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Olga edited Methods Description.tex
over 9 years ago
Commit id: 1a26b06f773c96332d0d9bd95f1122ec60ffe22e
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index aa7a35f..96a62d7 100644
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$T^{(t)}_j=P(Z_i=j|X_i=x_i,\theta^{(t)})=\frac{P(z_{j})f(x_i|\mu^{(t)}_{j}, \sigma^{2(t)}_{j})}{p^{(t)} f(x_i|\mu^{(t)}_{1}, \sigma^{2(t)}_{1})+(1-p^{(t)})f(x_i|\mu^{(t)}_{2}, \sigma^{2(t)}_{2})}$
$Q(\mathbf{\theta}|\mathbf{\theta^{(t)}})=E_{\textbf{z}|\textbf{x},\mathbf{\theta^{(t)}}}(logL(\mathbf{\theta};\textbf{x};\textbf{z})) = E[(
log \log \prod \limits_{i=1}^n L(\mathbf{\theta};x_{i};z_{i})] = \sum\limits_{i=1}^n E[( log L(\mathbf{\theta};x_{i};z_{i})] = \sum\limits_{i=1}^n \sum\limits_{j=1}^2 T^{(t)}_j[logP(z_{j}) - 0.5log\sigma^{2}_{j} - 0.5(x_{i}-\mu_{j})^2]$
t - iterations, continue until |logL(t+1) -logL(t)| <10^{-3}