Showing papers on "Mixture model published in 1986"
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TL;DR: For an arbitrary one parameter exponential family density, the authors showed how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more)parameter exponential family.
Abstract: For an arbitrary one parameter exponential family density it is shown how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more) parameter exponential family. Reweighted infinitely divisible distributions are shown to be the parametric mixing distributions for which this occurs. As an illustration conditions are given under which a parametric mixture of negative exponentials is in the exponential family. Properties of the posterior are given, including linearity of the posterior mean in the natural parameter. For the discrete case a class of simply-computed yet fully-efficient least-squares estimators is given. A Poisson example is used to demonstrate the strengths and weaknesses of the approach.
30 citations
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01 Apr 1986
TL;DR: The principal result is that the use of the likelihood ratio receiver associated with the mixture model leads to improvements with respect to the classical matched filter, this improvement being measured in term of R O C curves.
Abstract: We study statistical modeling by a Gaussian-Gaussian mixture for two different underwater noise samples. We show that one of them can be adequately described by a Gaussian-Gaussian mixture whereas the other one is very close to a Gaussian model and is described by a mixture with a very small perturbating term. The first noise is also studied with emphasis on the optimal receiver structure for the detection of a deterministic signal. The performance of two test-functions are studied. The principal result is that the use of the likelihood ratio receiver associated with the mixture model leads to improvements with respect to the classical matched filter, this improvement being measured in term of R O C curves.
6 citations
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TL;DR: In this article, the authors investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration of recidivism data, and show that not all mixture models display decreasing heterogeneity over time.
Abstract: Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.
3 citations
01 Jan 1986
TL;DR: The principal results of this study are that, in terms of the receiving operating curves (ROC), the adaptive receiver performs better than the linear one which, in turn, performsbetter than the robust soft limiter.
Abstract: Three receivers are compared for the detection of a known signal in additive ambient underwater noise of seagoing merchant ves- sels. These receivers are: the matched filter, which is the classical lin- ear receiver based on a Gaussian assumption; the soft-limiter, which is the robust receiver when the noise uncertainty is modeled as a mix- ture process with a Gaussian nominal; and the Gaussian-Gaussian mixture likelihood ratio receiver. This last receiver is adaptive in the sense that it is based on a parametric model whose parameters are computed from the actual data. The principal results of this study are that, in terms of the receiving operating curves (ROC), the adaptive receiver performs better than the linear one which, in turn, performs better than the robust soft limiter. This study illustrates the merit of the simple mixture model in adaptive processing for signal detection purposes. Abstract-The reconstruction problem we address is that of working backwards from a spectrogram to a waveform producing it. We de- velop a time-sequential algorithm for reconstruction and investigate its performance as various parameters are changed. Because the algo- rithm is time sequential, memory requirements do not grow linearly with the length of the desired reconstruction. We have found this bounded-memory property important in efficiently using an array pro- cessor to speed up computer simulations requiring reconstruction. Ad- ditionally, a time-sequential bounded-memory, algorithm would be es- sential if a hardware realization intended for continuous operation in real time were eyer to be attempted.
1 citations
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TL;DR: In this article, the authors considered the problem of estimating the number of components in a finite mixture of distributions from some parametric families and developed an estimation procedure using a numerical algorithm for accelerating the convergence of slowly convergent sequences.