# Hierarchical Bayesian model or ensemble of predictors?

My model has 3 independent parameters $$\{\rho, \alpha, \beta\}$$ (polar coordinates), and a set of observables $$\{Q_i\}$$ and $$\{T_{ij}\}$$ where $$i=1,2,...,642$$ and $$j=1,2,...,Q_i$$ (if $$Q_i=0$$, there is no $$T_{ij}$$).

From $$\{\rho, \alpha, \beta\}$$, a set of intermediate (spherical harmonic) coefficients $$q^m_l(\rho, \alpha, \beta)$$ and $$t^m_1(\rho, \alpha, \beta)$$ where $$l=1,2,3~m=-l,...,-1,0,1,...,l$$ are obtained:

1. A rotational transformation $$R_l^m(\alpha, \beta)$$ (trigonometric polynomials in $$(\alpha, \beta)$$):

$$q^m_l(\rho, \alpha, \beta) = q^0_l(\rho, 0, 0) R^m_l(\alpha, \beta)$$

$$t^m_1(\rho, \alpha, \beta) = t^0_1(\rho, 0, 0) R^m_l(\alpha, \beta)$$

2. $$q^0_l(\rho, 0, 0)$$ and $$t^0_l(\rho, 0, 0)$$ are calibrated empirical functions.

$$Q_i$$ obeys Poisson distribution[a],

$$Q_i \sim \text{Pois}(\sum_{l=1}^3\sum_{m=-l}^lq^m_l(\rho, \alpha, \beta)S^m_l(\theta_i, \phi_i))$$, where $$S^m_l(\theta_i, \phi_i)$$ is the value of real spherical harimonic function at $$i$$.

$$T_{ij}$$ obeys shifted exponential and is treated with quantile regression[b] at 1% (empirical) percentile,

$$T_{ij} \sim \text{Quant}_{0.01}(\sum_{l=1}^3\sum_{m=-l}^lq^m_l(\rho, \alpha, \beta)S^m_l(\theta_i, \phi_i))$$

I would like to do inference, and I can see 2 options.

1. Hierarchical Bayesian model: use the above generative process and fit with MCMC. I know stan and pymc.

I have millions of observations, and am concerned about the feasibility of this approach on a small cluster (less than 1000 processor cores).

2. Ensemble of predictors: given an observation $$\{Q_i, T_{ij}\}$$, fit $$\hat{q}^m_l$$ and $$\hat{t}^m_l$$. For each $$l$$ fit $$\rho, \alpha, \beta$$ by $$q$$ or $$t$$. With 6 predictors $$(\hat{\rho}_l^{t/q}, \hat{\alpha}_l^{t/q}, \hat{\beta}_l^{t/q})$$, what is the best way to make a combined predictor? I know boosting for classifiers, is there a continuous counterpart?

Am I going to lose accuracy compared to hierarchical Bayesian? How can I estimate that loss?

Footnotes:

a. actually quasi-Poisson, where the variance is proportional to mean.