Although large language models (LLMs) are highly interactive and extendable, current approaches to ensure reliability in deployments remain mostly limited to rejecting outputs with high uncertainty in order to avoid misinformation. This conservative strategy reflects the current lack of tools to systematically distinguish and respond to different sources of uncertainty. In this paper, we advocate for the adoption of Bayesian Modeling of Experiments -- a framework that provides a coherent foundation to reason about uncertainty and clarify the reducibility of uncertainty -- for managing and proactively addressing uncertainty that arises in LLM deployments. This framework enables LLMs and their users to take contextually appropriate steps, such as requesting clarification, retrieving external information, or refining inputs. By supporting active resolution rather than passive avoidance, it opens the door to more reliable, transparent, and broadly applicable LLM systems, particularly in high-stakes, real-world settings.

This paper proposed the population posterior distribution for Bayesian modeling of streams of data and showed how stochastic optimization could be used to find a good approximation. The proposed framework and algorithm were demonstrated on both latent Dirichlet allocation and Dirichlet process mixture models on text and geolocation data and were shown to perform better than previous work in some cases. Overall, I think the main idea of the paper is very interesting and it would fit in well at NIPS. There are a few aspects of the paper that could use some more discussion though. First, the authors were very careful throughout the paper to use the term "Bayesian modeling", except the title uses "Bayesian inference", which this paper definitely does not provide a method for.

In previous work [6, 9, 10], we advanced a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity based primarily on a Bayesian (MAP) analysis of image differ(cid:173) ences, leading to a "dual" basis similar to eigenfaces [13]. The performance advantage of this probabilistic matching technique over standard Euclidean nearest-neighbor eigenface matching was recently demonstrated using results from DARPA's 1996 "FERET" face recognition competition, in which this probabilistic matching algorithm was found to be the top performer. We have further developed a simple method of replacing the costly com put ion of nonlinear (online) Bayesian similarity measures by the relatively inexpensive computation of linear (offline) subspace projections and simple (online) Euclidean norms, thus resulting in a significant computational speed-up for implementation with very large image databases as typically encountered in real-world applications.

I consider the problem of learning concepts from small numbers of pos(cid:173) itive examples, a feat which humans perform routinely but which com(cid:173) puters are rarely capable of. Bridging machine learning and cognitive science perspectives, I present both theoretical analysis and an empirical study with human subjects for the simple task oflearning concepts corre(cid:173) sponding to axis-aligned rectangles in a multidimensional feature space. Existing learning models, when applied to this task, cannot explain how subjects generalize from only a few examples of the concept. I propose a principled Bayesian model based on the assumption that the examples are a random sample from the concept to be learned. The model gives precise fits to human behavior on this simple task and provides qualitati ve insights into more complex, realistic cases of concept learning.

Bayesian hierarchical models are well-suited to analyzing the often noisy data from electroencephalography experiments in cognitive neuroscience: these models provide an intuitive framework to account for structures and correlations in the data, and they allow a straightforward handling of uncertainty. In a typical neurolinguistic experiment, event-related potentials show only very small effect sizes and frequentist approaches to data analysis fail to establish the significance of some of these effects. Here, we present a Bayesian approach to analyzing event-related potentials using as an example data from an experiment which relates word surprisal and neural response. Our model is able to estimate the effect of word surprisal on most components of the event-related potential and provides a richer description of the data. The Bayesian framework also allows easier comparison between estimates based on surprisal values calculated using different language models.

Artificial intelligence (AI) and machine learning models are being increasingly deployed in real-world applications.

We can also see this visually. We can verify the convergence of the chains formally using the Gelman Rubin test. Values close to 1.0 mean convergence. We can also test for correlation between samples in the chains. We are aiming for zero auto-correlation to get "random" samples from the posterior distribution.

A new Bayesian modeling method is proposed by combining the maximization of the marginal likelihood with a momentum-space renormalization group transformation for Gaussian graphical models. Moreover, we present a scheme for computint the statistical averages of hyperparameters and mean square errors in our proposed method based on a momentumspace renormalization transformation.

I wrote a series of blog posts on Bayesian modeling with R and Stan. Stan is a growing platform for MC(MC) computing implemented with C . Compared to WinBUGS or OpenBUGS, it is very fast and programmable intuitively. This series of the posts show how to install Stan on R, how to run it, and how to apply it to actual datasets. I hope you'll find it to practice Bayesian modeling easier than ever.

There are several reasons why everyone isn't using Bayesian methods for regression modeling. One reason is that Bayesian modeling requires more thought: you need pesky things like priors, and you can't assume that if a procedure runs without throwing an error that the answers are valid. A second reason is that MCMC sampling -- the bedrock of practical Bayesian modeling -- can be slow compared to closed-form or MLE procedures. A third reason is that existing Bayesian solutions have either been highly-specialized (and thus inflexible), or have required knowing how to use a generalized tool like BUGS, JAGS, or Stan. This third reason has recently been shattered in the R world by not one but two packages: brms and rstanarm.