arXiv subjects

Stef van Buuren

Publications and source records attributed to Stef van Buuren.

12 recordsLinked to original sources

arXiv2026

LLMs as Implicit Imputers: Uncertainty Should Scale with Missing Information

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated against a criterion from the multiple imputation (MI) literature: uncertainty should scale with the amount of missing information. We assess this criterion on SQuAD, using a controlled framework in which context availability is varied across five levels. We evaluate two answer-level uncertainty measures that can be estimated from repeated sampling: sampling-based confidence (empirical mode frequency) and response entropy. Confidence fails to reflect increasing missingness: it remains high even as accuracy collapses. Entropy, by contrast, increases with context removal, consistent with the MI analogy, and explains substantially more variance in accuracy than confidence across all evidence levels (quadratic $R^2$ gap up to 0.057). We further introduce a black-box diagnostic $ρ_R(α)$ that estimates the proportion of baseline uncertainty resolved by context level $α$, requiring only repeated sampling with and without context. These results suggest that entropy is a more responsive black-box uncertainty measure than confidence under incomplete context.

stat.ML↗

arXiv2026

HIMCE: High-dimensional multiple imputation via covariance-mode updating for neuroimaging and spatiotemporal blocks

High-dimensional neuroimaging and spatiotemporal blocks often contain structured missingness from acquisition artifacts, preprocessing failures, and sensor dropout. Multiple imputation propagates uncertainty, but fully conditional specification methods such as multivariate imputation by chained equations (MICE) can be slow or unstable when block dimension is large and correlations are strong. A multivariate normal (MVN) working model provides a coherent posterior predictive target and an exact data augmentation sampler, but repeated covariance sampling and matrix factorizations become costly in large dimensions. We propose High-dimensional Imputation via covariance Mode and Chained Equations (HIMCE), a hybrid multiple-imputation procedure for continuous blocks. Relative to exact MVN data augmentation, HIMCE preserves the Gaussian conditional imputation law and propagates mean- parameter uncertainty through stochastic coefficient or local-ridge draws. In high-dimensional blocks, it approximates covariance uncertainty through covariance-mode updating, optionally with a scalar bridge; in small blocks, it can restore exact covariance uncertainty through a conditional inverse-Wishart refresh. We record the exact Bayesian reference sampler and prove fixed-dimensional posterior consistency and asymptotic equivalence of mode plug-in prediction in total variation. We also develop diagnostics based on randomized rank-cell probability integral transform (PIT), PIT-consistent empirical coverage, and marginal distribution overlays. In the primary spatial benchmark, HIMCE improves posterior-mean error relative to HIMA and screened MICE, runs at HIMA-like speed and below half the MICE runtime, and improves interval coverage over HIMA, although MICE remains better calibrated. A repeated low- dimensional NHANES illustration shows improved coverage with competitive point prediction.

stat.ME↗

arXiv2026

Predicting missing values: A good idea?

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses. These biases affect key parameters such as variance, prevalence, correlation, slope, and explained variance. The root cause is that imputed values optimized for MSE are averages, which reduce the natural variability in the data. This paper demonstrates that adding noise to imputed values can effectively eliminate these biases. The required noise level is proportional to the MSE. Using a toy example in a multivariate normal setting, we compare two methods: predictive imputation, which minimizes MSE, and stochastic imputation, which incorporates random noise. Simulation results show that predictive methods systematically introduce bias, while stochastic methods preserve the data's natural variability and produce unbiased estimates. We also evaluate three popular imputation tools -- missForest, softImpute, and mice -- and observe consistent biases in predictive methods. These findings highlight that MSE is an inadequate measure of imputation quality, as it prioritizes accuracy over variability. Incorporating noise into imputation methods is essential to prevent biases and ensure valid downstream analyses, underscoring the importance of stochastic approaches for handling incomplete data.

stat.ML↗

arXiv2025

Sensitivity analysis for multivariable missing data using multiple imputation: a tutorial

Multiple imputation is a popular method for handling missing data, with fully conditional specification (FCS) being one of the predominant imputation approaches for multivariable missingness. Unbiased estimation with standard implementations of multiple imputation depends on assumptions concerning the missingness mechanism (e.g. that data are "missing at random"). The plausibility of these assumptions can only be assessed using subject-matter knowledge, and not data alone. It is therefore important to perform sensitivity analyses to explore the robustness of results to violations of these assumptions (e.g. if the data are in fact "missing not at random"). In this tutorial, we provide a roadmap for conducting sensitivity analysis using the Not at Random Fully Conditional Specification (NARFCS) procedure for multivariate imputation. Using a case study from the Longitudinal Study of Australian Children, we work through the steps involved, from assessing the need to perform the sensitivity analysis, and specifying the NARFCS models and sensitivity parameters, through to implementing NARFCS using FCS procedures in R and Stata.

stat.ME↗

arXiv2024

Random Indicator Imputation for Missing Not At Random Data

Imputation methods for dealing with incomplete data typically assume that the missingness mechanism is at random (MAR). These methods can also be applied to missing not at random (MNAR) situations, where the user specifies some adjustment parameters that describe the degree of departure from MAR. The effect of different pre-chosen values is then studied on the inferences. This paper proposes a novel imputation method, the Random Indicator (RI) method, which, in contrast to the current methodology, estimates these adjustment parameters from the data. For an incomplete variable $X$, the RI method assumes that the observed part of $X$ is normal and the probability for $X$ to be missing follows a logistic function. The idea is to estimate the adjustment parameters by generating a pseudo response indicator from this logistic function. Our method iteratively draws imputations for $X$ and the realization of the response indicator $R$, to which we refer as $\dot{R}$, for $X$. By cross-classifying $X$ by $R$ and $\dot{R}$, we obtain various properties on the distribution of the missing data. These properties form the basis for estimating the degree of departure from MAR. Our numerical simulations show that the RI method performs very well across a variety of situations. We show how the method can be used in a real life data set. The RI method is automatic and opens up new ways to tackle the problem of MNAR data.

stat.ME↗

arXiv2022

How to relate potential outcomes: Estimating individual treatment effects under a given specified partial correlation

In most medical research, the average treatment effect is used to evaluate a treatment's performance. However, precision medicine requires knowledge of individual treatment effects: What is the difference between a unit's measurement under treatment and control conditions? In most treatment effect studies, such answers are not possible because the outcomes under both experimental conditions are not jointly observed. This makes the problem of causal inference a missing data problem. We propose to solve this problem by imputing the individual potential outcomes under a specified partial correlation (SPC), thereby allowing for heterogeneous treatment effects. We demonstrate in simulation that our proposed methodology yields valid inferences for the marginal distribution of potential outcomes. We highlight that the posterior distribution of individual treatment effects varies with different specified partial correlations. This property can be used to study the sensitivity of optimal treatment outcomes under different correlation specifications. In a practical example on HIV-1 treatment data, we demonstrate that the proposed methodology generalises to real-world data. Imputing under the SPC, therefore, opens up a wealth of possibilities for studying heterogeneous treatment effects on incomplete data and the further adaptation of individual treatment effects.

stat.CO↗

arXiv2022

Graphical and numerical diagnostic tools to assess multiple imputation models by posterior predictive checking

Missing data are often dealt with multiple imputation. A crucial part of the multiple imputation process is selecting sensible models to generate plausible values for incomplete data. A method based on posterior predictive checking is proposed to diagnose imputation models based on posterior predictive checking. To assess the congeniality of imputation models, the proposed diagnostic method compares the observed data with their replicates generated under corresponding posterior predictive distributions. If the imputation model is congenial with the substantive model, the observed data are expected to be located in the centre of corresponding predictive posterior distributions. Simulation and application are designed to investigate the proposed diagnostic method for parametric and semi-parametric imputation approaches, continuous and discrete incomplete variables, univariate and multivariate missingness patterns. The results show the validity of the proposed diagnostic method.

stat.CO↗

arXiv2022

Joint distribution properties of Fully Conditional Specification under the normal linear model with normal inverse-gamma priors

Fully conditional specification (FCS) is a convenient and flexible multiple imputation approach. It specifies a sequence of simple regression models instead of a potential complex joint density for missing variables. However, FCS may not converge to a stationary distribution. Many authors have studied the convergence properties of FCS when priors of conditional models are non-informative. We extend to the case of informative priors. This paper evaluates the convergence properties of the normal linear model with normal-inverse gamma prior. The theoretical and simulation results prove the convergence of FCS and show the equivalence of prior specification under the joint model and a set of conditional models when the analysis model is a linear regression with normal inverse-gamma priors.

stat.CO↗

arXiv2022

A blended distance to define "people-like-me"

Curve matching is a prediction technique that relies on predictive mean matching, which matches donors that are most similar to a target based on the predictive distance. Even though this approach leads to high prediction accuracy, the predictive distance may make matches look unconvincing, as the profiles of the matched donors can substantially differ from the profile of the target. To counterbalance this, similarity between the curves of the donors and the target can be taken into account by combining the predictive distance with the Mahalanobis distance into a `blended distance' measure. The properties of this measure are evaluated in two simulation studies. Simulation study I evaluates the performance of the blended distance under different data-generating conditions. The results show that blending towards the Mahalanobis distance leads to worse performance in terms of bias, coverage, and predictive power. Simulation study II evaluates the blended metric in a setting where a single value is imputed. The results show that a property of blending is the bias-variance trade off. Giving more weight to the Mahalanobis distance leads to less variance in the imputations, but less accuracy as well. The main conclusion is that the high prediction accuracy achieved with the predictive distance necessitates the variability in the profiles of donors.

stat.ME↗

arXiv2021

Missing the Point: Non-Convergence in Iterative Imputation Algorithms

Iterative imputation is a popular tool to accommodate missing data. While it is widely accepted that valid inferences can be obtained with this technique, these inferences all rely on algorithmic convergence. There is no consensus on how to evaluate the convergence properties of the method. Our study provides insight into identifying non-convergence in iterative imputation algorithms. We found that--in the cases considered--inferential validity was achieved after five to ten iterations, much earlier than indicated by diagnostic methods. We conclude that it never hurts to iterate longer, but such calculations hardly bring added value.

stat.CO↗

arXiv2017

Multiple imputation for multilevel data with continuous and binary variables

We present and compare multiple imputation methods for multilevel continuous and binary data where variables are systematically and sporadically missing. The methods are compared from a theoretical point of view and through an extensive simulation study motivated by a real dataset comprising multiple studies. Simulations are reproducible. The comparisons show why these multiple imputation methods are the most appropriate to handle missing values in a multilevel setting and why their relative performances can vary according to the missing data pattern, the multilevel structure and the type of missing variables. This study shows that valid inferences can only be obtained if the dataset gathers a large number of clusters. In addition, it highlights that heteroscedastic MI methods provide more accurate inferences than homoscedastic methods, which should be reserved for data with few individuals per cluster. Finally, the method of Quartagno and Carpenter (2016a) appears generally accurate for binary variables, the method of Resche-Rigon and White (2016) with large clusters, and the approach of Jolani et al. (2015) with small clusters.

stat.ME↗

arXiv2014

Pooling multiple imputations when the sample happens to be the population

Current pooling rules for multiply imputed data assume infinite populations. In some situations this assumption is not feasible as every unit in the population has been observed, potentially leading to over-covered population estimates. We simplify the existing pooling rules for situations where the sampling variance is not of interest. We compare these rules to the conventional pooling rules and demonstrate their use in a situation where there is no sampling variance. Using the standard pooling rules in situations where sampling variance should not be considered, leads to overestimation of the variance of the estimates of interest, especially when the amount of missingness is not very large. As a result, populations estimates are over-covered, which may lead to a loss of statistical power. We conclude that the theory of multiple imputation can be extended to the situation where the sample happens to be the population. The simplified pooling rules can be easily implemented to obtain valid inference in cases where we have observed essentially all units and in simulation studies addressing the missingness mechanism only.

math.ST↗