Changes between Version 2 and Version 3 of OfficialTolArchiveNetworkBysPrior

Timestamp:

Dec 24, 2010, 4:19:07 PM (14 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkBysPrior

@@ -25 +25 @@
 but this an admisible restricion in almost all cases.
 
-== Chained priors ==
-
-A prior can depend on a set of parameters that can be defined as constant 
-values or another subset of the model variables. For example we can define 
-hierarquical structures among the variables using a latent variable that is
-the average of a normal prior for a subset of variables. We also can consider
-that the varianze of these normal prior is another variable and to define 
-an inverse chi-square prior over this one.
-
 == Non informative priors ==
 
@@ -53 +44 @@
 bounds:[[BR]][[BR]]
 
-[[LatexEquation( \beta\in\Omega\Longleftrightarrow l_{k}\leq\beta\leq u_{k}\wedge-\infty\leq l_{k}<u_{k}\leq\infty )]]
+[[LatexEquation( \beta\in\Omega\Longleftrightarrow l_{k}\leq\beta_{i_k}\leq u_{k}\wedge-\infty\leq l_{k}<u_{k}\leq\infty\forall k=1\ldots r )]]
 
 === Polytope prior ===
@@ -60 +51 @@
 [[LatexEquation( A\beta\leq a\wedge A\in\mathbb{R}^{r\times n}\wedge a\in\mathbb{R}^{r} )]]
 
-We can define this type of prior bye means of a set of [[LatexEquation( r )]] 
-inequations due NonLinGloOpt doesn't have any special behaviour for linear 
-inequations, and it could be an inefficient implementation.
+An special and common case of polytope region is the defined by order relations like
+
+[[LatexEquation( \beta_{i}}\leq\beta_{j}})]]
+
+We can implement this type of prior by means of a set of [[LatexEquation( r )]] 
+inequations but, since NonLinGloOpt doesn't have any special behaviour for linear 
+inequations, it could be an inefficient implementation.
 
 However we can define just one non linear inequation that is equivalent to the
@@ -82 +77 @@
 
 The feasibility condition can then be defined as a single continuous nonlinear 
-inequality and twice differentiable everywhere
+inequality and differentiable everywhere
 
 [[LatexEquation( g\left(\beta\right)=\underset{k=1}{\overset{r}{\sum}}D_{k}^{3}\left(\beta\right)\leq0 )]]
@@ -90 +85 @@
 [[LatexEquation( \frac{\partial g\left(\beta\right)}{\partial\beta_{i}}=3\underset{k=1}{\overset{r}{\sum}}D_{k}^{2}\left(\beta\right)A_{ki} )]]
 
-
 == Multinormal prior ==
 
-== Scalar bounded normal prior ==
 
 == Inverse chi-square prior ==
 
 
+
+