Related papers: Prior Elicitation for Generalised Linear Models an…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-Gamma distributions, which are constructed in detail. A variety of examples are…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We address regularised versions of the Expectation-Maximisation (EM) algorithm for Generalised Linear Mixed Models (GLMM) in the context of panel data (measured on several individuals at different time-points). A random response y is…
Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…
Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model by…
We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation…
The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with…
We study program-learning methods that are efficient in both samples and computation. Classical learning theory suggests that when the target admits a short program description (for example, a short piece of ``Python code''), it can be…
We develop an extension of the classical Zellner's g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class…
This paper introduces distribution-based prediction, a novel approach to using Large Language Models (LLMs) as predictive tools by interpreting output token probabilities as distributions representing the models' learned representation of…
Pre-validation is a way to build prediction model with two datasets of significantly different feature dimensions. Previous work showed that the asymptotic distribution of the resulting test statistic for the pre-validated predictor…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
In this work, we show that under specific choices of the copula, the lasso, elastic net, and $g$-prior are particular cases of `copula prior,' for regularization and variable selection method. We present `lasso with Gauss copula prior' and…
We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…
We propose a generalisation of the logistic regression model, that aims to account for non-linear main effects and complex interactions, while keeping the model inherently explainable. This is obtained by starting with log-odds that are…
Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse…
We introduce a Bayesian prior distribution, the Logit-Normal continuous analogue of the spike-and-slab (LN-CASS), which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and…
The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme),…