Related papers: On adaptive resampling strategies for sequential M…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…

Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case…

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers…

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…

We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo…

One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more…

Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…

Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…

We propose a Markov chain Monte Carlo (MCMC) scheme to perform state inference in non-linear non-Gaussian state-space models. Current state-of-the-art methods to address this problem rely on particle MCMC techniques and its variants, such…

Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but…

This paper is a tutorial and literature review on sampling algorithms. We have two main types of sampling in statistics. The first type is survey sampling which draws samples from a set or population. The second type is sampling from…

Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard…

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…

Practitioners have access to an abundance of language models and prompting strategies for solving many language modeling tasks; yet prior work shows that modeling performance is highly sensitive to both choices. Classical machine learning…