  Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and
Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in
generalized linear models; however, these algorithms are prohibitively slow in
massive data settings because they require multiple passes through the full
data in every iteration. Addressing this problem, we develop a scalable
extension of these algorithms using the divide-and-conquer (D&C) technique that
divides the data into a sufficiently large number of subsets, draws parameters
in parallel on the subsets using a \textit{powered} likelihood, and produces
Monte Carlo draws of the parameter by combining parameter draws obtained from
each subset. These combined parameter draws play the role of draws from the
original sampling algorithm. Our main contributions are two-fold. First, we
demonstrate through diverse simulated and real data analyses that our
distributed algorithm is comparable to the current state-of-the-art D&C
algorithm in terms of statistical accuracy and computational efficiency.
Second, providing theoretical support for our empirical observations, we
identify regularity assumptions under which the proposed algorithm leads to
asymptotically optimal inference. We illustrate our methodology through normal
linear and logistic regressions, where parts of our D&C algorithm are
analytically tractable.
