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Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum…
A significant tension has become manifest between the current expansion rate of our Universe measured from the cosmic microwave background by the Planck satellite and from local distance probes, which has prompted for interpretations of…
Approximate Bayesian computation (ABC) has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical…
Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in…
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed…
The Standard Cosmological Model has experienced tremendous success at reproducing observational data by assuming a universe dominated by a cosmological constant and dark matter in a flat geometry. However, several studies, based on local…
The estimation of the Hubble constant in the past few decades has increasingly become more accurate with the advance of new techniques. But its value seems to depend on the epoch at which the measurements are made. The Planck estimate of…
Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging.…
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…
Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate…
We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate…
The standard model of cosmology, the $\Lambda$CDM model, describes the evolution of the Universe since the Big Bang with just a few parameters, six in its basic form. Despite being the simplest model, direct late-time measurements of the…
The current Hubble constant tension is usually presented by comparing constraints on $H_0$ only. However, the post-recombination background cosmic evolution is determined by two parameters in the standard $\Lambda$CDM model, the Hubble…
Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis…
We propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even…
The evolution of the Hubble parameter $H(z)$ with redshift $z$ is estimated from the Pantheon+ data of Type Ia supernovae, for the $\Lambda$CDM model and the three special cases of the eternal coasting (EC) cosmological model with three…
Mechanistic models are essential tools across ecology, epidemiology, and the life sciences, but parameter inference remains challenging when likelihood functions are intractable. Approximate Bayesian Computation with Sequential Monte Carlo…
An exact determination of the Hubble constant remains one of key problems in cosmology for almost a century. However, its modern values derived by various methods still disagree from each other by almost 10%; the greater values being…
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…
Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The…