Difference between revisions of "Documentation:Monte Carlo Equilibration"
From ALPS
(→Theory) |
(→Theory) |
||
| Line 5: | Line 5: | ||
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 | + | 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> or |
Revision as of 11:56, 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 
or
