreundschuh ◽  
Patrick Eriksson ◽  
David Duncan ◽  
Bengt Rydberg ◽  
Nina Håkansson ◽  
...  
Keyword(s):  
Neural Network ◽  
Remote Sensing ◽  
Monte Carlo ◽  
Monte Carlo Integration ◽  
A Posteriori ◽  
Retrieval Performance ◽  
Neural Network Approach ◽  
Novel Approach ◽  
Uncertainty Estimates ◽  
Similar Accuracy

Abstract. This work is concerned with the retrieval of physical quantities from remote sensing measurements. A neural network based method, Quantile Regression Neural Networks (QRNNs), is proposed as a novel approach to estimate the a posteriori distribution of Bayesian remote sensing retrievals. The advantage of QRNNs over conventional neural network retrievals is that they not only learn to predict a single retrieval value but also the associated, case specific uncertainties. In this study, the retrieval performance of QRNNs is characterized and compared to that of other state-of-the-art retrieval methods. A synthetic retrieval scenario is presented and used as a validation case for the application of QRNNs to Bayesian retrieval problems. The QRNN retrieval performance is evaluated against Markov chain Monte Carlo simulation and another Bayesian method based on Monte Carlo integration over a retrieval database. The scenario is also used to investigate how different hyperparameter configurations and training set sizes affect the retrieval performance. In the second part of the study, QRNNs are applied to the retrieval of cloud top pressure from observations by the moderate resolution imaging spectroradiometer (MODIS). It is shown that QRNNs are not only capable of achieving similar accuracy as standard neural network retrievals, but also provide statistically consistent uncertainty estimates for non-Gaussian retrieval errors. The results presented in this work show that QRNNs are able to combine the flexibility and computational efficiency of the machine learning approach with the theoretically sound handling of uncertainties of the Bayesian framework. Together with this article, a Python implementation of QRNNs is released through a public repository to make the method available to the scientific community.

scholarly journals Análise Bayesiana no estudo do tempo de retorno das precipitações pluviais máximas em Jaboticabal (SP)

2009 ◽  
Vol 33 (1) ◽  
pp. 261-270 ◽  
Author(s):  
Luiz Alberto Beijo ◽  
Mário Javier Ferrua Vivanco ◽  
Joel Augusto Muniz
Keyword(s):  
Monte Carlo ◽  
A Priori ◽  
A Posteriori ◽  
Inferencia Bayesiana

Dados históricos de precipitação máxima são utilizados para realizar previsões de chuvas extremas, cujo conhecimento é de grande importância na elaboração de projetos agrícolas e de engenharia hidráulica. A distribuição generalizada de valores extremos (GEV) tem sido aplicada com freqüência nesses tipos de estudos, porém, algumas dificuldades na obtenção de estimativas confiáveis sobre alguma medida dos dados têm ocorrido devido ao fato de que, na maioria das situações, tem-se uma quantidade escassa de dados. Uma alternativa para obter melhorias na qualidade das estimativas seria utilizar informações dos especialistas de determinada área em estudo. Sendo assim, objetiva-se neste trabalho analisar a aplicação da Inferência Bayesiana com uma distribuição a priori baseada em quantis extremos, que facilite a incorporação dos conhecimentos fornecidos por especialistas, para obter as estimativas de precipitação máxima para os tempos de retorno de 10 e 20 anos e seus respectivos limites superiores de 95%, para o período anual e para os meses da estação chuvosa em Jaboticabal (SP). A técnica Monte Carlo, via Cadeias de Markov (MCMC), foi empregada para inferência a posteriori de cada parâmetro. A metodologia Bayesiana apresentou resultados mais acurados e precisos, tanto na estimação dos parâmetros da distribuição GEV, como na obtenção dos valores de precipitação máxima provável para a região de Jaboticabal, apresentando-se como uma boa alternativa na incorporação de conhecimentos a priori no estudo de dados extremos.

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