Alternative Equation Formats

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MathML

\begin{array}{rcl} l_{n} (θ, σ) = & \frac{n g}{2} & \ln (2 π) - \sum_{t = 1}^{n} \ln (| \frac{\partial q (y_{t}, x_{t}, θ)}{\partial y_{t}^{^{'}}} |) + \frac{n}{2} \ln (| Σ (σ) |) \\ + & \frac{1}{2} tr (Σ (σ)^{- 1} \sum_{t = 1}^{n} q (y_{t}, x_{t}, θ) q^{'} (y_{t}, x_{t}, θ)) \end{array}

MathML rendered with MathJax

\begin{array}{rcl} l_{n} (θ, σ) = & \frac{n g}{2} & \ln (2 π) - \sum_{t = 1}^{n} \ln (| \frac{\partial q (y_{t}, x_{t}, θ)}{\partial y_{t}^{^{'}}} |) + \frac{n}{2} \ln (| Σ (σ) |) \\ + & \frac{1}{2} tr (Σ (σ)^{- 1} \sum_{t = 1}^{n} q (y_{t}, x_{t}, θ) q^{'} (y_{t}, x_{t}, θ)) \end{array}

Math as LaTeX Source

\begin{eqnarray*} \Strong{l}_{n}(\btheta , \bsigma ) = & \frac{ng}{2}& {\ln }(2{\pi }) - \sum _{t=1}^{n}{{\ln } \left( \left| \frac{{\partial }\Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta )}{{\partial } \Strong{y}_{t}^{'}} \right| \right)} + \frac{n}{2} {\ln } \left( |{\bSigma }({\sigma })| \right) \\ & +& \frac{1}{2} \textrm{tr} \left( {\bSigma }({\sigma })^{-1} \sum _{t=1}^{n}{\Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta ) \Strong{q} '(\Strong{y}_{t}, \Strong{x}_{t}, \btheta )} \right) \nonumber \end{eqnarray*}