Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...

A new algorithm is proposed which accelerates the mini-batch k-means algorithm of Sculley (2010) by using the distance bounding approach of Elkan (2003). We argue that, when incorporating distance bounds into a mini-batch algorithm, already used data should preferentially be reused. To this end we propose using nested mini-batches, whereby data in a mini-batch at iteration t is automatically re...

A new algorithm is proposed which accelerates the mini-batch k-means algorithm of Sculley (2010) by using the distance bounding approach of Elkan (2003). We argue that, when incorporating distance bounds into a mini-batch algorithm, already used data should preferentially be reused. To this end we propose using nested mini-batches, whereby data in a mini-batch at iteration t is automatically re...

One of the existing methods to build a confidence interval (c.i.) for the mean response in a single steady state simulation system is the batch means method. This method, compared to the other existing methods (autoregressive representation, regenerative cycles, spectrum analysis, standardized time series), is quite easy to understand and to implement and performs relatively well. However, the ...

Mini Batch K-means ([11]) has been proposed as an alternative to the K-means algorithm for clustering massive datasets. The advantage of this algorithm is to reduce the computational cost by not using all the dataset each iteration but a subsample of a fixed size. This strategy reduces the number of distance computations per iteration at the cost of lower cluster quality. The purpose of this pa...

In analyzing the output process generated by a steady-state simulation, we often seek to estimate the expected value of the output. The sample mean based on a finite sample of size n is usually the estimator of choice for the steady-state mean; and a measure of the sample mean’s precision is the variance parameter, i.e., the limiting value of the sample size multiplied by the variance of the sa...

We show that there is no batch-means estimation procedure for consistently estimating the asymptotic variance when the number of batches is held fixed as the run length increases. This result suggests that the number of batches should increase as the run length increases for sequential stopping rules based on batch means.

We present a new method for obtaining confidence intervals in steady-state simulation. In our replicated batch means method, we do a small number of independent replications to estimate the steady-state mean of the underlying stochastic process. In order to obtain a variance estimator, we further group the observations from these replications into nonoverlapping batches. We show that for large ...

We formulate and evaluate the Automated Simulation Analysis Procedure (ASAP), an algorithm for steady-state simulation output analysis based on the method of nonoverlapping batch means (NOBM). ASAP delivers a confidence interval for an expected response that is centered on the sample mean of a portion of a simulation-generated time series and satisfies a user-specified absolute or relative prec...

Batch means are sample means of subsets of consecutive subsamples from a simulation output sequence. Independent and normally distributed batch means are not only the requirement for constructing a confidence interval for the mean of the steady-state distribution of a stochastic process, but are also the prerequisite for other simulation procedures such as ranking and selection (R&S). We propos...