Monte Carlo experiment

Bunker D L and Davidson B S 1972 Photolytic cage effect. Monte Carlo experiments J. Am. Chem. Soc. 94 1843... 

Muller, P and Parmigiani, G. (1995). Optimal design via curve fitting of Monte Carlo experiments. Journal of the American Statistical Association, 90, 1322-1330. 

The proposed approach may also be useful in simulating thermochromatography in vacuum columns, chromathermography and other separation techniques in open columns. Moreover, repeated Monte Carlo experiments with small number of molecules serve to visualize the uncertainties imposed by poor statistics. They are very helpful in evaluating Bayesian confidence intervals for the parameters measured in the experiment performed in non-ideal conditions, when any attempt to obtain an analytical solution fails completely. This will be discussed and illustrated in Sect. 6.2. 

A Monte Carlo experiment was conducted comparing the different algorithms. Dose-effect data were simulated using an Emax model with intercept where E0 was set equal to 200, Emax was set equal to -100, ED50 was set equal to 25, and dose was fixed at the following levels 0, 10, 20, 40, 80, 160, and 320. A total of 25 subjects were simulated per dose level. The only source of error in this simulation was random error, which was added to each observation under the following residual variance models ... 

The ideal Monte Carlo experiment should probe the physical and structural properties of the protein during the folding process, while simultaneously converging to the global minimum structure or native state. Although a great deal of effort has already been expended on the development of computational models for this purpose, most have focused on energy functions or structural analysis. Very few have examined the ther-... 

The Monte Carlo experiment consists of first simulating movements in short-term interest rates, then using the simulated term structure to price the securities at the target rate. 

A source of random numbers is required by any Monte Carlo experiment. It is certainly possible, in principle, to produce numbers that are random in that they are the result of some random physical process such as radioactive decay, but such techniques are almost never used today. Instead one uses a mathematical relation that produces a sequence of numbers that will pass a specified battery of statistical tests. The numbers are not random in that their sequence is determined by the generator, but various statistical tests cannot distinguish them from random numbers. To be more specific we want a sequence of numbers / = 1,2,3,... that are uniform in the interval (0,1) and that are not seriously correlated. A possible sequence of statistical tests would examine uniformity of < in the unit interval, of 2i 2i+i in the unit square, of 3h 3i+u 31+2 in the unit cube, and so on until correlation behavior of a sufficient order (for the experiment in question) has been considered. 

It is worth mentioning that calculations such as these can be extremely economical, since often only small numbers of particles are needed in the sample. That is because the N-dependences of the Monte Carlo properties of the system and its (rather similar) reference system will be very much the same. The differences between the systems, measured by the Monte Carlo experiments, will therefore be rather insensitive to the size of the system. That is especially true for high densities This conjecture is borne out in practice accurate energies and free energies of the Lennard-Jones system can be obtained with only N = 32 particles. ... 

Monte Carlo methods (or Monte Carlo experiments) are used to simulate the probability of failure for a slope. Because of many coupled degrees of freedom such as the soil physical characteristics, statistical parameters and mathematical models, the Monte Carlo methods are especially useful to solve such a complicated system. The computational algorithms of the Monte Carlo method seek numerical solution by repeating random sampling. Its formulation is given by... 

In Table 6 we summarize the energetic data for the four Monte Carlo experiments, presenting the water-water, water-DNA, ion-water, ion-DNA and ion-ion average interaction energies, E(W-W), E(W-DNA), E(I-W), E(I-DNA) and E(I-I), respectively. 

Along the whole percolation line Pc(T) the critical exponents are the same as for random percolation, ao rding to theory and the Monte Carlo experiments except for the spedal point p = 1/2, T = Tc in two dimensions, where percolation and aitical point coincide. At this point, the following inequalities between perrolation exponents and lattice gas exponents have been proved ) ... 

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