Alternative Equation Formats

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MathML

\begin{array}{rcl} \nabla_{i} (t) & = & - tr ({(\frac{\partial q (y_{t}, x_{t}, θ)}{\partial y_{t}^{^{'}}})}^{- 1} \frac{\partial^{2} q (y_{t}, x_{t}, θ)}{\partial y_{t}^{^{'}} \partial θ_{i}}) \\ + & \frac{1}{2} tr (Σ (θ)^{- 1} \frac{\partial Σ (θ)}{\partial θ_{i}} \\ [I - Σ (θ)^{- 1} q (y_{t}, x_{t}, θ) q (y_{t}, x_{t}, θ)^{'}]) \\ + & q (y_{t}, x_{t}, θ^{'}) Σ (θ)^{- 1} \frac{\partial q (y_{t}, x_{t}, θ)}{\partial θ_{i}} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} {\nabla }_{i}(t) & =& -\textrm{tr} \left( \left( \frac{{\partial }\Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta )}{{\partial } \Strong{y}_{t}^{'}} \right)^{-1} \frac{{\partial }^{2}\Strong{q} (\Strong{y}_{t}, \Strong{x}_{t},\btheta )}{{\partial } \Strong{y}_{t}^{'} {\partial } \theta _{i}} \right) \\ & +& \frac{1}{2} \textrm{tr} \left( \bSigma (\theta )^{-1} ~ \frac{{\partial }{\bSigma }(\theta )}{{\partial } \theta _{i}} \right. \\ & & \left. \left[ I - {\bSigma }(\theta )^{-1} \Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta ) \Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta )' \right] \right) \\ & +& \Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta ') {\bSigma }(\theta )^{-1} \frac{{\partial }\Strong{q} (\Strong{y}_{t}, \Strong{x}_{t}, \btheta )}{{\partial } \theta _{i}} \end{eqnarray*}