  Statistical machine learning often uses probabilistic algorithms, such as
Markov Chain Monte Carlo (MCMC), to solve a wide range of problems. Many
accelerators are proposed using specialized hardware to address sampling
inefficiency, the critical performance bottleneck of probabilistic algorithms.
These accelerators usually improve the hardware efficiency by using some
approximation techniques, such as reducing bit representation, truncating small
values to zero, or simplifying the Random Number Generator (RNG). Understanding
the influence of these approximations on result quality is crucial to meeting
the quality requirements of real applications. Although a common approach is to
compare the end-point result quality using community-standard benchmarks and
metrics, we claim a probabilistic architecture should provide some measure (or
guarantee) of statistical robustness.
  This work takes a first step towards quantifying the statistical robustness
of specialized hardware MCMC accelerators by proposing three pillars of
statistical robustness: sampling quality, convergence diagnostic, and goodness
of fit. Each pillar has at least one quantitative metric without the need to
know the ground truth data. We apply this method to analyze the statistical
robustness of an MCMC accelerator proposed by previous work, with some
modifications, as a case study. The method also applies to other probabilistic
accelerators and can be used in design space exploration.
