# Documentation:Monte Carlo Equilibration

From ALPS

## Contents

# Equilibration in Monte Carlo simulations

## Description

### Synposis

pyalps.checkSteadyState(sets=None, outfile=None, observable=None, confidenceInterval=0.6827, simplified=False, includeLog=False)

### Description

argument | default | type | remark |

sets | None | Pyalps Dataset | usually returned by pyalps.loadMeasurements |

outfile | None | Python str | ALPS hdf5 output file(name) |

observable | None | Python str | measurement observable |

confidenceInterval | 0.6827 | Python float | confidence interval in which steady state has been reached |

simplified | False | Python bool | shall we combine the checks of all observables as 1 final boolean answer? |

includeLog | False | Python bool | shall we print the detailed log? |

## 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 .

, :

### Slope of best-fitted line

### Error in slope of best-fitted line

Denoting , we have:

### Hypothesis testing

Using the standard z-test, we reject at confidence interval if