# Difference between revisions of "Documentation:Monte Carlo Equilibration"

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\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) **