What are the conditions for valid extrapolation of statistical predictions?

It is maintained that the most important conditions to obtain valid statistical predictions are (1) to be aware of the fundaments of probability, statistics and stochastics, (2) to formulate the problem as clearly as possible, (3) to know the statistical/stochastic properties of the variables involved, such as marginal and dependence properties, and (4) to use correct statistical results, i.e. those results that correspond to the nature of the problem and the variables involved. These conditions are not always met in scientific publications and practical applications.