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Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
Probabilistic programming (PP) allows flexible specification of Bayesian statistical models in code. PyMC3 is a new, open-source PP framework with an intutive and readable, yet powerful, syntax that is close to the natural syntax…
The Bayesian paradigm is becoming an increasingly popular framework for estimation and uncertainty quantification of unknown parameters in geo-physical inversion problems. Badlands is a basin and landscape evolution forward model for…
The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires…
Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially…
Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical…
Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to approximate the joint distribution of the states given observations from a state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new particle…
Inference-time methods that aggregate and prune multiple samples have emerged as a powerful paradigm for steering large language models, yet we lack any principled understanding of their accuracy-cost tradeoffs. In this paper, we introduce…
A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…
We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the…
The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…