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Open research questions in Gaussian Processes and Bayesian Inference

86 unresolved questions extracted from the limitations and future-work sections of 407 Gaussian Processes and Bayesian Inference papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • Further development of the proposed approaches to improve predictive accuracy and predictive coverage. Application of the approaches to various fields, including hydrology and systems biology.

    Bayesian surrogate training on multiple data sources: a hybrid modeling strategy · 2026 · DOI

  • The simulation model is itself an imperfect approximation of real-world processes. The lack of integration of simulation data and real-world measurement data during surrogate training.

    Bayesian surrogate training on multiple data sources: a hybrid modeling strategy · 2026 · DOI

  • High cost of high-quality reference sensors. Limited number of sensors that can be deployed. Need for accurate spatial mapping of pollutant concentrations.

    Efficient Uncertainty-Guided Sensor Placement for Air Quality Mapping using Gaussian Processes and Spatial Indexing · 2026 · DOI

  • The curse of dimensionality. The need for a method that can approximate complex distributions. The need for a method that can achieve faster convergence rates than standard Monte Carlo.

    Transport Quasi-Monte Carlo · 2026 · DOI

  • The optimization of the latent factor matrix in the Stiefel manifold in each step of the optimization can be unstable. The numerical optimization in high-dimensional parameter space can be unstable.

    Fast Data Inversion for High-Dimensional Ornstein–Uhlenbeck Processes from Noisy Measurements · 2026 · DOI

  • The presence of an unknown multiplicative constant. The non-negligible computational cost of evaluating the likelihood. The high dimensionality of the parameter space.

    Estimating intractable posterior distributions through Gaussian process regression and metropolis-adjusted Langevin procedure · 2026 · DOI

  • The uncertainty of reservoir properties severely compromises the predictive accuracy of subsurface flow dynamics. Existing inversion methods require adaptation for each new observational configuration.

    SURGIN: SURrogate-guided Generative INversion for subsurface multiphase flow with quantified uncertainty · 2026 · DOI

  • The approach requires the choice of a shrinkage strength parameter m. The paper discusses the sensitivity of the results to the choice of m. The approach is limited to the analysis of a single sector or outcome.

    Bayesian-smoothed location quotients for small regions with credible intervals and specialisation probabilities · 2026 · DOI

  • Future research can explore the application of the approach to other fields, including spatial epidemiology and disease mapping. Future research can investigate the use of different prior distributions and models. Future research can examine the sensitivity of the results to different choices of the shrinkage strength parameter m.

    Bayesian-smoothed location quotients for small regions with credible intervals and specialisation probabilities · 2026 · DOI

  • Future research should focus on extending the proposed strategy to other types of machine learning models, such as support vector machines and random forests. Future research should focus on applying the proposed strategy to other engineering applications, such as materials science and computer vision. Future research should focus on improving the efficiency and scalability of the proposed strategy.

    Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models · 2026 · DOI

  • The research gap is the need for a practical multi-fidelity machine learning strategy that combines deterministic and Bayesian models. The research gap is the need for a strategy that can address the accuracy-efficiency trade-off in machine learning. The research gap is the need for a strategy that can be used in a variety of engineering applications.

    Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models · 2026 · DOI

  • Future research can explore the application of the γ-Stein operator to larger datasets. The method can be extended to other types of probability models.

    Robust inference using density-powered Stein operators · 2026 · DOI

  • The paper identifies the need for robust inference with unnormalized probability models. The current methods can be sensitive to outliers and data contamination.

    Robust inference using density-powered Stein operators · 2026 · DOI

  • Future research should investigate the performance of lazyHMC on large-scale problems. Future research should investigate the application of lazyHMC to other domains, such as computer vision and natural language processing.

    LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programs · 2026 · DOI

  • The paper identifies a gap in the existing literature on probabilistic programming, which is the lack of a formulation of HMC that can handle infinite-dimensional parameter spaces. The paper identifies a gap in the existing literature on HMC, which is the need for a formulation that can handle lazy evaluation.

    LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programs · 2026 · DOI

  • Limited onboard computation. Privacy requirements. Communication bandwidth constraints.

    Federated Gaussian Process Learning via Pseudo-Representations for Large-Scale Multi-Robot Systems · 2026 · DOI

  • Strong process nonlinearity. Limited evaluation budgets. Strict operational constraints.

    Risk-sensitive collaborative parameter tuning via calibrated deep surrogates for rare-earth electrolysis energy efficiency · 2026 · DOI

  • Expensive computer simulations - Heteroscedastic stochastic simulations - Limited computational budgets

    Fully Bayesian Sequential Design for Heteroscedastic Stochastic Simulations · 2026 · DOI

  • Counterexamples show that terminal $W_4$ convergence alone is insufficient for variance consistency.

    Diffusion Bootstrap for High-Dimensional Linear Models · 2026

  • Bayesian calibration of material constitutive parameters from multimodal mechanical test data is often limited by the need to specify a joint likelihood across measurement modalities that differ in dimensionality, noise structure, and physical units.

    Amortized Posteriors for Estimation of Material Constitutive Parameters from Multimodal Measurements on Small Punch Tests · 2026

  • Alternative distributions have been proposed for the prior specifically, while the effect of distribution choice on the likelihood distribution remains unexplored.

    Rethinking Likelihood distributions: Student's t Likelihood Boosts Bayesian Neural Network Performance · 2026

  • The computational challenges associated with prior-free possibilistic statistical inference. The lack of efficient methods for approximating the possibilistic output of inferential models.

    An efficient Monte Carlo method for valid prior-free possibilistic statistical inference · 2026 · DOI

  • Validation on real urban data. Investigation of batch Bayesian optimization for global designs. Development of adaptive sensing strategies for real-time air quality monitoring.

    Efficient Uncertainty-Guided Sensor Placement for Air Quality Mapping using Gaussian Processes and Spatial Indexing · 2026 · DOI

  • Existing automated approaches struggle in high dimensions for two bottlenecks: their kernel search space is limited to additions and multiplications of base kernels, and LLM-based approaches require conditioning on raw observations, which becomes infeasible due to context-length limits and the difficulty of extracting meaningful patterns.

    Automated Kernel Discovery Towards Understanding High-dimensional Bayesian Optimization · 2026

  • The method assumes a fixed set of participating agents. The experiments are limited to synthetic and real-world datasets with fleet sizes from 16 to 100 agents.

    Federated Gaussian Process Learning via Pseudo-Representations for Large-Scale Multi-Robot Systems · 2026 · DOI

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86 open questions have been extracted from the limitations and future-work passages of 407 Gaussian Processes and Bayesian Inference papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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