作者：
Ghahramani, ZUCL
Gatsby Computat Neurosci Unit London WC1N 3AR England
We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Mark...
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We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Markov models with multiple hidden state variables, multiscale representations, and mixed discrete and continuous variables. Although exact inference in these generalizations is usually intractable, one can use approximate inference algorithms such as Markov chain sampling and variational methods. We describe how such methods are applied to these generalized hidden Markov models. We conclude this review with a discussion of Bayesian methods for model selection in generalized HMMs.
We address the procurement of new components for recyclable products in the context of Kodak's single-use camera. The objective is to find an ordering policy that minimizes the total expected procurement, inventor...
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We address the procurement of new components for recyclable products in the context of Kodak's single-use camera. The objective is to find an ordering policy that minimizes the total expected procurement, inventory holding, and lost sales cost. Distinguishing characteristics of the system are the uncertainty and unobservability associated with return flows of used cameras. We model the system as a closed queueing network, develop a heuristic procedure for adaptive estimation and control, and illustrate our methods with disguised data from Kodak. Using this framework, we investigate the effects of various system characteristics such as informational structure, procurement delay, demand rate, and length of the product's life cycle.
A new methodology is introduced for spatial sampling design when the variable of interest cannot be directly observed, but information on it can be obtained by sampling a related variable, and estimation of the underl...
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A new methodology is introduced for spatial sampling design when the variable of interest cannot be directly observed, but information on it can be obtained by sampling a related variable, and estimation of the underlying model is required. An approach based on entropy has been proposed by Bueso. Angulo, and Alonso (1198, Environ. Ecol. Statist. 5. No. 1, 29-44) in the case where a model for the involved variables is given. However. in some cases a predetermined structure modelling the behaviour of the variables cannot be assumed. In this context, we derive criteria ibr solving the design problem based on the stochastic complexity theory and on the philosophy of the em algorithm. For applying the proposed criteria a computational procedure is developed based on the supplemented em algorithms. The methodology is illustrated with a numerical example. (C) 1999 Academic Press.
Rubin and Thayer recently presented equations to implement maximum likelihood (ML) estimation in factor analysis via the em algorithm. They present an example to demonstrate the efficacy of the algorithm, and propose ...
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Rubin and Thayer recently presented equations to implement maximum likelihood (ML) estimation in factor analysis via the em algorithm. They present an example to demonstrate the efficacy of the algorithm, and propose that their recovery of multiple local maxima of the ML function “certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.” It is shown here, in contrast, that these second derivatives verify that Rubin and Thayer did not find multiple local maxima as claimed. The only known maximum remains the one found by Jöreskog over a decade earlier. The standard errors obtained from the second derivatives and the Fisher information matrix thus remain appropriate where ML assumptions are met. The advantages of the em algorithm over other algorithms for ML factor analysis remain to be demonstrated.
The details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least s...
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The details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least squares regression operations; the largest matrix inversion required is for aq ×q symmetric matrix whereq is the matrix of factors. The example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other; such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.
In generalized linear models each observation is linked with a predicted value based on a linear function of some systematic effects. We sometimes require to link each observation with a linear function of more than o...
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In generalized linear models each observation is linked with a predicted value based on a linear function of some systematic effects. We sometimes require to link each observation with a linear function of more than one predicted value. We embed such models into the generalized linear model framework using composite link functions. The computer program GLIM-3 can be used to fit these models. Illustrative examples are given including a mixed-up contingency table and grouped normal data.
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