B-splines as density functions of sum of random variables, that are independent and uniformly distributed, play key role in computer simulation.
In the presentation basic properties of B-spline base are described together with their consequences in generation process.
B-spline base, with unrestricted choice of knots, is used in proposal kernel construction in classical Metropolis Hastings method. We present theorems on monitoring chains and assessing convergence, optimalise the way of choosing parameters by moment methods and easiness in implementation. Construction is similar to grid based chains construction (see L. Tierney Ann. Statist. 22 1701-1762).
Incorporating B-spline density estimators into Metropolis Hastings method we can easily obtain simulation prediction of data.
This methodology can be the default procedure in Metropolis Hastings simulation area.