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We present a novel probabilistic programming framework that couples directly to existing large-scale simulators through a cross-platform probabilistic execution protocol, which allows general-purpose inference engines to record and control…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…

Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…

For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering the conductivity $f>0$ in the divergence form equation $$…

We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…

We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…

For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is…

We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…

Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

The observations in many applications consist of counts of discrete events, such as photons hitting a dector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model.…

We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…

Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…

We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to~\cite{BertsimasS03}, once the schedule is…

Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…

Denoising diffusions sample from a probability distribution $\mu$ in $\mathbb{R}^d$ by constructing a stochastic process $({\hat{\boldsymbol x}}_t:t\ge 0)$ in $\mathbb{R}^d$ such that ${\hat{\boldsymbol x}}_0$ is easy to sample, but the…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…