Monte-Carlo analysis

Selection 8 from the FTAPSUIT menu runs MONTE (Monte Carlo). It requests the name of the input file, FN.MI (e.g., dgn.mi). The Monte Carlo analysis is contained in file FN.MO. 

MONTE performs a Monte Carlo analysis using uncertainties in the data to estimate uncertainties in the calculation of the system and subsystem failure probability. 

V. Path Integral Monte Carlo — Analysis of Quantum Effects in... 

V. PATH INTEGRAL MONTE CARLO — ANALYSIS OF QUANTUM EFFECTS IN ADSORBED LAYERS... 

E. Eisenriegler, K. Kremer, K. Binder. Adsorption of polymer chains at surfaces Scaling and Monte Carlo analysis. J Chem Phys 77 6296-6320, 1982. 

Blau et al. [22] have applied probabilistic network models to model resource needs and success probabilities in pharmaceutical and agrochemical development, through Monte Carlo analysis. This requires solving the problem of scheduling a portfolio of projects under uncertainty about progression. This approach is tractable for drug development. However, the inherent complex-... 

Cronin WJ, Oswald EJ, Shelley ML, et al. 1995. A trichloroethylene risk assessment using a Monte Carlo analysis of parameter uncertainty in conjunction with physiologically-based pharmacokinetic modeling. Risk Anal 15 555-565. 

U.S. males age 18-65 years old (NHANES III) 0.001-0.003 Slope derived from model anaylzed using Monte Carlo analysis to predict population Stern 1996... 

Local sensitivity analysis is of limited value when the chemical system is non-linear. In this case global methods, which vary the parameters over the range of their possible values, are preferable. Two global uncertainty methods have been used in this work, a screening method, the so-called Morris One-At-A-Time (MOAT) analysis and a Monte Carlo analysis with Latin Hypercube Sampling (Saltelli et al., 2000 Zador et al., submitted, 20041). The analyses were performed by varying rate parameters, branching ratios and constrained concentrations within their uncertainty interval,... 

Monte-Carlo analysis is typically applied to handle uncertainty if several data sources are available to identify most probable costs. 

The estimates of an NCE s expected sales trajectory can be analyzed using a Monte Carlo technique, which produces a range of possible outcomes, given uncertainty about the actual magnitudes of various input assumptions. The results of a Monte Carlo analysis... 

Examples of stretch, most likely, and worst-case scenario outputs from Monte Carlo analysis. 

In the case of a single pesticide found on a single commodity, a Monte Carlo analysis would randomly select a residue data point and a food consumption level value and multiply them together to yield an exposure level. By repeating this process, often thousands or tens of thousands of times, it is possible to develop a distribution of daily exposures that would allow a determination of which levels represent, for example, the 50th, 99th, and 99.9th percentiles of consumption. 

USEPA] US Environmental Protection Agency. 1997. Policy for use of probabilistic analysis in risk assessment guiding principles for Monte Carlo analysis. Washington (DC) ORD, USEPA. 

Burmaster and Anderson (1994) have proposed 14 principles of good practice for using Monte Carlo techniques. They suggest that before an analyst undertakes a Monte Carlo risk assessment, the growing literature on probabilistic risk assessment should be thoroughly examined. Principles for a properly conducted Monte Carlo analysis have also been proposed by the USEPA (1997). 

The analyst is better able to explain and communicate the results of the Monte Carlo analysis and the statistical endpoints. 

By Bayes s rule, the posterior probability on a Monte Carlo realization of a model equals the probability of observing the site-specific output data if the realization is correct, times the prior probability that the realization is correct, normalized such that the sum of the posterior probabilities of the Monte Carlo realizations equals 1. In Monte Carlo analysis, all realizations are equally likely (i.e., the pritM probability on each realization of an n-realization Monte Carlo simulation is 1/n). Therefore, the BMC acceptance-rejection procedure boils down to the following The probability that a model realization is correct, given new data, equals the relative likelihood of the having observed the new data if the realization is correct. 

CHRONIC RISK CURVES FOR ATRAZINE IN TENNESSEE PONDS USING MONTE CARLO ANALYSIS... 

FIGURE 4.3 Exceedence curve for annual maximum atrazine concentrations in Tennessee pond water, based on exposure simulation using Monte Carlo analysis. 

If you can perform an uncertainty analysis with a calculator, do not use Monte Carlo analysis or at least compare the calculator and simulation method for consistency. 

Dakins ME, Toll JE, Small MJ, Brand K. 1996. Risk-based environmental remediation Bayesian Monte Carlo analysis and the expected value of sample information. Risk Anal 16 67-69. 

Warren-Hicks WJ, Butcher B. 1996. Monte Carlo analysis classical and Bayesian applications. Human Ecol Risk Assess 2 643-649. 

Table 6.3 lists the summary statistical measures yielded by 3 analyses of this hypothetical calculation. The 2nd column gives the results that might be obtained by a standard Monte Carlo analysis under an independence assumption (the dotted lines in Figure 6.7). The 3rd and 4th columns give results from probability bounding analyses, either with or without an assumption of independence. 

The following section describes the most commonly used technique for propagating variability and parameter uncertainty separately, 2nd-order Monte Carlo analysis. A brief case study illustrating the technique is included in Section 7.3. 

Second-order Monte Carlo analysis consists of 2 loops, the inner loop representing variability and the outer loop representing parameter uncertainty. To conduct an analysis, the following steps are required (also see Figure 7.1) ... 

Specify the number of inner and outer loop simulations for the 2nd-order Monte Carlo analysis. In the 1st outer loop simulation, values for the parameters with uncertainty (either constants or random variables) are randomly selected from the outer loop distributions. These values are then used to specify the inner loop constants and random variable distributions. The analysis then proceeds for the number of simulations specified by the analyst for the inner loop. This is analogous to a Ist-order Monte Carlo analysis. The analysis then proceeds to the 2nd outer loop simulation and the process is repeated. When the number of outer loop simulations reaches the value specified by the analyst, the analysis is complete. The result is a distribution of distributions, a meta-distribution that expresses uncertainty both from uncertainty and from variability (Figure 7.1). 

There are some issues associated with 2nd-order Monte Carlo analysis. Computational time can be a problem because the necessary number of replicates is squared with 2nd-order Monte Carlo analyses (i.e., number of inner loop simulations times number of outer loop simulations). In practice, specifying variability and uncertainty with random variables is a difficult exercise because the analyst is essentially trying to quantify what he or she does not know or only partially understands. 

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