Related papers: Synthetic Priors
Foundation models, and in particular large language models, can generate highly informative responses, prompting growing interest in using these ''synthetic'' outputs as data in empirical research and decision-making. This paper introduces…
Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors.…
Catalytic prior distributions provide general, easy-to-use, and interpretable specifications of prior distributions for Bayesian analysis. They are particularly beneficial when the observed data are inadequate to stably estimate a complex…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
Modern predictive systems encode beliefs that can act as useful prior information for statistical inference in data-limited settings. Using them for prior construction introduces a tradeoff: an informative prior built from a predictive…
Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…
The use of synthetic data to deidentify data and to improve predictive models is well-attested to. The augmentation of datasets using synthetically generated data is an alluring proposition: in the best case, it generates realistic data…
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…
We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using…
Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…
A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate t prior distribution for the…
In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
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.…
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…
Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…
In this paper, we introduce a new methodology for Bayesian variable selection in linear regression that is independent of the traditional indicator method. A diagonal matrix $\mathbf{G}$ is introduced to the prior of the coefficient vector…
The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…