id	summary	reporter	owner	description	type	status	priority	milestone	component	version	severity	resolution	keywords	cc
666	BSR Fixing and reloading partially for main linear block	Víctor de Buen Remiro	Víctor de Buen Remiro	"We can separate a linear constrained regression block 

[[LatexEquation(Y = X \beta + e; e ~ N\left(0,I\right) $$)]][[BR]]
[[LatexEquation(A \beta \leq a $$)]][[BR]]

in two sub-blocks

[[LatexEquation(Y = X_{1} \beta_{1} +X_{2} \beta_{2} + e; e \sim N\left(0,I\right) $$)]][[BR]]
[[LatexEquation(A_{1}\beta_{1} + A_{2}\beta_{2} \leq a $$)]][[BR]]

If we have an inconditional sample or a fixed set of values for [[LatexEquation(\beta_{1} $$)]], then we can sample [[LatexEquation(\beta_{2} | \beta_{1} $$)]] from reduced regression

[[LatexEquation(Y_{1}  = X_{2} \beta_{2} + e; e \sim N\left(0,I\right) $$)]][[BR]]
[[LatexEquation(A_{2} \beta_{2} \leq a_{1} $$)]][[BR]]

where

[[LatexEquation(Y_{1} = Y - X_{1} \beta_{1} $$)]][[BR]]
[[LatexEquation(a_{1} = a - A_{1} \beta_{1} $$)]][[BR]]
"	enhancement	closed	highest	BSR reestimation	Math	2.0.1	normal	fixed	BSR, reestimation, forecast, inference, partial simulation