scholarly journals A transformation‐based approach to Gaussian mixture density estimation for bounded data

2019 ◽  
Author(s):  
Luca Scrucca
Keyword(s):  
Density Estimation ◽  
Gaussian Mixture ◽  
Mixture Density ◽  
Bounded Data

Differential Log Likelihood for Evaluating and Learning Gaussian Mixtures

2006 ◽  
Vol 18 (2) ◽  
pp. 430-445 ◽  
Author(s):  
Marc M. Van Hulle
Keyword(s):  
Density Estimation ◽  
Learning Strategy ◽  
Gaussian Mixture ◽  
Optimal Number ◽  
Data Sets ◽  
Gaussian Mixtures ◽  
Real World Data ◽  
Mixture Density ◽  
Wide Range ◽  
Log Likelihood

We introduce a new unbiased metric for assessing the quality of density estimation based on gaussian mixtures, called differential log likelihood. As an application, we determine the optimal smoothness and the optimal number of kernels in gaussian mixtures. Furthermore, we suggest a learning strategy for gaussian mixture density estimation and compare its performance with log likelihood maximization for a wide range of real-world data sets.

scholarly journals Reconciling differences in stratospheric ozone composites

2017 ◽  
Vol 17 (20) ◽  
pp. 12269-12302 ◽  
Author(s):  
William T. Ball ◽  
Justin Alsing ◽  
Daniel J. Mortlock ◽  
Eugene V. Rozanov ◽  
Fiona Tummon ◽  
...  
Keyword(s):  
Time Series ◽  
Likelihood Function ◽  
Stratospheric Ozone ◽  
Gaussian Mixture ◽  
Robust Estimate ◽  
Mixture Density ◽  
Source Data ◽  
Ozone Trends ◽  
Decadal Trend

Abstract. Observations of stratospheric ozone from multiple instruments now span three decades; combining these into composite datasets allows long-term ozone trends to be estimated. Recently, several ozone composites have been published, but trends disagree by latitude and altitude, even between composites built upon the same instrument data. We confirm that the main causes of differences in decadal trend estimates lie in (i) steps in the composite time series when the instrument source data changes and (ii) artificial sub-decadal trends in the underlying instrument data. These artefacts introduce features that can alias with regressors in multiple linear regression (MLR) analysis; both can lead to inaccurate trend estimates. Here, we aim to remove these artefacts using Bayesian methods to infer the underlying ozone time series from a set of composites by building a joint-likelihood function using a Gaussian-mixture density to model outliers introduced by data artefacts, together with a data-driven prior on ozone variability that incorporates knowledge of problems during instrument operation. We apply this Bayesian self-calibration approach to stratospheric ozone in 10° bands from 60° S to 60° N and from 46 to 1 hPa (∼ 21–48 km) for 1985–2012. There are two main outcomes: (i) we independently identify and confirm many of the data problems previously identified, but which remain unaccounted for in existing composites; (ii) we construct an ozone composite, with uncertainties, that is free from most of these problems – we call this the BAyeSian Integrated and Consolidated (BASIC) composite. To analyse the new BASIC composite, we use dynamical linear modelling (DLM), which provides a more robust estimate of long-term changes through Bayesian inference than MLR. BASIC and DLM, together, provide a step forward in improving estimates of decadal trends. Our results indicate a significant recovery of ozone since 1998 in the upper stratosphere, of both northern and southern midlatitudes, in all four composites analysed, and particularly in the BASIC composite. The BASIC results also show no hemispheric difference in the recovery at midlatitudes, in contrast to an apparent feature that is present, but not consistent, in the four composites. Our overall conclusion is that it is possible to effectively combine different ozone composites and account for artefacts and drifts, and that this leads to a clear and significant result that upper stratospheric ozone levels have increased since 1998, following an earlier decline.

scholarly journals Bayesian classification of vegetation types with Gaussian mixture density fitting to indicator values

2007 ◽  
Vol 18 (4) ◽  
pp. 605-612 ◽  
Author(s):  
Jan‐Philip M. Witte ◽  
Rafał B. Wójcik ◽  
Paul J.J.F. Torfs ◽  
Martin W.H. Haan ◽  
Stephan Hennekens
Keyword(s):  
Gaussian Mixture ◽  
Bayesian Classification ◽  
Vegetation Types ◽  
Indicator Values ◽  
Mixture Density ◽  
Density Fitting

Kernel-Based Topographic Map Formation by Local Density Modeling

2002 ◽  
Vol 14 (7) ◽  
pp. 1561-1573 ◽  
Author(s):  
Marc M. Van Hulle
Keyword(s):  
Learning Algorithm ◽  
Local Density ◽  
Gaussian Mixture ◽  
Density Model ◽  
Topographic Map ◽  
Mixture Density ◽  
Gaussian Kernels ◽  
New Learning ◽  
Local Input ◽  
Density Modeling

We introduce a new learning algorithm for kernel-based topographic map formation. The algorithm generates a gaussian mixture density model by individually adapting the gaussian kernels' centers and radii to the assumed gaussian local input densities.

Nonparametric Least Squares Mixture Density Estimation

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Chew-Seng Chee
Keyword(s):  
Least Squares ◽  
Density Estimation ◽  
Least Squares Method ◽  
Bandwidth Selection ◽  
Estimation Problem ◽  
Density Estimator ◽  
Mixing Distribution ◽  
Mixture Density ◽  
Integrated Squared Error ◽  
Nonparametric Mixture Model

In this paper, we consider using nonparametric mixtures for density estimation. The mixture density estimation problem simply reduces to the problem of estimating a mixing distribution in the nonparametric mixture model. We focus on the least squares method for mixture density estimation problem. In a simulation experiment, the performance of the least squares mixture density estimator (MDE) and the kernel density estimator (KDE) is assessed by the mean integrated squared error. The performance improvement of MDE over KDE for some common densities is achieved by using cross-validation method for bandwidth selection.

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