arXiv subjects

Collin Cademartori

Publications and source records attributed to Collin Cademartori.

6 recordsLinked to original sources

arXiv2026

Variance Deltas for Visualizing and Explaining Posterior Uncertainty

In observational settings, where the data generating process and possibly the sample size are not controlled, it is typically impossible to guarantee a priori that quantities of interest will be estimated with sufficient precision. However, even when the data do not determine the quantities of interest, they may still allow determination of what is missing -- unobserved information which, if observed, would meaningfully reduce uncertainty. We propose an interactive visualization system, termed variance deltas, to enable the discovery of such missing information from a Bayesian posterior distribution. This system, which we provide as a software package, represents missing information as subsets of unobserved model quantities, organized into a tree based on how well each subset explains uncertainty about the quantity of interest. This system both automates the construction of candidate subsets from minimal user input and implements interactive operations for the division and combination of subsets, allowing the efficient discovery of interesting and useful explanations. We demonstrate this system by using it to discover nonobvious explanations of uncertainty for (1) a treatment effect parameter in a simulated causal inference problem and (2) a population proportion in a forecasting model of real polling data with many sources of bias.

stat.ME↗

arXiv2025

Identifiability and Falsifiability: Two Challenges for Bayesian Model Expansion

We study the identifiability of parameters and falsifiability of predictions under the process of model expansion in a Bayesian setting. Identifiability is represented by the closeness of the posterior to the prior distribution and falsifiability by the power of posterior predictive tests against alternatives. To study these two concepts formally, we develop information-theoretic proxies, which we term the identifiability and falsifiability mutual information. We argue that these are useful indicators, with lower values indicating a risk of poor parameter inference and underpowered model checks, respectively. Our main result establishes that a sufficiently complex expansion of a base statistical model forces a trade-off between these two mutual information quantities -- at least one of the two must decrease relative to the base model. We illustrate our result in three worked examples and extract implications for model expansion in practice. In particular, we show as an implication of our result that the negative impacts of model expansion can be limited by offsetting complexity in the likelihood with sufficiently constraining prior distributions.

math.ST↗

arXiv2023

Joint $p$-Values for Higher-Powered Bayesian Model Checking with Frequentist Guarantees

We introduce a joint posterior $p$-value, an extension of the posterior predictive $p$-value for multiple test statistics, designed to address limitations of existing Bayesian $p$-values in the setting of continuous model expansion. In particular, we show that the posterior predictive $p$-value, as well as its sampled variant, become more conservative as the parameter dimension grows, and we demonstrate the ability of the joint $p$-value to overcome this problem in cases where we can select test statistics that are negatively associated under the posterior. We validate these conclusions with a pair of simulation examples in which the joint $p$-value achieves substantial gains to power with only a modest increase in computational cost.

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arXiv2023

A Non-asymptotic Analysis of Generalized Approximate Message Passing Algorithms with Right Rotationally Invariant Designs

Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its iterates, for $N \times M$ design matrices $\mathbf{A}$ with i.i.d. Gaussian entries, the asymptotic distribution of the estimate at any iteration of the algorithm can be exactly characterized in the large system limit as $M/N \rightarrow δ\in (0, \infty)$ via a scalar recursion referred to as state evolution. In this paper, we show that appropriate functionals of the iterates, in fact, concentrate around their limiting values predicted by these asymptotic distributions with rates exponentially fast in $N$ for a large class of AMP-style algorithms, including those that are used when high-dimensional generalized linear regression models are assumed to be the data-generating process, like the generalized AMP algorithm, or those that are used when the measurement matrix is assumed to be right rotationally invariant instead of i.i.d. Gaussian, like vector AMP and generalized vector AMP. In practice, these more general AMP algorithms have many applications, for example in in communications or imaging, and this work provides the first study of finite sample behavior of such algorithms.

math.ST↗

arXiv2020

Adaptive Path Sampling in Metastable Posterior Distributions

The normalizing constant plays an important role in Bayesian computation, and there is a large literature on methods for computing or approximating normalizing constants that cannot be evaluated in closed form. When the normalizing constant varies by orders of magnitude, methods based on importance sampling can require many rounds of tuning. We present an improved approach using adaptive path sampling, iteratively reducing gaps between the base and target. Using this adaptive strategy, we develop two metastable sampling schemes. They are automated in Stan and require little tuning. For a multimodal posterior density, we equip simulated tempering with a continuous temperature. For a funnel-shaped entropic barrier, we adaptively increase mass in bottleneck regions to form an implicit divide-and-conquer. Both approaches empirically perform better than existing methods for sampling from metastable distributions, including higher accuracy and computation efficiency.

stat.CO↗

arXiv2018

Automatic Conflict Detection in Police Body-Worn Audio

Automatic conflict detection has grown in relevance with the advent of body-worn technology, but existing metrics such as turn-taking and overlap are poor indicators of conflict in police-public interactions. Moreover, standard techniques to compute them fall short when applied to such diversified and noisy contexts. We develop a pipeline catered to this task combining adaptive noise removal, non-speech filtering and new measures of conflict based on the repetition and intensity of phrases in speech. We demonstrate the effectiveness of our approach on body-worn audio data collected by the Los Angeles Police Department.

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