We consider the use of Monte Carlo methods to obtain maximum likelihood estimates for random effects models and distinguish between the pointwise and functional approaches. We explore the relationship between the two ...
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We consider the use of Monte Carlo methods to obtain maximum likelihood estimates for random effects models and distinguish between the pointwise and functional approaches. We explore the relationship between the two approaches and compare them with the em algorithm. The functional approach is more ambitious but the approximation is local in nature which we demonstrate graphically using two simple examples. A remedy is to obtain successively better approximations of the relative likelihood function near the true maximum likelihood estimate. To save computing time, we use only one Newton iteration to approximate the maximiser of each Monte Carlo likelihood and show that this is equivalent to the pointwise approach. The procedure is applied to fit a latent process model to a set of polio incidence data. The paper ends by a comparison between the marginal likelihood and the recently proposed hierarchical likelihood which avoids integration altogether.
For clustering mixed categorical and continuous data, Lawrence and Krzanowski (1996) proposed a finite mixture model in which component densities conform to the location model. In the graphical models literature the l...
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For clustering mixed categorical and continuous data, Lawrence and Krzanowski (1996) proposed a finite mixture model in which component densities conform to the location model. In the graphical models literature the location model is known as the homogeneous Conditional Gaussian model. In this paper it is shown that their model is not identifiable without imposing additional restrictions. Specifically, for g groups and m locations, (g!)(m-1) distinct sets of parameter values (not including permutations of the group mixing parameters) produce the same likelihood function. Excessive shrinkage of parameter estimates in a simulation experiment reported by Lawrence and Krzanowski (1996) is shown to be an artifact of the model's non-identifiability. Identifiable finite mixture models can be obtained by imposing restrictions on the conditional means of the continuous variables. These new identified models are assessed in simulation experiments. The conditional mean structure of the continuous variables in the restricted location mixture models is similar to that in the underlying variable mixture models proposed by Everitt (1988), but the restricted location mixture models are more computationally tractable.
This paper proposes a novel framework of online hierarchical transformation of hidden Markov model (HMM) parameters for adaptive speech recognition. Our goal is to incrementally transform (or adapt) all the HMM parame...
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This paper proposes a novel framework of online hierarchical transformation of hidden Markov model (HMM) parameters for adaptive speech recognition. Our goal is to incrementally transform (or adapt) all the HMM parameters to a new acoustical environment even though most of HMM units are unseen in observed adaptation data. We establish a hierarchical tree of HMM units and apply the tree to dynamically search the transformation parameters for individual HMM mixture components. In this paper, the transformation framework is formulated according to the approximate Bayesian estimate, which the prior statistics and the transformation parameters can be jointly and incrementally refreshed after each consecutive adaptation data is presented. Using this formulation, only the refreshed prior statistics and the current block of data are needed for online transformation. In a series of speaker adaptation experiments on the recognition of 408 Mandarin syllables, we examine the effects on constructing various types of hierarchical trees. The efficiency and effectiveness of proposed method on incremental adaptation of overall HMM units are also confirmed. Besides, we demonstrate the superiority of proposed online transformation to Hue's on-line adaptation [16] for a wide range of adaptation data.
A non-homogeneous hidden Markov model is proposed for relating precipitation occurrences at multiple rain-gauge stations to broad scale atmospheric circulation patterns (the so-called 'downscaling problem'). W...
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A non-homogeneous hidden Markov model is proposed for relating precipitation occurrences at multiple rain-gauge stations to broad scale atmospheric circulation patterns (the so-called 'downscaling problem'). We model a 15-year sequence of winter data from 30 rain stations in south-western Australia. The first 10 years of data are used for model development and the remaining 5 years are used for model evaluation. The fitted model accurately reproduces the observed rainfall statistics in the reserved data despite a shift in atmospheric circulation land, consequently, rainfall) between the two periods. The fitted;model also provides some useful insights into the processes driving rainfall in this region.
As an extension to the conventional em algorithm, tree-structured em algo rithm is proposed for the ML estimation of parameters of superimposed signals. For the special case of superimposed signals in Gaussian n...
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As an extension to the conventional em algorithm, tree-structured em algo rithm is proposed for the ML estimation of parameters of superimposed signals. For the special case of superimposed signals in Gaussian noise, the IQML al gorithm of Bresler and Macovski [19] is incorporated to the M-step of the em based algorithms resulting in more efficient and reliable maximization. Based on simulations, it is observed that TSem converges significantly faster than em, but it is more sensitive to the initial parameter estimates. Hybrid-em al gorithm, which performs a few em iterations prior to the TSem iterations, is proposed to capture the desired features of both the em and TSem algorithms. Based on simulations, it is found that Hybrid-em algorithm has significantly more robust convergence than both the em and TSem algorithms.
The S-dimensional (S-D) assignment algorithm is a recently-favored approach to multitarget tracking in which the data association is formulated as a generalized multidimensional matching problem, and solved by a Lagra...
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ISBN:
(纸本)081943194X
The S-dimensional (S-D) assignment algorithm is a recently-favored approach to multitarget tracking in which the data association is formulated as a generalized multidimensional matching problem, and solved by a Lagrangian (dual) relaxation approach. The Probabilistic Multiple Hypothesis Tracking (PMHT) algorithm is a relatively new method, which uses the em algorithm and a modified probabilistic model to develop a "soft" association tracker. In this paper, we implement the two algorithms (S = 3, in the S-D assignment algorithm) in the multitarget tracking problem, presented with false alarms and imperfect target detection. Simulation results for various scenarios are presented and the performances of the two algorithms are compared in terms of computational time and percentage of lost tracks.
We develop an algorithm for estimating generalized autoregressive conditional heteroscedasticity models for time series containing some censored observations. Motivation for the algorithm comes from those futures mark...
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We develop an algorithm for estimating generalized autoregressive conditional heteroscedasticity models for time series containing some censored observations. Motivation for the algorithm comes from those futures markets and some equity markets that have limits constraining the maximum allowable movement in price in a day. When a limit is reached, trading stops and the equilibrium price is not observed. We maximize the likelihood function by replacing the unobservable squared error terms with their expected values. We evaluate the algorithm performance by extensive simulation and apply it to treasury-bill futures data from a period of high volatility and frequent limit moves.
This paper investigates interactions between seasonal and cyclical movements in U.S. payroll employment. Using a multivariate unobserved components model, we test for such interactions and find that they are statistic...
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This paper investigates interactions between seasonal and cyclical movements in U.S. payroll employment. Using a multivariate unobserved components model, we test for such interactions and find that they are statistically significant in a number of industries. Still, most industry-level seasonality appears to be idiosyncratic. The model also identifies an unobserved common cycle that exhibits similar business cycle properties, but smaller seasonal variation, than aggregate payroll employment. The overall industry-level seasonal factors generated by our model do not differ much from univariate X-ll seasonals in sample, but some differences arise in out-of-sample experiments. (C) 1999 Published by Elsevier Science B.V. All rights reserved.
Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two ...
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Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in rime will be partially spurious. Latent Markov models make it possible to separate true change from measurement error. The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both time-constant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.
A novel approach is proposed to estimate the seemingly unrelated regressions model in which the dependent variables might be censored. Our method via the Monte Carlo version of the em algorithm can be used to retrieve...
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A novel approach is proposed to estimate the seemingly unrelated regressions model in which the dependent variables might be censored. Our method via the Monte Carlo version of the em algorithm can be used to retrieve the latent values which greatly simplify the computation of the E-step and a sequence of conditional maximizations is performed to implement the M-step. Its practicality is illustrated by estimating a bivariate SUR Tobit model to determine the payments of cash and stock dividends. (C) 1999 Elsevier Science S.A. All rights reserved. JEL classification: C15;C34.
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