# Optimal batch sizes for variance estimators in MCMC

@inproceedings{Liu2018OptimalBS, title={Optimal batch sizes for variance estimators in MCMC}, author={Ying Liu and Dootika Vats and James M. Flegal}, year={2018} }

This paper proposes optimal mean squared error batch sizes for multivariate batch means and spectral variance estimators. We propose a novel estimation technique for the optimal batch sizes, which is computationally inexpensive and has low variability. Further, the asymptotic mean squared error for a family of spectral variance estimators is derived under conditions convenient to verify for Markov chain Monte Carlo simulations. Vector auto-regressive, Bayesian logistic regression, and Bayesian…

## References

SHOWING 1-10 OF 43 REFERENCES

Weighted batch means estimators in Markov chain Monte Carlo.

- Mathematics
- 2018

This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo…

Batch means and spectral variance estimators in Markov chain Monte Carlo

- Mathematics
- 2010

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based…

Optimal mean-squared-error batch sizes

- Mathematics
- 1995

When an estimator of the variance of the sample mean is parameterized by batch size, one approach for selecting batch size is to pursue the minimal mean squared error (mse). We show that the…

Automatic Optimal Batch Size Selection for Recursive Estimators of Time-Average Covariance Matrix

- Mathematics
- 2017

ABSTRACT The time-average covariance matrix (TACM) , where Γk is the auto-covariance function, is an important quantity for the inference of the mean of an -valued stationary process (d ⩾ 1). This…

Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo

- MathematicsBernoulli
- 2018

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate…

Lugsail lag windows and their application to MCMC

- Mathematics
- 2018

Lag windows are commonly used in the time series, steady state simulation, and Markov chain Monte Carlo literature to estimate the long range variances of estimators arising from correlated data. We…

Strong consistency and other properties of the spectral variance estimator

- Mathematics
- 1991

Consistent estimation of the variance parameter of a stochastic process allows construction, under certain conditions, of a confidence interval for the mean of the process. If the variance estimator…

Multivariate output analysis for Markov chain Monte Carlo

- MathematicsBiometrika
- 2019

Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have…

Mean-Square Consistency of the Variance Estimator in Steady-State Simulation Output Analysis

- MathematicsOper. Res.
- 1995

This paper proves mean-square consistency of the process-variance estimator for the methods of batch means, overlappingbatch means, standardized time series area, and spaced batch means by rigorously computing the rate of decay of the variance of the Process Variance estimators.

Overlapping batch means: something for nothing?

- MathematicsWSC '84
- 1984

This paper considers an overlapping batch means (OLBM) estimator that, based on the same assumptions and batch size as NOLBM, has essentially the same mean and only 2/3 the asymptotic variance of N OLBM.