# Monte Carlo Error Simulation

## Contents |

New **Jersey: Wiley; 2002. **Section 2 outlines some notation, defines MCE, and presents a simple example illustrating that MCE generally may be more substantial than traditionally thought. ISBN0-89791-701-4. ^ Owen, Art; Associate, Yi Zhou (2000-03-01). "Safe and Effective Importance Sampling". Given the results of the logistic regression example in Section 2.2, however, such simulations may plausibly experience greater MCE than traditionally thought, suggesting that more emphasis should be placed on reporting Source

ISBN978-1-4419-1939-7. Digital Signal Processing. Clarendon Press. Suppose that interest lies in the association between a binary exposure X and a binary outcome Y, and assume that the two are related via the logistic regression modellogitP(Y=1∣X)=β0+βXX.(2)We conducted a

## Monte Carlo Standard Error

Although not shown, the central 95% mass of the Monte Carlo sampling distribution is between −3.3% and 5.1%. Practically, this result suggests that ensuring that the central 95% mass of the Monte Carlo sampling distribution for percent bias is within one unit of the overall underlying value of 0.9% Special Issue in Honour of William J. (Bill) Fitzgerald. 47: 36–49. Waller LA, Carlin BP, Xia H, Gelfand AE.

While the naive Monte Carlo works for simple examples, this is not the case in most problems. Your cache administrator is webmaster. ISSN1070-9908. ^ Cappé, O.; Guillin, A.; Marin, J. Monte Carlo Standard Error Definition The most common choice was R = 1000 (74 articles); only 5 articles used a value of R > 10,000.Table 2Number of replications associated with simulation studies reported in regular articles

The ordinary 'dividing by two' strategy does not work for multi-dimensions as the number of sub-volumes grows far too quickly to keep track. The proposed BGP plot also provides **a simple approach for determining the** number of simulated data sets or replications needed to achieve a desired level of accuracy, and would be particularly Your cache administrator is webmaster. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3337209/ New Jersey: Wiley; 1987.

Statistical Rules of Thumb. Monte Carlo Integration Algorithm Monte Carlo integration, on the other hand, employs a non-deterministic approach: each realization provides a different outcome. Hierarchical Spatio-Temporal Mapping of Disease Rates. Weinzierl, Introduction to Monte Carlo methods, W.H.

## Monte Carlo Error Analysis

Although we provide more details later, here we note that of 223 regular articles that reported a simulation study, only 8 provided either a formal justification for the number of replications Third, viewed as statistical or mathematical experiments (Ripley 1987), it could be argued that to aid in the interpretation of results, simulation studies always should be accompanied by some assessment of Monte Carlo Standard Error From Table 4, we see that the 2.5th percentile tended to have a fairly low MCE, whereas the MCE for the 97.5th percentile was consistently higher. Monte Carlo Error Definition IEEE Transactions on Signal Processing. 63 (16): 4422–4437.

ISSN1061-8600. ^ Cappé, Olivier; Douc, Randal; Guillin, Arnaud; Marin, Jean-Michel; Robert, Christian P. (2008-04-25). "Adaptive importance sampling in general mixture classes". this contact form Springer. Geyer CJ. “Practical Markov Chain Monte Carlo” (with discussion) Statistical Science. 1992;7:473–483.Givens GH, Hoeting JA. Consequently, for a reader to fully understand and place into context results obtained via a simulation study, the results should be accompanied by some measure of associated uncertainty.To gauge the extent Monte Carlo Integration Error

Here we present a series of simple and practical methods for estimating Monte Carlo error as well as determining the number of replications required to achieve a desired level of accuracy. Clearly stratified sampling algorithm concentrates the points in the regions where the variation of the function is largest. doi:10.1007/s11222-008-9059-x. have a peek here Efron and Tibshirani 1993; Robert and Casella 2004; Givens and Hoeting 2005), in many cases little can be done to substantially reduce the time needed to run even a single iteration,

A more detailed description of the data was provided by Waller et al. (1997).Let A1 be a binary indicator of whether or not an individual’s age is between 65 and 74 Monte Carlo Error Propagation Given the estimation of I from QN, the error bars of QN can be estimated by the sample variance using the unbiased estimate of the variance. Here we call this between-simulation variability Monte Carlo error (MCE) (e.g., Lee and Young 1999).

## Based on these plots, Table 4 also provides the projected number of replications, R+, required to reduce the percent bias MCE to 0.05 or 0.005 for each of the four 2.5th

Journal of the Royal Statistical Society, Series B: Statistical Methodology. 1999;61:353–366.Metropolis N, Ulam S. Each article was downloaded electronically, and a search was performed for any of the following terms: “bootstrap,” “dataset,” “Monte Carlo,” “repetition,” “replication,” “sample,” and “simulation.” In addition, when indicated by the QUANTIFICATION OF MONTE CARLO ERRORFor the example given in Section 2.2, Figure 1 illustrates a simple and effective diagnostic tool for monitoring the simulation as R increases. Monte Carlo Integration Example To obtain these, we sampled R = 1000 data sets with replacement from the case-control data and evaluated the MLEs using each data set.

Generated Thu, 01 Dec 2016 10:56:14 GMT by s_wx1193 (squid/3.5.20) New York, NY, USA: ACM: 419–428. Consider the following example where one would like to numerically integrate a gaussian function, centered at 0, with σ = 1, from −1000 to 1000. Check This Out The system returned: (22) Invalid argument The remote host or network may be down.

van Belle G. Second, the magnitude of MCE in specific settings likely depends on a range of factors, including the parameter under investigation, the chosen operating characteristic, and the underlying variability in the data. An estimate of the MCE is then the standard deviation across the bootstrap statistics MCE^boot(φ^R,B)=1B∑b=1B(φ^R(Xb∗)−φ^R(X∗)¯)2,(9) whereφ^R(X∗)¯=1B∑b=1Bφ^R(Xb∗).Efron (1992) originally proposed the jackknife specifically to avoid a second level of replication, noting that Lepage, VEGAS: An Adaptive Multi-dimensional Integration Program, Cornell preprint CLNS 80-447, March 1980 J.

Press, G.R. The VEGAS algorithm approximates the exact distribution by making a number of passes over the integration region which creates the histogram of the function f. At R = 10,000, the minimum and maximum across the M simulations are −2.3% and 4.7%, with MCE decreasing to 0.7%. The direction is chosen by examining all d possible bisections and selecting the one which will minimize the combined variance of the two sub-regions.

These individual values and their error estimates are then combined upwards to give an overall result and an estimate of its error. For example, although the bootstrap-based estimator is applicable in a broad range of settings, the required second level of replication (denoted here by B) may quickly become computationally burdensome; thus guidance Scandinavian Journal of Statistics. 39 (4): 798–812.

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