Difference between revisions of "Documentation:Monte Carlo Equilibration"
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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> | + | <math>\frac{\partial S}{\partial \beta_0 } = 0 </math> , <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 
.
, 
:
