eldo_user

Monte Carlo Analysis
Monte Carlo Basic Features
may be approximated with the summation:
This property implies that a convergence test can be constructed and that confidence bounds on
the computations can be provided. In Eldo it is possible to use the .MC AUTOSTOP parameter
to control the run length for estimating the average value E(H(X)) (this can save CPU time).
For example, a convergence test based on confidence interval techniques can be defined with
the extract function MCCONV as follows:
* EXTRACT SECTION
* THE PERFORMANCE CRITERIA OF INTEREST IS:
* THE OSCILLATION FREQUENCY: OFREQ
.EXTRACT TRAN LABEL=OFREQ 1/(XDOWN(V(1),2.5,END)-XDOWN(V(1),2.5,START))
* MONTECARLO ANALYSIS
.MC 1000 AUTOSTOP=’mc_conv_freq’
.EXTRACT MC LABEL=mc_conv_freq MCCONV(OFREQ, AVG, CONFIDENCE, 100, 0.95)
where the expression MCCONV(OFREQ, AVG, CONFIDENCE, 100, 0.95) is a Boolean
value, which is true if some specific criterion is satisfied for the sample mean value AVG.
Example with multiple MCCONV extracts:
* MONTE CARLO ANALYSIS
.MC 1000 AUTOSTOP='mc_conv_avg && mc_conv_std'
.EXTRACT MC LABEL=mc_conv_avg
+ MCCONV(V1,AVG,CONFIDENCE, 100, 0.99, 0.0004, 0)
.EXTRACT MC LABEL=mc_conv_std
+ MCCONV(V1,STD,CONFIDENCE, 100, 0.99, 0.0003, 0)
Note that the Central Limit Theorem says that the sample mean converges to the expected value
at the rate O(n −1/2 ) which means that in practice an extra digit of accuracy requires 100 times as
many simulations. The convergence is therefore slow compared to more efficient numerical
methods such as Riemann quadrature or Simpson method, but the convergence of the MC
method is completely independent of the dimension of the input space.
Related Topics
Specifying a Monte Carlo Analysis
CONFIDENCE Technique
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Eldo® User's Manual, 15.3