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38
Maximum A Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains
 IEEE Transactions on Speech and Audio Processing
, 1994
"... In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addr ..."
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Cited by 491 (39 self)
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In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addressed. Using HMMs with Gaussian mixture state observation densities as an example, it is assumed that the prior densities for the HMM parameters can be adequately represented as a product of Dirichlet and normalWishart densities. The classical maximum likelihood estimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and MAP estimation formulas are developed. Prior density estimation issues are discussed for two classes of applications: parameter smoothing and model adaptation, and some experimental results are given illustrating the practical interest of this approach. Because of its adaptive nature, Bayesian learning is shown to serve as a unified approach for a wide range of speech recognition applications
A Scaled Difference Chisquare Test Statistic for Moment Structure Analysis
"... A family of scaling corrections aimed to improve the chisquare approximation of goodnessoffit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, SatorraBentler's (SB) scaling corrections are available in ..."
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Cited by 45 (0 self)
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A family of scaling corrections aimed to improve the chisquare approximation of goodnessoffit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, SatorraBentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say M 0 implies on a less restricted one M 1 .IfT 0 and T 1 denote the goodnessoffit test statistics associated to M 0 and M 1 , respectively, then typically the difference T d = T 0 ; T 1 is used as a chisquare test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models M 0 and M 1 . As in the case of the goodnessoffit test, it is of interest to scale the statistic T d in order to improveitschisquare approximation in realistic, i.e., nonasymptotic and nonn...
Optimal Structure from Motion: Local Ambiguities and Global Estimates
, 2000
"... “Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a threedimensional scene from the motion of its projection onto a twodimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably o ..."
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Cited by 23 (5 self)
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“Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a threedimensional scene from the motion of its projection onto a twodimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably optimal with respect to a chosen norm. In particular, we cast SFM as the minimization of a highdimensional quadratic cost function, and show how it is possible to reduce it to the minimization of a twodimensional function whose stationary points are in onetoone correspondence with those of the original cost function. As a consequence, we can plot the reduced cost function and characterize the configurations of structure and motion that result in local minima. As an example, we discuss two local minima that are associated with wellknown visual illusions. Knowledge of the topology of the residual in the presence of such local minima allows us to formulate minimization algorithms that, in addition to provably converge to stationary points of the original cost function, can switch between different local extrema in order to converge to the global minimum, under suitable conditions. We also offer an experimental study of the distribution of the estimation error in the presence of noise in the measurements, and characterize the sensitivity of the algorithm using the structure of Fisher’s Information matrix.
A Bayesian Approach to Robust Binary Nonparametric Regression
, 1997
"... This paper presents a Bayesian approach to binary nonparametric regression which assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The paper makes the following contributions. First, a comprehensive approach is presented ..."
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Cited by 14 (1 self)
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This paper presents a Bayesian approach to binary nonparametric regression which assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The paper makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out, and the estimates made robust to outliers. Second, the approach can handle a wide rage of link functions. Third, efficient state space based algorithms are used to carry out the computations. Fourth, an extensive set of simulations is carried out which show that the Bayesian estimator works well and compares favorably to two estimators which are widely used in practice.
Estimation of Structural Parameters and Marginal Effects in Binary Choice Panel Data Models with Fixed Effects
, 2005
"... Fixed effects estimates of structural parameters in nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper I show that the first term in a largeT expansion of the incidental parameters bias for probit fixed effects estimators of index coefficients is ..."
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Cited by 11 (3 self)
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Fixed effects estimates of structural parameters in nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper I show that the first term in a largeT expansion of the incidental parameters bias for probit fixed effects estimators of index coefficients is proportional to the true parameter value for general distributions of regressors and individual effects. This result allows me to derive a lower bound for the bias that depends only on the number of time periods of the panel. Proportionality is also used to show that the biases of ratios of coefficients and average marginal effects are identically zero in the absence of heterogeneity. Moreover, for a wide range of distributions of regressors and individual effects, numerical examples show that these biases are also very small. These results help explain previous Monte Carlo evidence for probit fixed effects estimates of index coefficients and marginal effects. Additional Monte Carlo examples suggest that the small bias property for fixed effects estimators of marginal effects holds for logit and linear probability models, and for the effects of exogenous variables in dynamic discrete choice models. The properties of logit and probit fixed effects estimates of model parameters and marginal effects are illustrated through an analysis of female labor force participation using data from the PSID. The results suggest that the significant biases in fixed effects estimates of model parameters do not contaminate the estimates of marginal effects in static models.
Dissecting the Random Component of Utility
, 2002
"... We illustrate and discuss several general issues associated with the random component of utility, or more generally ‘‘unobserved variability’’. We posit a general conceptual framework that suggests a variance components view as an appropriate structure for unobserved variability. This framework sugg ..."
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Cited by 6 (2 self)
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We illustrate and discuss several general issues associated with the random component of utility, or more generally ‘‘unobserved variability’’. We posit a general conceptual framework that suggests a variance components view as an appropriate structure for unobserved variability. This framework suggests that ‘‘unobserved heterogeneity’ ’ is only one component of unobserved variability; hence, a more general view is required. We review a considerable amount of empirical research that suggests that random components are unlikely to be independent of systematic components, and random component variances are unlikely to be constant between or within individuals, time periods, locations, etc. We also review evidence that random components are functions of (elements of) systematic components. The latter suggests considerable caution in the use and interpretation of complex choice model specifications, in particular recently introduced forms of random parameter models that purport to estimate distributions of preference parameters. Several areas for future research are identified and discussed.
Score Statistics for Mapping Quantitative Trait Loci
, 2004
"... We propose a method to detect the existence of a quantitative trait loci (QTL) in a backcross population using a score test.Under the null hypothesis of no QTL, all phenotype random variables are independent and identically distributed, and the maximum likelihood estimates (MLEs) of parameters in th ..."
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Cited by 4 (0 self)
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We propose a method to detect the existence of a quantitative trait loci (QTL) in a backcross population using a score test.Under the null hypothesis of no QTL, all phenotype random variables are independent and identically distributed, and the maximum likelihood estimates (MLEs) of parameters in the model are usually easy to obtain. Since the score test only uses the MLEs of parameters under the null hypothesis, it is computationally simpler than the likelihood ratio test (LRT). Moreover, because the location parameter of the QTL is unidentifiable under the null hypothesis, the distribution of the maximum of the LRT statistics, typically the statistic of choice for testing H0: no QTL, does not have the standard chisquare distribution asymptotically under the null hypothesis. From the simple structure of the score test statistics, the asymptotic null distribution can be derived for the maximum of the square of score test statistics. Numerical methods are proposed to compute the asymptotic null distribution and the critical thresholds can be obtained accordingly. A simple backcross design is used to demonstrate the application of the score test to QTL mapping. The proposed method can be readily extended to more complex situations.
Statistical Analysis of Cell Motion
, 2001
"... Statistical Analysis of Cell Motion by Edward Luke Ionides Doctor of Philosophy in Statistics University of California, Berkeley Professor David R. Brillinger, Chair Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using s ..."
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Cited by 3 (3 self)
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Statistical Analysis of Cell Motion by Edward Luke Ionides Doctor of Philosophy in Statistics University of California, Berkeley Professor David R. Brillinger, Chair Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic di#erential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of cells and for underlying biophysical mechanisms. A state space model formulation is used to link models proposed for cell velocity to observed data. Sequential Monte Carlo methods enable parameter estimation and model assessment for a range of applicable models. One particular experimental situation, involving the e#ect of an electric field on cell behavior, is considered in detail.
Optimal Experimental Design: Spatial Sampling
, 1994
"... this paper it is assumed that an observed surface (function, field) is a realization of some random process y(x; t), where x 2 X, t 2 T , and X and T are compact. Measurement (observation, sampling) provides realizations y ij at the points x i and the times ..."
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Cited by 2 (1 self)
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this paper it is assumed that an observed surface (function, field) is a realization of some random process y(x; t), where x 2 X, t 2 T , and X and T are compact. Measurement (observation, sampling) provides realizations y ij at the points x i and the times
Design Of Spatial Experiments: Model Fitting And Prediction
"... The main objective of the paper is to describe and develop model oriented methods and algorithms for the design of spatial experiments. Unlike many other publications in this area, the approach proposed here is essentially based on the ideas of convex design theory. 1. ..."
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Cited by 2 (0 self)
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The main objective of the paper is to describe and develop model oriented methods and algorithms for the design of spatial experiments. Unlike many other publications in this area, the approach proposed here is essentially based on the ideas of convex design theory. 1.