**5. Conclusions**

This chapter discussed the most important Bayesian frameworks and their applications. These frameworks play a crucial role in statistical and causal inferences. Learning from observations is one of the most fundamental concepts. Learning should be unbiased, systematic, replicable, generalizable, sample and other resources efficient and also provide a sufficient information gain. Since learning problems are often mathematically intractable, Bayesian reasoning can guide development of corresponding numerical algorithms. The algorithms can be considered to be concise representations of data, which can be generated by these algorithms. Bayesian frameworks allow building much more sophisticated models and carry out more complex computer simulations.

*Bayesian Methods and Monte Carlo Simulations DOI: http://dx.doi.org/10.5772/intechopen.108699*

Bayesian experiment design is especially important due to a widespread adoption of computer simulations in designing and analyzing various real-world systems. Research in machine learning is slowly moving from statistical correlations-based models to models exploiting causal relationships. As discussed in this chapter, the causal relationships in SCM (or SEM) can be analyzed by statistical inference methods, which were developed for Bayesian probabilistic models. Bayesian machine learning assigns a distribution to data labels. It improves the performance of semisupervised learning and enables automated data labeling and data label corrections. Bayesian optimization is particularly useful for optimizing real-world complex systems, which are very expensive to evaluate. Both Bayesian optimization and Bayesian machine learning are very active areas of research with many exciting open research problems. Bayesian Monte Carlo simulations aim at providing a systematic, semiautomated, explainable simulation framework. They augment the set of observations and leverage SEM or SCM in order to move from traditional descriptive simulations to predictive and even prescriptive simulations. Such research is still little explored in the existing literature.
