Difference between revisions of "Documentation:Monte Carlo Equilibration"
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| Line 12: | Line 12: | ||
\left( | \left( | ||
\begin{array}{cc} | \begin{array}{cc} | ||
| − | + | N & \sum_i x_i \\ | |
| + | \sum_i x_i & \sum_i x_i^2 | ||
\end{array} | \end{array} | ||
\right) | \right) | ||
| + | \left(\beta_0 \\ \beta_1\right) = | ||
| + | \left(\sum_i y_i \\ \sum_i x_i y_i \right) | ||
</math> | </math> | ||
Revision as of 12:00, 9 September 2013
Monte Carlo equilibration
Theory
We have a timeseries of N measurements obtained from a Monte Carlo simulation, i.e. 
.
Suppose 
(s.t. 
) is the least-squares best fitted line, we attempt to minimize 
w.r.t. 
and 
.
, 
:
Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \left( \begin{array}{cc} N & \sum_i x_i \\ \sum_i x_i & \sum_i x_i^2 \end{array} \right) \left(\beta_0 \\ \beta_1\right) = \left(\sum_i y_i \\ \sum_i x_i y_i \right)
