Related papers: Marginal Likelihood Computation via Arrogance Samp…

This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…

Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…

The marginal likelihood, or evidence, plays a central role in Bayesian model selection, yet remains notoriously challenging to compute in likelihood-free settings. While Simulation-Based Inference (SBI) techniques such as Sequential Neural…

Statistical procedures such as Bayes factor model selection and Bayesian model averaging require the computation of normalizing constants (e.g., marginal likelihoods). These normalizing constants are notoriously difficult to obtain, as they…

We describe briefly in this note a procedure for consistently estimating the marginal likelihood of a statistical model through a sample from the posterior distribution of the model parameters.

This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…

Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…

Computing ratios of normalizing constants plays an important role in statistical modeling. Two important examples are hypothesis testing in latent variables models, and model comparison in Bayesian statistics. In both examples, the…

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such…

Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes…

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…

The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…

We investigate the efficiency of a marginal likelihood estimator where the product of the marginal posterior distributions is used as an importance-sampling function. The approach is generally applicable to multi-block parameter vector…