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

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We have a timeseries of N measurements obtained from a Monte Carlo simulation, i.e. <math>y_0,y_1,\cdots,y_{N-1}</math>. | We have a timeseries of N measurements obtained from a Monte Carlo simulation, i.e. <math>y_0,y_1,\cdots,y_{N-1}</math>. | ||

− | Suppose <math>\bar{y}_i = \beta_0 + \beta_1 x_i </math> (s.t. <math>i = 0, 1, \cdots, N-1</math>) is the least-squares best fitted line, we attempt to minimize <math> S = \sum_i (y_i - \bar{y}_i)^2 </math> w.r.t. <math>\beta_0</math> and <math> \beta_1</math> | + | Suppose <math>\bar{y}_i = \beta_0 + \beta_1 x_i </math> (s.t. <math>i = 0, 1, \cdots, N-1</math>) is the least-squares best fitted line, we attempt to minimize <math> S = \sum_i (y_i - \bar{y}_i)^2 </math> w.r.t. <math>\beta_0</math> and <math> \beta_1</math>. |

+ | |||

+ | <math>\frac{\partial S}{\partial \beta_0 } = 0 </math> and <math>\frac{\partial S}{\partial \beta_1 } = 0 </math> |

## Revision as of 11:57, 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 .

and