Changes between Version 5 and Version 6 of OfficialTolArchiveNetworkBysPrior

Timestamp:

Dec 25, 2010, 11:41:12 PM (15 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkBysPrior

@@ -26 +26 @@
 but this an admisible restricion in almost all cases.
 
-== Non informative priors ==
+== Deterministic priors ==
+
+Very often it is possible to know that a variable should be in a certain range 
+or belonging to a particular region of space. This kind of deterministic knowledge 
+can be expressed as a constrained uniform distribution.
 
 Let [[LatexEquation( \beta )]] a uniform random variable in a region 
@@ -41 +45 @@
 prior, is to stablish a domain interval for one or more variables. 
 
-In this cases, you mustn't to define the log-logarithm nor the constraining 
+|| ''bounded region''[[BR]][[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image000.png)]] || ''unbounded region''[[BR]][[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image001.png)]] ||
+
+In this cases, you mustn't to define the log-likelihood nor the constraining 
 inequation functions, but simply it's needed to fix the lower and upper 
 bounds:[[BR]][[BR]]
@@ -50 +56 @@
 prior, that is equivalent to don't define any prior.
 
+If all lower and upper bounds are finite, then the fesasible region is an
+hyperrectangle.
+
+
 === Polytope prior ===
 A polytope prior is defined by a system of compatible linear inequalities [[BR]]
 
 [[LatexEquation( A\beta\leq a\wedge A\in\mathbb{R}^{r\times n}\wedge a\in\mathbb{R}^{r} )]]
+
+|| ''bounded region''[[BR]][[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image003.png)]] || ''unbounded region''[[BR]][[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image002.png)]] ||
+
 
 An special and common case of polytope region is the defined by order relations like
@@ -88 +101 @@
 [[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 ==
+== Random priors ==
+
+When you have a vague idea of where it could be a variable, it is possible to express 
+by a probability distribution consistent with that knowledge.
+
+=== Multinormal prior ===
 
 When we know that a single variable should fall symmetrically close to a known value 
@@ -113 +131 @@
  [[LatexEquation( \left(\frac{\partial^{2}L\left(\beta\right)}{\partial\beta_{i}\partial\beta_{j}}\right)_{i,j=1\ldots n}=-\Sigma^{-1} )]]
  
- 
-== Inverse chi-square prior ==
-
 
 == Transformed prior ==
@@ -153 +168 @@
 
 
-