Changes between Version 20 and Version 21 of OfficialTolArchiveNetworkBysPrior

Timestamp:

Dec 28, 2010, 10:50:41 AM (14 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkBysPrior

@@ -134 +134 @@
 
  [[LatexEquation( \left(\frac{\partial^{2}L\left(x\right)}{\partial x_{i}\partial x_{j}}\right)_{i,j=1\ldots n}=-\Sigma^{-1} )]]
- 
-
-=== Inverse chi-square prior ===
-
-In a model with normal residuals is permissible to award the unknown variance an 
-inverse chi-square distribution with scale parameter equal to the average of 
-squares of residuals and freedom degrees the data length.
-
-The likelihood is now the scalar function
-
- [[LatexEquation( lk\left(x\right)=\frac{\left(\frac{\nu}{2}\right)^{\frac{\nu}{2}}}{\Gamma\left(\frac{\nu}{2}\right)}x^{-\frac{\nu}{2}-1}e^{-\frac{\nu}{2x}} )]]
- 
-with the domain constrain
- 
- [[LatexEquation( x \ge 0 )]]
-
-The log-likelihood is
- 
- [[LatexEquation( L\left(x\right)=\frac{\nu}{2}\ln\left(\frac{\nu}{2}\right)-\ln\left(\Gamma\left(\frac{\nu}{2}\right)\right)-\left(\frac{\nu}{2}+1\right)x-\frac{\nu}{2x} )]]
-
-The first derivative is
- 
- [[LatexEquation( \frac{dL\left(x\right)}{dx}=-\left(\frac{\nu}{2}+1\right)+\frac{\nu}{2x^{2}} )]]
-
-The second derivative is
- 
- [[LatexEquation( \frac{d^{2}L\left(x\right)}{d^{2}x}=-\frac{\nu}{6x^{3}} )]]
- 
 
 
@@ -171 +143 @@
 as in the case of latent variables in hierarquical models
 
-[[LatexEquation( x_{i}\sim N\left(x_{1},\sigma\right)\forall i=2\ldots n )]]
+[[LatexEquation( x_{i}\sim N\left(x_{1},\sigma^2\right)\forall i=2\ldots n )]]
 
 Then we can define a variable transformation like this