Related papers: Gibbs Sampling for a Bayesian Hierarchical General…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

In Smyl et al. [Local and global trend Bayesian exponential smoothing models. International Journal of Forecasting, 2024.], a generalised exponential smoothing model was proposed that is able to capture strong trends and volatility in time…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs…

Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…

This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…

I present all the details in calculating the posterior distribution of the conjugate Normal-Gamma prior in Bayesian Linear Models (BLM), including correlated observations, prediction, model selection and comments on efficient numeric…

In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…

Contemporary focus on selective inference has renewed interest in the theory of selection models. In this paper, we analyze the asymptotic properties of selection models built on independent and identically distributed observations. We show…

We analyze the convergence rate of a simplified version of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a very strong form of ergodicity (uniform).…

Generalized linear mixed models (GLMMs) are commonly used to analyze correlated discrete or continuous response data. In Bayesian GLMMs, the often-used improper priors may yield undesirable improper posterior distributions. Thus, verifying…

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…

Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and…

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance…

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…

A novel method is proposed for the exact posterior mean and covariance of the random effects given the response in a generalized linear mixed model (GLMM) when the response does not follow normal. The research solves a long-standing problem…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under…

Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC)…

This paper explores Bayesian inference for a biased sampling model in situations where the population of interest cannot be sampled directly, but rather through an indirect and inherently biased method. Observations are viewed as being the…