## Bayesian hierarchical modeling

As a rule of thumb, if you have less than 100 observations
and not a lot of trials, machine learning is not likely to perform well.
If on top, you have a lot of variables (e.g., age, weight, sex, etc...),
you are likely to face the multiple comparisons problem if using classical statistics.

The Bayesian hierarchical modeling estimates the parameters
of the posterior distribution using the Bayesian method. "Hierarchical" because information
is available on several different levels of observational units and we want to separately
estimate the posterior distribution of each individual predictor and its group-level effects.

The Bayesian hierarchical modeling is useful in case of nested data.
And we can consider that every dataset is kind of nested. Let's say you have a control
group of heatlhy subjects, they could still be divided into subgroups (per gender, age, etc...).
Hierarchical modeling is perfectly adapted to such setting. It fits to dataset with more
parameters than observations. Prof. Gelman suggested to use the Bayesian hierarchical modeling
by default.

Nowadays, we have a much richer description of people =>
more meta-information than before which explains why the Bayesian hierarchical
modeling is emerging. In psychiatry, location is a nested hidden variable rarely
exploited. The dataset size is usually quite small and by dividing your sample
into subsamples, the risk of overfitting is increased because of the lack of data.
Using a frequentist or a machine learning approach would not deal well with the
information lost. Using the Bayesian hierarchical modeling improves the parameter
estimates and reduce the risk of overfitting. It shares the statistical strength
by doing partial pooling.

Great introduction to hierarchical modeling: http://mfviz.com/hierarchical-models/

More info on multilevel modeling by Andrew Gelman: http://www.stat.columbia.edu/~gelman/research/published/multi2.pdf/

The Bayesian hierarchical modeling page on Wikipedia is also great: https://en.wikipedia.org/wiki/Bayesian_hierarchical_modeling