We derive and investigate a variant of AIC, the Akaike information criterion, for model selection in settings where the observed data is incomplete. Our variant is based on the motivation provided for the PDIO ('p...
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We derive and investigate a variant of AIC, the Akaike information criterion, for model selection in settings where the observed data is incomplete. Our variant is based on the motivation provided for the PDIO ('predictive divergence for incomplete observation models') criterion of Shimodaira (1994, in: Selecting Models from Data: Artificial Intelligence and Statistics IV, Lecture Notes in Statistics, vol. 89, Springer, New York, pp. 21-29). However, our variant differs from PDIO in its 'goodness-of-fit' term. Unlike AIC and PDIO, which require the computation of the observed-data empirical log-likelihood, our criterion can be evaluated using only complete-data tools, readily available through the em algorithm and the Sem ('supplemented' em) algorithm of Meng and Rubin (Journal of the American Statistical Association 86 (1991) 899-909). We compare the performance of our AIC variant to that of both AIC and PDIO in simulations where the data being modeled contains missing values. The results indicate that our criterion is less prone to overfitting than AIC and less prone to underfitting than PDIO. (C) 1998 Elsevier Science B.V. All rights reserved.
Latent profile analysis is a version of latent structure analysis in which the observed variables are continuous and the latent variables are discrete. The latent structure can be enriched if the latent variables are ...
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Latent profile analysis is a version of latent structure analysis in which the observed variables are continuous and the latent variables are discrete. The latent structure can be enriched if the latent variables are multivariate, but computational difficulties can arise in the implementation of the appropriate version of the em algorithm. These difficulties can be eased by incorporating mean-field approximations in the E-step of the em algorithm. Simple examples, treated in detail, show the effectiveness of these methods, which were first proposed in the engineering and neural-computing literatures. (C) 1998 Elsevier Science B.V. All rights reserved.
An order-restricted version of the standard interval mapping procedure is introduced. The usual LOD scores (base 10 logs of likelihood ratios) used in interval mapping are replaced with LOD scores based on restricted ...
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An order-restricted version of the standard interval mapping procedure is introduced. The usual LOD scores (base 10 logs of likelihood ratios) used in interval mapping are replaced with LOD scores based on restricted likelihood ratio test statistics, which make use of known orderings in the genotype effects at the putative quantitative trait loci (QTL). Simulations demonstrate that individual tests based on the restricted LOD scores can be more powerful than tests based on the standard LOD scores. The new procedure appears to improve QTL detection capability and estimates of both position and genotype effects in certain circumstances, Techniques from order-restricted inference are combined with the em algorithm to estimate genotype effects and compute the restricted LOD scores.
Superresolved image reconstruction is demonstrated by use of multiple images taken through atmospheric turbulence under photon-limited conditions. An iterative reconstruction algorithm applies estimate-maximize techni...
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Superresolved image reconstruction is demonstrated by use of multiple images taken through atmospheric turbulence under photon-limited conditions. An iterative reconstruction algorithm applies estimate-maximize techniques to a series of short-exposure images of the desired object scene along with the corresponding image sequence of a guide star. Simulations show that estimates of the Fourier components both below and above the diffraction limit are improved at successive iterations. The estimated images give finer detail of the original object than does the diffraction-limited image. Effects of photon-noise levels on restoration performance are investigated, and a modification to the reconstruction algorithm is derived that accounts for the effects of CCD read noise. (C) 1998 Optical Society of America.
The paper introduces;array channel division multiple access (AChDMA), which is a new blind algorithm for advanced SDMA in mobile communications systems, As an SDMA technique, AChDMA increases the system capacity by im...
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The paper introduces;array channel division multiple access (AChDMA), which is a new blind algorithm for advanced SDMA in mobile communications systems, As an SDMA technique, AChDMA increases the system capacity by improving its time and frequency reuse, Being a blind algorithm, it requires no training sequences, previously known directions of arrival, or user codes, AChDMA separates the moving sources by tracking their multipath configuration and resolving their distinct generalized steering vectors, It maximizes a finite mixture log-likelihood function, combining an efficient initialization procedure with an em-based algorithm that provides fast convergence to the global maximum. AChDMA reconstructs the mobile data sequences using only internal variables of the em algorithm, These characteristics and its parallel structure make AChDMA suitable for real-time mobile communications. We test AChDMA with synthetic data in a number of different scenarios, illustrating the ability of the blind algorithm to separate and track in time the moving sources, and showing its good performance in a variety of practical situations.
作者：
Zhou, XHRodenberg, CAIndiana Univ
Sch MedRegenstrief Inst Hlth Care Dept Med Div Biostat Bloomington IN 47405 USA Pfizer Inc
Div Cent Res Div Biometr Groton CT 06340 USA
Verification bias can occur in studies of test's accuracy if only some of tested patients receive disease verification. The current methods for correcting for verification bias assume conditional independence for ...
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Verification bias can occur in studies of test's accuracy if only some of tested patients receive disease verification. The current methods for correcting for verification bias assume conditional independence for verification, which means that the probability of verifying a patient depends only on the test result, not on the unobserved disease status of the patient.
Analysis of convergence of the algebraic reconstruction technique (ART) shows it to be predisposed to converge to a solution faster than simultaneous methods, such as those of the Cimmino-Landweber type, the expectati...
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Analysis of convergence of the algebraic reconstruction technique (ART) shows it to be predisposed to converge to a solution faster than simultaneous methods, such as those of the Cimmino-Landweber type, the expectation maximization maximum likelihood method for the Poisson model (emML), and the simultaneous multiplicative ART (SMART), which use all the data at each step, Although choice of ordering of the data and of relaxation parameters are important, as Herman and Meyer have shown, they are not the full story, The analogous multiplicative ART (MART), which applies only to systems y = Pr in which y > 0, P greater than or equal to 0 and a nonnegative solution is sought, is also sequential (or "row-action"), rather than simultaneous, but does not generally exhibit the same accelerated convergence relative to its simultaneous version, SMART. By dividing each equation by the maximum of the corresponding row of P, we find that this rescaled MART (RMART) does converge faster, when solutions exist, significantly so in cases in which the row maxima are substantially less than one, Such cases arise frequently in tomography and when the columns of P have been normalized to have sum one. Between simultaneous methods, which use all the data at each step, and sequential (or row-action) methods, which use only a single data value at each step, there are the block-iterative (or ordered subset) methods, in which a single block or subset of the data is processed at each step. The ordered subset em (OSem) of Hudson et al, is significantly faster than the emML, but often fails to converge. The "rescaled block-iterative" emML RBI-emML) is an accelerated block-iterative version of emML that converges, in the consistent case, to a solution, for any choice of subsets;it reduces to OSem when the restrictive "subset balanced" condition holds, Rescaled block-iterative versions of SMART and MART also exhibit accelerated convergence.
This paper is concerned with situations in which there are missing or otherwise incomplete data and the full likelihood may not be available. Extensions of the em algorithm are developed to deal with estimation via ge...
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This paper is concerned with situations in which there are missing or otherwise incomplete data and the full likelihood may not be available. Extensions of the em algorithm are developed to deal with estimation via general estimating functions and in particular the quasi-score. The E-step is replaced by projecting the quasi-score and the M-step requires the solution of an estimating equation. The standard em algorithm can be obtained as a particular case if the likelihood is available.
We continue the theme of previous papers [J. Opt. Sec. Am. A 7, 1266 (1990);12, 834 (1995)] on objective (task-based) assessment of image quality. We concentrate on signal-detection tasks and figures of merit related ...
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We continue the theme of previous papers [J. Opt. Sec. Am. A 7, 1266 (1990);12, 834 (1995)] on objective (task-based) assessment of image quality. We concentrate on signal-detection tasks and figures of merit related to the ROC (receiver operating characteristic) curve. Many different expressions for the area under an ROC curve (AUC) are derived for an arbitrary discriminant function, with different assumptions on what information about the discriminant function is available. In particular, it is shown that AUC can be expressed by a principal-value integral that involves the characteristic functions of the discriminant. Then the discussion is specialized to the ideal observer, defined as one who uses the likelihood ratio (or some monotonic transformation of it, such as its logarithm) as the discriminant function. The properties of the ideal observer are examined from first principles. Several strong constraints on the moments of the likelihood ratio or the log likelihood are derived, and it is shown that the probability density functions for these test statistics are intimately related. In particular, some surprising results are presented for the case in which the log likelihood is normally distributed under one hypothesis. To unify these considerations, a new quantity called the likelihood-generating function is defined. It is shown that all moments of both the likelihood and the log likelihood under both hypotheses can be derived from this one function. Moreover, the AUC can be expressed, to an excellent approximation, in terms of the likelihood-generating function evaluated at the origin. This expression is the leading term in an asymptotic expansion of the AUG;it is exact whenever the likelihood-generating function behaves linearly near the origin. It is also shown that the likelihood-generating function at the origin sets a lower bound on the AUC in all cases. (C) 1998 Optical Society of America.
The likelihood function of a multivariate Cauchy distribution with unknown location and scatter parameters in p dimensions has a unique maximum provided the sample is in general position and is of size n > p + 1 (s...
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The likelihood function of a multivariate Cauchy distribution with unknown location and scatter parameters in p dimensions has a unique maximum provided the sample is in general position and is of size n > p + 1 (see Kent and Tyler 1991 and Kent et al., 1994). fn this paper, we show that when n = p + 1, the maximum of the location-scatter Cauchy likelihood function occurs when the parameters lie on a p-dimensional surface.
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