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1. Bilby -MCMC: an MCMC sampler for gravitational-wave inference

   https://doi.org/10.1093/mnras/stab2236  

   Ashton, G; Talbot, C (August 2021, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We introduce Bilby-MCMC, a Markov chain Monte Carlo sampling algorithm tuned for the analysis of gravitational waves from merging compact objects. Bilby-MCMC provides a parallel-tempered ensemble Metropolis-Hastings sampler with access to a block-updating proposal library including problem-specific and machine learning proposals. We demonstrate that learning proposals can produce over a 10-fold improvement in efficiency by reducing the autocorrelation time. Using a variety of standard and problem-specific tests, we validate the ability of the Bilby-MCMC sampler to produce independent posterior samples and estimate the Bayesian evidence. Compared to the widely used Dynesty nested sampling algorithm, Bilby-MCMC is less efficient in producing independent posterior samples and less accurate in its estimation of the evidence. However, we find that posterior samples drawn from the Bilby-MCMC sampler are more robust: never failing to pass our validation tests. Meanwhile, the Dynesty sampler fails the difficult-to-sample Rosenbrock likelihood test, over constraining the posterior. For CBC problems, this highlights the importance of cross-sampler comparisons to ensure results are robust to sampling error. Finally, Bilby-MCMC can be embarrassingly and asynchronously parallelized making it highly suitable for reducing the analysis wall-time using a High Throughput Computing environment. Bilby-MCMC may be a useful tool for the rapid and robust analysis of gravitational-wave signals during the advanced detector era and we expect it to have utility throughout astrophysics. 

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2. Exact Privacy Guarantees for Markov Chain Implementations of the Exponential Mechanism with Artificial Atoms

   J. Seeman, M. Reimherr (January 2021, Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021)

   Marc'Aurelio Ranzato, Alina Beygelzimer (Ed.)

   Implementations of the exponential mechanism in differential privacy often require sampling from intractable distributions. When approximate procedures like Markov chain Monte Carlo (MCMC) are used, the end result incurs costs to both privacy and accuracy. Existing work has examined these effects asymptotically, but implementable finite sample results are needed in practice so that users can specify privacy budgets in advance and implement samplers with exact privacy guarantees. In this paper, we use tools from ergodic theory and perfect simulation to design exact finite runtime sampling algorithms for the exponential mechanism by introducing an intermediate modified target distribution using artificial atoms. We propose an additional modification of this sampling algorithm that maintains its ǫ-DP guarantee and has improved runtime at the cost of some utility. We then compare these methods in scenarios where we can explicitly calculate a δ cost (as in (ǫ, δ)-DP) incurred when using standard MCMC techniques. Much as there is a well known trade-off between privacy and utility, we demonstrate that there is also a trade-off between privacy guarantees and runtime. 

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3. Efficient Rejection Sampling in the Entropy-Optimal Range

   https://doi.org/10.1109/TIT.2026.3658044  

   Draper, Thomas L; Saad, Feras A (May 2026, IEEE Transactions on Information Theory)

   We study the problem of generating a random variate X from a finite discrete probability distribution P using an entropy source of independent fair coin flips. A classic result from Knuth and Yao shows that the optimal expected number of input coin flips per output sample lies between H(P) and H(P)+2, where H is the Shannon entropy function. However, implementing the Knuth and Yao ``entropy-optimal'' sampler entails a tradeoff between using either exponential space with low runtime per sample, or linear space with high runtime per sample. We introduce a new sampling algorithm that avoids this tradeoff: it requires linearithmic space, incurs negligible runtime overhead per sample, and uses an expected number of coin flips that lies in the entropy-optimal range [H(P),H(P)+2). No previous sampler for discrete distributions simultaneously achieves these space, time, and entropy characteristics. Numerical experiments demonstrate improvements in runtime and entropy of the proposed method compared to the celebrated alias method. 

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4. Privacy-Aware Rejection Sampling

   Awan, Jordan; Rao, Vinayak (February 2023, Journal of machine learning research)

   Weller, Adrian (Ed.)

   While differential privacy (DP) offers strong theoretical privacy guarantees, implementations of DP mechanisms may be vulnerable to side-channel attacks, such as timing attacks. When sampling methods such as MCMC or rejection sampling are used to implement a privacy mechanism, the runtime can leak private information. We characterize the additional privacy cost due to the runtime of a rejection sampler in terms of both (, δ)-DP as well as f -DP. We also show that unless the acceptance probability is constant across databases, the runtime of a rejection sampler does not satisfy -DP for any . We show that there is a similar breakdown in privacy with adaptive rejection samplers. We propose three modifications to the rejection sampling algorithm, with varying assumptions, to protect against timing attacks by making the runtime independent of the data. The modification with the weakest assumptions is an approximate sampler, introducing a small increase in the privacy cost, whereas the other modifications give perfect samplers. We also use our techniques to develop an adaptive rejection sampler for log-H ̈older densities, which also has data-independent runtime. We give several examples of DP mechanisms that fit the assumptions of our methods and can thus be implemented using our samplers. 

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5. Privacy-Aware Rejection Sampling

   Awan, Jordan; Rao, Vinayak (January 2023, Journal of machine learning research)

   Weller, Adrian (Ed.)

   Differential privacy (DP) offers strong theoretical privacy guarantees, though implementations of DP mechanisms may be vulnerable to side-channel attacks, such as timing attacks. When sampling methods such as MCMC or rejection sampling are used to implement a mechanism, the runtime can leak private information. We characterize the additional privacy cost due to the runtime of a rejection sampler in terms of both (epsilon,delta)-DP as well as f-DP. We also show that unless the acceptance probability is constant across databases, the runtime of a rejection sampler does not satisfy epsilon-DP for any epsilon. We show that there is a similar breakdown in privacy with adaptive rejection samplers. We propose three modifications to the rejection sampling algorithm, with varying assumptions, to protect against timing attacks by making the runtime independent of the data. The modification with the weakest assumptions is an approximate sampler, introducing a small increase in the privacy cost, whereas the other modifications give perfect samplers. We also use our techniques to develop an adaptive rejection sampler for log-Holder densities, which also has data-independent runtime. We give several examples of DP mechanisms that fit the assumptions of our methods and can thus be implemented using our samplers. 

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