@inproceedings{11740,
  abstract     = {{In this contribution we derive the Maximum A-Posteriori (MAP) estimates of the parameters of a Gaussian Mixture Model (GMM) in the presence of noisy observations. We assume the distortion to be white Gaussian noise of known mean and variance. An approximate conjugate prior of the GMM parameters is derived allowing for a computationally efficient implementation in a sequential estimation framework. Simulations on artificially generated data demonstrate the superiority of the proposed method compared to the Maximum Likelihood technique and to the ordinary MAP approach, whose estimates are corrected by the known statistics of the distortion in a straightforward manner.}},
  author       = {{Chinaev, Aleksej and Haeb-Umbach, Reinhold}},
  booktitle    = {{38th International Conference on Acoustics, Speech and Signal Processing (ICASSP 2013)}},
  issn         = {{1520-6149}},
  keywords     = {{Gaussian noise, maximum likelihood estimation, parameter estimation, GMM parameter, Gaussian mixture model, MAP estimation, Map-based estimation, maximum a-posteriori estimation, maximum likelihood technique, noisy observation, sequential estimation framework, white Gaussian noise, Additive noise, Gaussian mixture model, Maximum likelihood estimation, Noise measurement, Gaussian mixture model, Maximum a posteriori estimation, Maximum likelihood estimation}},
  pages        = {{3352--3356}},
  title        = {{{MAP-based Estimation of the Parameters of a Gaussian Mixture Model in the Presence of Noisy Observations}}},
  doi          = {{10.1109/ICASSP.2013.6638279}},
  year         = {{2013}},
}

@inproceedings{11845,
  abstract     = {{The paper proposes a modification of the standard maximum a posteriori (MAP) method for the estimation of the parameters of a Gaussian process for cases where the process is superposed by additive Gaussian observation errors of known variance. Simulations on artificially generated data demonstrate the superiority of the proposed method. While reducing to the ordinary MAP approach in the absence of observation noise, the improvement becomes the more pronounced the larger the variance of the observation noise. The method is further extended to track the parameters in case of non-stationary Gaussian processes.}},
  author       = {{Krueger, Alexander and Haeb-Umbach, Reinhold}},
  booktitle    = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)}},
  keywords     = {{Gaussian processes, MAP-based estimation, maximum a posteriori method, maximum likelihood estimation, nonstationary Gaussian processes}},
  pages        = {{3596--3599}},
  title        = {{{MAP-based estimation of the parameters of non-stationary Gaussian processes from noisy observations}}},
  doi          = {{10.1109/ICASSP.2011.5946256}},
  year         = {{2011}},
}