Basic Sampling Theory and Simulation

The mathematical formalism behind the basic estimation theory requires defining the product space denoted by (ftj X ftj— ft ), where all the ft, are equal to ft. This is needed because ft will be sampled n times, and these samples should be distinguishable. A configuration of this space is represented by the vector (x,, x,), where x, is a 3N coordinate vector of ft, A random 

To estimate E , one can select from ft n configurations with the Boltzmann PD and calculate the arithmetic average of the energy, E  

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In Section 42.2 we have discussed that queuing theory may provide a good qualitative picture of the behaviour of queues in an analytical laboratory. However the analytical process is too complex to obtain good quantitative predictions. As this was also true for queuing problems in other fields, another branch of Operations Research, called Discrete Event Simulation emerged. The basic principle of discrete event simulation is to generate sample arrivals. Each sample is characterized by a number of descriptors, e.g. one of those descriptors is the analysis time. In the jargon of simulation software, a sample is an object, with a number of attributes (e.g. analysis time) and associated values (e.g. 30 min). Other objects are e.g. instruments and analysts. A possible attribute is a list of the analytical... 

The MC and MD simulation approaches have become viable only after the introduction of fast computers. Starting from the pioneering works of Metropolis etal. [101] and Alder and Wainwright [102], the basic algorithms on which computer simulations are based were developed in the ensuing 20-30 years. They are now well established and described in standard textbooks [95,96], and able to provide a useful link between experiment and theory. Nowadays MC simulations are typically used for lattice and simple off-lattice models, while MD models are largely employed for atomistic systems (which are tricky to sample with MC) but also for coarse-grained models. 

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