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Biological tissues are complex structures composed of many elements which make light-based tissue diagnostics challenging. Over the past decades, Monte Carlo technique has been used as a fundamental and versatile approach toward modeling…
Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series…
In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo…
We present a Monte Carlo algorithm for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…
Sequential Monte Carlo has become a standard tool for Bayesian Inference of complex models. This approach can be computationally demanding, especially when initialized from the prior distribution. On the other hand, deter-ministic…
Inverse problems defined on the sphere arise in many fields, including seismology and cosmology where problems are defined on the globe and the cosmic sphere. These are generally high-dimensional and computationally very complex and, as a…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
We derive a Markov Chain Monte Carlo sampler based on following ray paths in a medium where the refractive index $n(x)$ is a function of the desired likelihood $\mathcal{L}(x)$. The sampling method propagates rays at constant speed through…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…
We present an implementation of a Monte Carlo algorithm that generates points randomly and uniformly on a set of arbitrary surfaces. The algorithm is completely general and only requires the geometry modeling software to provide the…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…
Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed…