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Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are modelled using a continuous-time stochastic process, and, depending on the application area of interest, this will typically take the form of a Markov jump process or an It\^o diffusion process. Widespread use of these models is typically precluded by their computational complexity. In particular, performing exact fully Bayesian inference in either modelling framework is challenging due to the intractability of the observed data likelihood, necessitating the use of computationally intensive techniques such as particle Markov chain Monte Carlo (particle MCMC). It is proposed to increase the computational and statistical efficiency of this approach by leveraging the tractability of an inexpensive surrogate derived directly from either the jump or diffusion process. The surrogate is used in three ways: in the design of a gradient-based parameter proposal, to construct an appropriate bridge and in the first stage of a delayed-acceptance step. The resulting approach, which exactly targets the posterior of interest, offers substantial gains in efficiency over a standard particle MCMC implementation.

We consider transporting a heavy payload that is attached to multiple quadrotors. The current state-of-the-art controllers either do not avoid inter-robot collision at all, leading to crashes when tasked with carrying payloads that are small in size compared to the cable lengths, or use computational demanding nonlinear optimization. We propose an extension to an existing efficient geometric payload transport controller to effectively avoid such collisions by designing an optimized cable force allocation method, and thus retaining the original stability properties. Our approach introduces a cascade of carefully designed quadratic programs that can be solved efficiently on highly constrained embedded flight controllers. We demonstrate our method on challenging scenarios with up to three small quadrotors with various payloads and cable lengths, with our controller running in real-time directly on the robots.

In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization paradigms. We also reformulate the proposed methods in a square-root form, resulting in improved numerical stability while preserving the parallelization capabilities. We then leverage the fixed-point structure of our methods to perform likelihood-based parameter estimation in logarithmic time with respect to the number of observations. Finally, we demonstrate the practical performance of the methodology with numerical experiments run on a graphics processing unit (GPU).

An information-theoretic estimator is proposed to assess the global identifiability of statistical models with practical consideration. The framework is formulated in a Bayesian statistical setting which is the foundation for parameter estimation under aleatoric and epistemic uncertainty. No assumptions are made about the structure of the statistical model or the prior distribution while constructing the estimator. The estimator has the following notable advantages: first, no controlled experiment or data is required to conduct the practical identifiability analysis; second, different forms of uncertainties, such as model form, parameter, or measurement can be taken into account; third, the identifiability analysis is global, rather than being dependent on a realization of parameters. If an individual parameter has low identifiability, it can belong to an identifiable subset such that parameters within the subset have a functional relationship and thus have a combined effect on the statistical model. The practical identifiability framework is extended to highlight the dependencies between parameter pairs that emerge a posteriori to find identifiable parameter subsets. Examining the practical identifiability of an individual parameter along with its dependencies with other parameters is informative for an estimation-centric parameterization and model selection. The applicability of the proposed approach is demonstrated using a linear Gaussian model and a non-linear methane-air reduced kinetics model.

Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often results in complex and intractable sampling distributions. In this paper, we propose to use the simulation-based "repro sample" approach to produce statistically valid confidence intervals and hypothesis tests based on privatized statistics. We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including 1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and 2) proposing efficient numerical algorithms to implement the confidence intervals and $p$-values.

We consider the measurement model $Y = AX,$ where $X$ and, hence, $Y$ are random variables and $A$ is an a priori known tall matrix. At each time instance, a sample of one of $Y$'s coordinates is available, and the goal is to estimate $\mu := \mathbb{E}[X]$ via these samples. However, the challenge is that a small but unknown subset of $Y$'s coordinates are controlled by adversaries with infinite power: they can return any real number each time they are queried for a sample. For such an adversarial setting, we propose the first asynchronous online algorithm that converges to $\mu$ almost surely. We prove this result using a novel differential inclusion based two-timescale analysis. Two key highlights of our proof include: (a) the use of a novel Lyapunov function for showing that $\mu$ is the unique global attractor for our algorithm's limiting dynamics, and (b) the use of martingale and stopping time theory to show that our algorithm's iterates are almost surely bounded.

In the field of sampling algorithms, MCMC (Markov Chain Monte Carlo) methods are widely used when direct sampling is not possible. However, multimodality of target distributions often leads to slow convergence and mixing. One common solution is parallel tempering. Though highly effective in practice, theoretical guarantees on its performance are limited. In this paper, we present a new lower bound for parallel tempering on the spectral gap that has a polynomial dependence on all parameters except $\log L$, where $(L + 1)$ is the number of levels. This improves the best existing bound which depends exponentially on the number of modes. Moreover, we complement our result with a hypothetical upper bound on spectral gap that has an exponential dependence on $\log L$, which shows that, in some sense, our bound is tight.

In Selk and Gertheiss (2022) a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, thus both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are developed. A uniform rate of convergence for the regression / classification estimator is given. Further it is shown that, asymptotically, a data-driven least squares cross-validation method can automatically remove irrelevant, noise variables.

The stochastic approximation (SA) algorithm is a widely used probabilistic method for finding a zero or a fixed point of a vector-valued funtion, when only noisy measurements of the function are available. In the literature to date, one makes a distinction between ``synchronous'' updating, whereby every component of the current guess is updated at each time, and ``asynchronous'' updating, whereby only one component is updated. In this paper, we study an intermediate situation that we call ``batch asynchronous stochastic approximation'' (BASA), in which, at each time instant, \textit{some but not all} components of the current estimated solution are updated. BASA allows the user to trade off memory requirements against time complexity. We develop a general methodology for proving that such algorithms converge to the fixed point of the map under study. These convergence proofs make use of weaker hypotheses than existing results. Specifically, existing convergence proofs require that the measurement noise is a zero-mean i.i.d\ sequence or a martingale difference sequence. In the present paper, we permit biased measurements, that is, measurement noises that have nonzero conditional mean. Also, all convergence results to date assume that the stochastic step sizes satisfy a probabilistic analog of the well-known Robbins-Monro conditions. We replace this assumption by a purely deterministic condition on the irreducibility of the underlying Markov processes. As specific applications to Reinforcement Learning, we analyze the temporal difference algorithm $TD(\lambda)$ for value iteration, and the $Q$-learning algorithm for finding the optimal action-value function. In both cases, we establish the convergence of these algorithms, under milder conditions than in the existing literature.

In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently used for the approximation of statistical moments, is combined with a suitable deterministic discretisation method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to a statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for the Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.