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We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting…

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…

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…

Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…

The main focus of the analysts who deal with clustered data is usually not on the clustering variables, and hence the group-specific parameters are treated as nuisance. If a fixed effects formulation is preferred and the total number of…

Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

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.…

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…

The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…

In this paper we develop a likelihood-free approach for population calibration, which involves finding distributions of model parameters when fed through the model produces a set of outputs that matches available population data. Unlike…

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…

It is proposed in the literature that in some complicated problems maximum likelihood estimates (MLE) are not suitable or even do not exist. An alternative to MLE for estimation of the parameters is the Bayesian method. The Markov chain…

Many scientific and engineering problems require to perform Bayesian inferences for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement,…

Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard…

Bayesian inference often faces a trade-off between computational speed and sampling accuracy. We propose an adaptive workflow that integrates rapid amortized inference with gold-standard MCMC techniques to achieve a favorable combination of…