The uncertainty of the fitted values of these two parameters has been estimated objectively by means of a Monte-Carlo simulation model. The data points on each curve in Figure 5 are the mean of 100 calculated points and each point is the "best-fit" of the parameter to a simulated measurement in a simulated indoor environment in which allowance is made for fluctuations of the parameters. [Pg.313]

From this dynamic interpretation of the Monte Carlo averaging we can obtain a formal estimate of the number of steps Mq that have to be omitted at the beginning of the averaging. Usually, the order parameter ijf is the slowest relaxing quantity and then [Pg.107]

If the Worst Case analysis determines that not all circuits will pass a specified performance parameter, the Monte Carlo analysis may be used to estimate what percentage of the circuits will pass. [Pg.547]

The third method used to interpret the level of risk associated with chlorpy-rifos use is Monte Carlo simulation. This method provides a range of exposure estimates for the evaluation of the uncertainty in a risk estimate based on ranges of input variables. The first step in performing a Monte Carlo simulation is determination of a model to describe the dose. This model describes the relationship between the input parameters and dose, and a specific model is presented here for one group of workers. [Pg.38]

In this method, each assessment factor is considered uncertain and characterized as a random variable with a lognormal distribution with a GM and a GSD. Propagation of the uncertainty can then be evaluated using Monte Carlo simulation (a repeated random sampling from the distribution of values for each of the parameters in a calculation to derive a distribution of estimates in the population), yielding a distribution of the overall assessment factor. This method requires characterization of the distribution of each assessment factor and of possible correlations between them. As a first approach, it can be assumed that all factors are independent, which in fact is not correct. [Pg.290]

Characterizing the overall uncertainties associated with the PBPK model estimates is also an important component of the PBPK model evaluation and application. This includes characterizing the uncertainties in model outputs resulting from the uncertainty in the PBPK model parameters. Traditionally, Monte Carlo has been employed for performing uncertainty analysis of PBPK models (39, 40). Some of the recent techniques that have been applied for the uncertainty analysis of PBPK models include the stochastic response surface method (SRSM) (38, 41) and the high-dimensional model reduction (HDMR) technique (42). [Pg.1078]

Selected entries from Methods in Enzymology [vol, page(s)] Generation, 240, 122-123 confidence limits, 240, 129-130 discrete variance profile, 240, 124-126, 128-129, 131-133, 146, 149 error response, 240, 125-126, 149-150 Monte Carlo validation, 240, 139, 141, 146, 148-149 parameter estimation, 240, 126-129 radioimmunoassay, 240, 122-123, 125-127, 131-139 standard errors of mean, 240, 135 unknown sample evaluation, 240, 130-131 zero concentration response, 240, 138, 150. [Pg.646]

In classical statistics, the most important type of criterion for judging estimators is a high probability that a parameter estimate will be close to the actual value of the parameter estimated. To implement the classical approach, it is necessary to quantify the closeness of an estimate to a parameter. One may rely on indices of absolute, relative, or squared error. Mean squared error (MSB) has often been used by statisticians, perhaps usually because of mathematical convenience. However, if estimators are evaluated using Monte Carlo simulation it is easy to use whatever criterion seems most reasonable in a given situation. [Pg.37]

Eurthermore, uncertainties in the exposure assessment should also be taken into account. However, no generally, internationally accepted principles for addressing these uncertainties have been developed. For predicted exposure estimates, an uncertainty analysis involving the determination of the uncertainty in the model output value, based on the collective uncertainty of the model input parameters, can be performed. The usual approach for assessing this uncertainty is the Monte Carlo simulation. This method starts with an analysis of the probability distribution of each of the variables in the uncertainty analysis. In the simulation, one random value from each distribution curve is drawn to produce an output value. This process is repeated many times to produce a complete distribution curve for the output parameter. [Pg.349]

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