To address just the left-hand term of the equation: It is possible to employ amatrix environmentinside a\left( ... \middle\vert ... \right) construct. To force the item\alpha_T to be typeset flush left inside the (one-column) matrix instead of centered, just add\hfill to its right. (This works because thematrix environment builds on thearray environment; by default, the columns of amatrix environment are centered, achieved by inserting\hfil on each side of each cell. Because\hfill is "more infinite" than\hfil, the contents of that row get pushed to the far left.)

\documentclass{article}\usepackage{amsmath} % for "matrix" environment\begin{document}\[\left(\begin{matrix}\alpha_T \hfill \\ \alpha_{T-1}\end{matrix}\, \middle\vert \,y_{1,T-1},\boldsymbol{\theta}\right) \sim N \dots\]\end{document}

Addendum, posted after the OP clarified the structure of the covariance matrix: Similarly, the mean vector and covariance matrix can be written withbmatrix (short for "matrix with brackets", I suppose) environments, again employing the\hfill device to set some of the items flush-left.

\dots\sim N\left(\begin{bmatrix}d_{T-1}+T_{T-1}\alpha_{T-1\mid T-1}\\\alpha_{T-1\mid T-1} \hfill\end{bmatrix},\begin{bmatrix} T_{T-1}P_{T-1|T-1}T_{T-1}'+Q_{T-1}  & T_{T-1}P_{T-1|T-1} \\P_{T-1|T-1}T_{T-1}' \hfill          & P_{T-1\mid T-1}\hfill\end{bmatrix}\right)\]

Since there has been some issues with the vertical spacing inside the first matrix, I've found a specific workaround that is based on the division of the two columns:

• The first is considered as a separatedarray environment, so the two expressions will be typeset correctly.

• The second is astandard displayed equation that will make the third expression lie just bewteen the first two. Notice that this is achieved with the command\middle (thanks to @Mico for pointing this out).

This is the final MWE:

\documentclass{article}%\usepackage{amsmath}% This command adjusts the horizontal shrinking % between columns inside the environment.\renewcommand\arraycolsep{2pt}%\begin{document}%\begin{equation*}%% Hhere starts the first "array" environment, now the delimiters are equal because% the middle command  "( | )" separates the array from the standard environment % in order to make the third expression vertically centered.\left(%\begin{array}{l} \alpha_T     \\ \alpha_{T-1}\end{array}%\middle\vert%\;y_{1:T-1},\,\boldsymbol{\theta}%\right)%\sim N%% Now there is the second matrix with the delimiter setting like% ( [ ],[ ] )%\left(  % starting delimiter%\left[ \begin{array}{l}  d_{T-1}+T_{T-1}a_{T-1|T-1}  \\  a_{T-1|T-1} \end{array}\right],% % Here is the second square delimited array.%\left[ \begin{array}{lcc}  T_{T-1}P_{T-1|T-1}T’_{T-1} & + & Q_{T-1}T_{T-1}P_{T-1|T-1}\\  P_{T-1|T-1}T’_{T-1}        &   & P_{T-1|T-1} \end{array}\right]%\right)     % Ending delimiter.%\end{equation*}%\end{document}

Here is the output:

EDIT:

Since two terms inside the second square-bracketed matrix were merged, this implementation should highlight the spacing:

 ... \begin{array}{lcl}  T_{T-1}P_{T-1|T-1}T’_{T-1}+Q_{T-1} & & T_{T-1}P_{T-1|T-1}\\  P_{T-1|T-1}T’_{T-1}                & & P_{T-1|T-1} \end{array} ...

Here is the correct output:

• Thanks! This is great. Just wondering, is there a way to achieve this output using the matrix environment?

  TrueTears

  – TrueTears

  2013-10-19 15:25:56 +00:00

  CommentedOct 19, 2013 at 15:25
• @TrueTears Right now I'm experimenting with my compiler, but it takes time to achieve such a result. If I find the correct solution, I'll edit the answer; until then you may want to take a look atthis discussion, it will shed some light on the function of\hline inside amatrix environment

  TheVal

  – TheVal

  2013-10-19 15:29:45 +00:00

  CommentedOct 19, 2013 at 15:29

Doing just the left-most matrix, seeing as that was your difficulty.

\documentclass{article}\usepackage[usestackEOL]{stackengine}[2013-10-15]\def\stackalignment{l}\begin{document}\[\left(\left. \Vectorstack{\alpha_T\\\alpha_{T-1}} \right| y_{1:T-1},\theta\right) = \ldots\]\end{document}

• matrices