Results 1  10
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22
Sequential MCMC for Bayesian model selection
 IEEE Higher Order Statistics Workshop
, 1999
"... In this paper, we address the problem of sequential Bayesian model selection. This problem does not usually admit any closedform analytical solution. We propose here an original sequential simulationbased method to solve the associated Bayesian computational problems. This method combines sequenti ..."
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Cited by 38 (17 self)
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In this paper, we address the problem of sequential Bayesian model selection. This problem does not usually admit any closedform analytical solution. We propose here an original sequential simulationbased method to solve the associated Bayesian computational problems. This method combines sequential importance sampling, a resampling procedure and reversible jump MCMC moves. We describe a generic algorithm and then apply it to the problem of sequential Bayesian model order estimation of autoregressive (AR) time series observed in additive noise. 1
Robust Full Bayesian Learning for Radial Basis Networks
, 2001
"... We propose a hierachical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters,... ..."
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Cited by 24 (4 self)
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We propose a hierachical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters,...
Assessing model mimicry using the parametric bootstrap
 Journal of Mathematical Psychology
, 2004
"... We present a general sampling procedure to quantify model mimicry, defined as the ability of a model to account for data generated by a competing model. This sampling procedure, called the parametric bootstrap crossfitting method (PBCM; cf. Williams (J. R. Statist. Soc. B 32 (1970) 350; Biometrics ..."
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Cited by 19 (3 self)
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We present a general sampling procedure to quantify model mimicry, defined as the ability of a model to account for data generated by a competing model. This sampling procedure, called the parametric bootstrap crossfitting method (PBCM; cf. Williams (J. R. Statist. Soc. B 32 (1970) 350; Biometrics 26 (1970) 23)), generates distributions of differences in goodnessoffit expected under each of the competing models. In the data informed version of the PBCM, the generating models have specific parameter values obtained by fitting the experimental data under consideration. The data informed difference distributions can be compared to the observed difference in goodnessoffit to allow a quantification of model adequacy. In the data uninformed version of the PBCM, the generating models have a relatively broad range of parameter values based on prior knowledge. Application of both the data informed and the data uninformed PBCM is illustrated with several examples. r 2003 Elsevier Inc. All rights reserved. 1.
Sequential Bayesian Estimation And Model Selection For Dynamic Kernel Machines
, 2000
"... In this paper, we address the complex problem of sequential Bayesian estimation and model selection/averaging. This problem does not usually admit any type of closedform analytical solutions and, as a result, one has to resort to numerical methods. We propose here an original and powerful sequentia ..."
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Cited by 14 (8 self)
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In this paper, we address the complex problem of sequential Bayesian estimation and model selection/averaging. This problem does not usually admit any type of closedform analytical solutions and, as a result, one has to resort to numerical methods. We propose here an original and powerful sequential simulationbased strategy to perform the necessary computations. This strategy is based on Monte Carlo particle methods and model selection/averaging using predictive distributions. It combines sequential importance sampling, RaoBlackwellisation, a selection procedure and reversible jump MCMC moves. We demonstrate the eectiveness of the method by performing inference and learning on a hybrid model consisting of a dynamic linear model and a dynamic mixture of kernel basis functions.
Robust Full Bayesian Learning for Neural Networks
, 1999
"... In this paper, we propose a hierarchical full Bayesian model for neural networks. This model treats the model dimension (number of neurons), model parameters, regularisation parameters and noise parameters as random variables that need to be estimated. We develop a reversible jump Markov chain Monte ..."
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Cited by 12 (9 self)
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In this paper, we propose a hierarchical full Bayesian model for neural networks. This model treats the model dimension (number of neurons), model parameters, regularisation parameters and noise parameters as random variables that need to be estimated. We develop a reversible jump Markov chain Monte Carlo (MCMC) method to perform the necessary computations. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible jump MCMC simulated annealing algorithm to optimise neural networks. This algorithm enables us to maximise the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima. We show that by calibrating the full hierarchical ...
Reversible Jump MCMC Simulated Annealing for Neural Networks
"... We propose a novel reversible jump Markov chain Monte Carlo (MCMC) simulated annealing algorithm to optimize radial basis function (RBF) networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis functions. It performs a global ..."
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Cited by 12 (2 self)
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We propose a novel reversible jump Markov chain Monte Carlo (MCMC) simulated annealing algorithm to optimize radial basis function (RBF) networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis functions. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima. We also show that by calibrating a Bayesian model, we can obtain the classical AIC, BIC and MDL model selection criteria within a penalized likelihood framework. Finally, we show theoretically and empirically that the algorithm converges to the modes of the full posterior distribution in an efficient way. likelihood estimation, with the aforementioned model selection criteria, is performed by maximizing the calibrated posterior distribution. To accomplish this goal, we propose an MCMC simulated annealing algorithm, which makes use of a homogeneous reversible jump MCMC kernel as proposal. This approach has the advantage that we can start with an arbitrary model order and the algorithm will perform dimension jumps until it finds the "true " model order. That is, one does not have to resort to the more expensive task of running a fixed dimension algorithm for each possible model order and subsequently selecting the best model. We also present a convergence theorem for the algorithm. The complexity of the problem does not allow for a comprehensive discussion in this short paper.
Bayesian Methods for Neural Networks
, 1999
"... Summary The application of the Bayesian learning paradigm to neural networks results in a flexible and powerful nonlinear modelling framework that can be used for regression, density estimation, prediction and classification. Within this framework, all sources of uncertainty are expressed and meas ..."
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Cited by 9 (0 self)
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Summary The application of the Bayesian learning paradigm to neural networks results in a flexible and powerful nonlinear modelling framework that can be used for regression, density estimation, prediction and classification. Within this framework, all sources of uncertainty are expressed and measured by probabilities. This formulation allows for a probabilistic treatment of our a priori knowledge, domain specific knowledge, model selection schemes, parameter estimation methods and noise estimation techniques. Many researchers have contributed towards the development of the Bayesian learning approach for neural networks. This thesis advances this research by proposing several novel extensions in the areas of sequential learning, model selection, optimisation and convergence assessment. The first contribution is a regularisation strategy for sequential learning based on extended Kalman filtering and noise estimation via evidence maximisation. Using the expectation maximisation (EM) algorithm, a similar algorithm is derived for batch learning. Much of the thesis is, however, devoted to Monte Carlo simulation methods. A robust Bayesian method is proposed to estimate,
Conditional Model Order Estimation
 IEEE Transactions on Signal Processing
, 2001
"... Abstract—A new approach to model order selection is proposed. Based on the theory of sufficient statistics, the method does not require any prior knowledge of the model parameters. It is able to discriminate between models by basing the decision on the part of the data that is independent of the mod ..."
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Cited by 5 (0 self)
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Abstract—A new approach to model order selection is proposed. Based on the theory of sufficient statistics, the method does not require any prior knowledge of the model parameters. It is able to discriminate between models by basing the decision on the part of the data that is independent of the model parameters. This is accomplished conceptually by transforming the data into a sufficient statistic and an ancillary statistic with respect to the model parameters. It is the probability density function of the ancillary statistic when adjusted for its dimensionality that is used to estimate the order. Furthermore, the rule is directly tied to the goal of minimizing the probability of error and does not employ any asymptotic approximations. The estimator can be shown to be consistent and, via computer simulation, is found to outperform the minimum description length estimator. Index Terms—Adaptive signal detection, modeling, spectral analysis, speech analysis. I.
Discrepancy Risk Model Selection Test Theory For Comparing Possibly Misspecified Or Nonnested Models
"... An extension of Vuong's model selection theory, Discrepancy Risk Model Selection Test (DRMST) Theory, is developed for testing the null hypothesis that two given probability models fit some underlying data generating process equally effectively with respect to a prespecified significance level. DRM ..."
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Cited by 5 (0 self)
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An extension of Vuong's model selection theory, Discrepancy Risk Model Selection Test (DRMST) Theory, is developed for testing the null hypothesis that two given probability models fit some underlying data generating process equally effectively with respect to a prespecified significance level. DRMST theory is applicable to a wide range of goodnessoffit (i.e., discrepancy risk) functions and is applicable in situations where the models might be nonnested or misspecified. Moreover, DRMST theory is applicable to statistical environments where the observations are identically distributed but not necessarily independent. Key words: asymptotic statistical theory, model selection, hypothesistesting, model misspecification 3 Introduction Let\Omega be a set of probability distributions. Let the distribution generating the data be the distinguished "environmental distribution" p e 2 \Omega\Gamma Define a "probability model" , M \Theta , (i.e., a "family of approximating distributions " f...
Bayesian Model Selection of Autoregressive Processes
 J. TIME SERIES ANALYSIS
, 2000
"... This paper poses the problem of model order determination of an autoregressive (AR) process within a Bayesian framework. Several original hierarchical prior models are proposed that allow for the stability of the model to be enforced and account for a possible unknown initial state. Obtaining the po ..."
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Cited by 4 (4 self)
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This paper poses the problem of model order determination of an autoregressive (AR) process within a Bayesian framework. Several original hierarchical prior models are proposed that allow for the stability of the model to be enforced and account for a possible unknown initial state. Obtaining the posterior model order probabilities requires integration of the resulting posterior distribution, an operation which is analytically intractable. Here stochastic reversible jump Markov chain Monte Carlo (MCMC) algorithms are developed to perform the required integration by simulating from the posterior distribution. The methods developed are evaluated in simulation studies on a number of synthetic and real data sets, and compared to standard model selection criteria.