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Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that AutoStep MCMC is $\pi$-invariant and has other desirable properties under mild assumptions on the target distribution $\pi$ and involutive proposal. Empirical results examine the effect of various step size selection design choices, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing the structure of the compute graph rather than the graphical model, we reduce the time per sweep of a full-scan Gibbs sampler from $O(d^2)$ to $O(d)$, where $d$ is the number of GLM parameters. Our simple changes to the implementation of the Gibbs sampler allow us to perform Bayesian inference on high-dimensional GLMs that are practically infeasible with traditional Gibbs sampler implementations. We empirically demonstrate a substantial increase in effective sample size per time when comparing our Gibbs algorithms to state-of-the-art HMC algorithms. While Gibbs is superior in terms of dimension scaling, neither Gibbs nor HMC dominate the other: we provide numerical and theoretical evidence that HMC retains an edge in certain circumstances thanks to its advantageous condition number scaling. Interestingly, for GLMs of fixed data size, we observe that increasing dimensionality can stabilize or even decrease condition number, shedding light on the empirical advantage of our efficient Gibbs sampler.

Selecting the step size for the Metropolis-adjusted Langevin algorithm (MALA) is necessary in order to obtain satisfactory performance. However, finding an adequate step size for an arbitrary target distribution can be a difficult task and even the best step size can perform poorly in specific regions of the space when the target distribution is sufficiently complex. To resolve this issue we introduce autoMALA, a new Markov chain Monte Carlo algorithm based on MALA that automatically sets its step size at each iteration based on the local geometry of the target distribution. We prove that autoMALA has the correct invariant distribution, despite continual automatic adjustments of the step size. Our experiments demonstrate that autoMALA is competitive with related state-of-the-art MCMC methods, in terms of the number of log density evaluations per effective sample, and it outperforms state-of-the-art samplers on targets with varying geometries. Furthermore, we find that autoMALA tends to find step sizes comparable to optimally-tuned MALA when a fixed step size suffices for the whole domain., Comment: Accepted to the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024

Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables i.i.d. sampling, ST is regenerative and can be parallelized across independent tours. However, the difficulty of tuning ST has hindered its widespread adoption. In this work, we develop a simple nonreversible ST (NRST) algorithm, a general theoretical analysis of ST, and an automated tuning procedure for ST. A core contribution that arises from the analysis is a novel performance metric -- Tour Effectiveness (TE) -- that controls the asymptotic variance of estimates from ST for bounded test functions. We use the TE to show that NRST dominates its reversible counterpart. We then develop an automated tuning procedure for NRST algorithms that targets the TE while minimizing computational cost. This procedure enables straightforward integration of NRST into existing probabilistic programming languages. We provide extensive experimental evidence that our tuning scheme improves the performance and robustness of NRST algorithms on a diverse set of probabilistic models.

We introduce a software package, Pigeons.jl, that provides a way to leverage distributed computation to obtain samples from complicated probability distributions, such as multimodal posteriors arising in Bayesian inference and high-dimensional distributions in statistical mechanics. Pigeons.jl provides simple APIs to perform such computations single-threaded, multi-threaded, and/or distributed over thousands of MPI-communicating machines. In addition, Pigeons.jl guarantees a property that we call strong parallelism invariance: the output for a given seed is identical irrespective of the number of threads and processes, which is crucial for scientific reproducibility and software validation. We describe the key features of Pigeons.jl and the approach taken to implement a distributed and randomized algorithm that satisfies strong parallelism invariance.

Bayesian inference for Continuous-Time Markov Chains (CTMCs) on countably infinite spaces is notoriously difficult because evaluating the likelihood exactly is intractable. One way to address this challenge is to first build a non-negative and unbiased estimate of the likelihood -- involving the matrix exponential of finite truncations of the true rate matrix -- and then to use the estimates in a pseudo-marginal inference method. In this work, we show that we can dramatically increase the efficiency of this approach by avoiding the computation of exact matrix exponentials. In particular, we develop a general methodology for constructing an unbiased, non-negative estimate of the likelihood using doubly-monotone matrix exponential approximations. We further develop a novel approximation in this family -- the skeletoid -- as well as theory regarding its approximation error and how that relates to the variance of the estimates used in pseudo-marginal inference. Experimental results show that our approach yields more efficient posterior inference for a wide variety of CTMCs.

COVID-19 pandemic has reshaped our world in a timescale much shorter than what we can understand. Particularities of SARS-CoV-2, such as its persistence in surfaces and the lack of a curative treatment or vaccine against COVID-19, have pushed authorities to apply restrictive policies to control its spreading. As data drove most of the decisions made in this global contingency, their quality is a critical variable for decision-making actors, and therefore should be carefully curated. In this work, we analyze the sources of error in typically reported epidemiological variables and usual tests used for diagnosis, and their impact on our understanding of COVID-19 spreading dynamics. We address the existence of different delays in the report of new cases, induced by the incubation time of the virus and testing-diagnosis time gaps, and other error sources related to the sensitivity/specificity of the tests used to diagnose COVID-19. Using a statistically-based algorithm, we perform a temporal reclassification of cases to avoid delay-induced errors, building up new epidemiologic curves centered in the day where the contagion effectively occurred. We also statistically enhance the robustness behind the discharge/recovery clinical criteria in the absence of a direct test, which is typically the case of non-first world countries, where the limited testing capabilities are fully dedicated to the evaluation of new cases. Finally, we applied our methodology to assess the evolution of the pandemic in Chile through the Effective Reproduction Number $R_t$, identifying different moments in which data was misleading governmental actions. In doing so, we aim to raise public awareness of the need for proper data reporting and processing protocols for epidemiological modelling and predictions.

The outbreak and propagation of COVID-19 have posed a considerable challenge to modern society. In particular, the different restrictive actions taken by governments to prevent the spread of the virus have changed the way humans interact and conceive interaction. Due to geographical, behavioral, or economic factors, different sub-groups among a population are more (or less) likely to interact, and thus to spread/acquire the virus. In this work, we present a general multi-group SEIRA model for representing the spread of COVID-19 among a heterogeneous population and test it in a numerical case of study. By highlighting its applicability and the ease with which its general formulation can be adapted to particular studies, we expect our model to lead us to a better understanding of the evolution of this pandemic and to better public-health policies to control it.

Miniaturization of continuous fluorescence detection is a challenging task due to the multiple and sensitive parameters intervening in the process. By analyzing fluorescence sensing architectures proposed during the last two years, this work has the goal to identify some trends in the process of fluorescence miniaturization for in-time liquid detection. A lack of postulated strategies regarding the miniaturization process was observed and this review tries to answer partially to this need. The identified integration strategies excel in fulfilling partially the desired functions of a fully autonomous miniaturized detector and further research is needed in order to develop sensing micro-system being capable to step outside of the lab world.