# Documentation:Monte Carlo Equilibration

From ALPS

## Contents

# Equilibration in Monte Carlo simulations

## Description

### Synposis 1

pyalps.checkSteadyState(sets=None, outfile=None, observables=None, confidenceInterval=0.63, simplified=False, includeLog=False)

argument | default | type | remark |

outfile | - | Python str | ALPS hdf5 output file(name) |

observables | - | (list of ) Python str | (list of) measurement observable(s) |

confidenceInterval | - | 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? |

### Synposis 2

pyalps.checkSteadyState(sets, confidenceInterval=0.63)

argument | default | type | remark |

sets | - | Pyalps Dataset | usually returned by pyalps.loadMeasurements |

confidenceInterval | 0.63 | Python float | confidence interval in which steady state has been reached |

## 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