By Christopher F. Baum

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**Additional resources for A review of Stata 8.1 and its time series**

**Sample text**

The equations below describe the famous Eyes model with independent page 27 November 27, 2014 12:17 BC: P794 – Nonlinear Mixture Models book Nonlinear Mixture Models: A Bayesian Approach 4 3 0 1 2 Frequency 5 6 7 28 525 530 535 540 545 550 555 Wavelength Fig. 1. Distribution of peak sensitivity wavelength (nm) of monkey eyes measured by microspectrophotometry. 35) μ1 ∼ N (·|λ1 , σ12 ), μ2 ∼ N (·|λ2 , σ22 ), λ1 = 540, λ2 = 540, σ1 = σ2 = 103 . In this book we will use this simple model (Eqs. 35)) to illustrate the main methods and concepts of mixture models in general.

Robert and Casella (2004, p. 393) state that the hybrid Gibbs–Metropolis algorithm generates a Markov chain with the same invariant distribution as the original Gibbs chain; the proof of this theorem is left for students as an exercise. In a 1990 technical report, Mueller (1990) proved that a “pure” Metropolis chain is irreducible and aperiodic. He also suggested how to extend this result to a hybrid Gibbs–Metropolis chain. In the next section, we illustrate the result for the special case of one Gibbs step and one Metropolis step.

2003) developed a method for modeling gene expression time series using a mixture model approach. They developed a method for probabilistic clustering of genes based on their expression proﬁle. Wakeﬁeld et al. used a multivariate Gaussian mixture model to describe gene expression data and used a birth-death (BD) MCMC method [Stephens (2000b)] to ﬁnd the optimal number of mixture components. One crucial diﬀerence between the approach of Wakeﬁeld et al. and other methods is the latter did not acknowledge time-ordering of the data.