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Estimating the variance of the sample mean is a classical problem of stochastic simulation. Traditional
batch means estimators require specification of the simulation run length a priori. Dynamic batch
means (DBM) is a new approach to implement the traditional batch means in fixed memory by
dynamically changing both batch size and number of batches...
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Estimating the variance of the sample mean is a classical problem of stochastic simulation.
Traditional batch means estimators require specification of the simulation run length a
priori. To our knowledge, the dynamic non-overlapping batch means estimator (DNBM)
and dynamic partial-overlapping batch means estimator (DPBM) are the only two existing...
Citations
... Song [14] further proposed a general form for the (100 f )% DOBM estimator using a recursive expression, where f = 0, 1/2, 3/4, 7/8, · · · . Several DBM variations [15,16,19] have been recently developed for steady-state simulation output analysis. ...
Batching is a well-known method used to estimate the variance of the sample mean in steady-state simulation. Dynamic batching is a novel technique employed to implement traditional batch means estimators without the knowledge of the simulation run length a priori. In this study, we reinvestigated the dynamic batch means (DBM) algorithm with binary tree hierarchy and further proposed a binary coding idea to construct the corresponding data structure. We also present a closed-form expression for the DBM estimator with binary tree coding idea. This closed-form expression implies a mathematical expression that clearly defines itself in an algebraic binary relation. Given that the sample size and storage space are known in advance, we can show that the computation complexity in the closed-form expression for obtaining the indexes c (k) j , i.e., the batch mean shifts s, is less than the effort in recursive expression.
... As stated, the measurement noise v(k) is unknown time-variable white noise. An unknown time-variable estimator should be used to estimate the mean and variance of the measurement noise [11][12][13][14]: ...
To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observation noise. Using the robust Kalman filtering, the ARMA model parameters are estimated accurately. The developed ARMA modeling method has the advantages of a rapid convergence and high accuracy. Thus, the required sample size is reduced. It can be applied to modeling applications for gyro random noise in which a fast and accurate ARMA modeling method is required.
Simulation modeling has been leveraged for a variety of health care applications. Data used to inform most parameters for these models are typically collected from a single site, thus limiting the generalizability of the results and insights for other populations. In this study, we explore the impact of using data collected from multiple sites to parameterize an agent-based model of multi-drug resistant organisms in an intensive care unit setting. We show that using single sites to inform model parameters can be highly variable, and that using even multiple sites can significantly improve the precision of these estimates and reduces the associated aggregated model error.
Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with \(O(1)\) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with \(O(1)\) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the \(O(1)\) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is \(2^{10/3}3^{-2} \fallingdotseq 1.12\) times that of the optimal off-line TAVC estimator.
