The wisdom of crowds is an umbrella term for phenomena suggesting that the collective judgment or decision of a large group can be more accurate than the individual judgments or decisions of the group members. A well-known example illustrating this concept is the competition at a country fair described by Galton, where the median value of the individual guesses about the weight of an ox resulted in an astonishingly accurate estimate of the actual weight. This phenomenon resembles classical results in probability theory and relies on independent decision-making. The accuracy of the group's final decision can be significantly reduced if the final agents' opinions are driven by a few influential agents. In this paper, we consider a group of agents who initially possess uncorrelated and unbiased noisy measurements of a common state of the world. Assume these agents iteratively update their estimates according to a simple non-Bayesian learning rule, commonly known in mathematical sociology as the French-DeGroot dynamics or iterative opinion pooling. As a result of this iterative distributed averaging process, each agent arrives at an asymptotic estimate of the state of the world, with the variance of this estimate determined by the matrix of weights the agents assign to each other. Every agent aims at minimizing the variance of her asymptotic estimate of the state of the world; however, such variance is also influenced by the weights allocated by other agents. To achieve the best possible estimate, the agents must then solve a game-theoretic, multi-objective optimization problem defined by the available sets of influence weights. We characterize both the Pareto frontier and the set of Nash equilibria in the resulting game. Additionally, we examine asynchronous best-response dynamics for the group of agents and prove their convergence to the set of strict Nash equilibria.

High-quality training data is critical to the performance of machine learning models, particularly Large Language Models (LLMs). However, obtaining real, high-quality data can be challenging, especially for smaller organizations and early-stage startups. Synthetic data generators provide a promising solution by replicating the statistical and structural properties of real data while preserving privacy and scalability. This study evaluates the performance of six tabular synthetic data generators from two widely used open-source libraries: SDV (Gaussian Copula, CTGAN, TVAE) and Synthicity (Bayesian Network, CTGAN, TVAE). Using a real-world dataset from the UCI Machine Learning Repository, comprising energy consumption and environmental variables from Belgium, we simulate a low-data regime by training models on only 1,000 rows. Each generator is then tasked with producing synthetic datasets under two conditions: a 1:1 (1,000 rows) and a 1:10 (10,000 rows) input-output ratio. Evaluation is conducted using two criteria: statistical similarity, measured via classical statistics and distributional metrics; and predictive utility, assessed using a "Train on Synthetic, Test on Real" approach with four regression models. While statistical similarity remained consistent across models in both scenarios, predictive utility declined notably in the 1:10 case. The Bayesian Network from Synthicity achieved the highest fidelity in both scenarios, while TVAE from SDV performed best in predictive tasks under the 1:10 setting. Although no significant performance gap was found between the two libraries, SDV stands out for its superior documentation and ease of use, making it more accessible for practitioners.

Large language models (LLMs) have shown significant potential to change how we write, communicate, and create, leading to rapid adoption across society. This dissertation examines how individuals and institutions are adapting to and engaging with this emerging technology through three research directions. First, I demonstrate how the institutional adoption of AI detectors introduces systematic biases, particularly disadvantaging writers of non-dominant language varieties, highlighting critical equity concerns in AI governance. Second, I present novel population-level algorithmic approaches that measure the increasing adoption of LLMs across writing domains, revealing consistent patterns of AI-assisted content in academic peer reviews, scientific publications, consumer complaints, corporate communications, job postings, and international organization press releases. Finally, I investigate LLMs' capability to provide feedback on research manuscripts through a large-scale empirical analysis, offering insights into their potential to support researchers who face barriers in accessing timely manuscript feedback, particularly early-career researchers and those from under-resourced settings.

Semiparametric Bayesian networks (SPBNs) integrate parametric and non-parametric probabilistic models, offering flexibility in learning complex data distributions from samples. In particular, kernel density estimators (KDEs) are employed for the non-parametric component. Under the assumption of data normality, the normal rule is used to learn the bandwidth matrix for the KDEs in SPBNs. This matrix is the key hyperparameter that controls the trade-off between bias and variance. However, real-world data often deviates from normality, potentially leading to suboptimal density estimation and reduced predictive performance. This paper first establishes the theoretical framework for the application of state-of-the-art bandwidth selectors and subsequently evaluates their impact on SPBN performance. We explore the approaches of cross-validation and plug-in selectors, assessing their effectiveness in enhancing the learning capability and applicability of SPBNs. To support this investigation, we have extended the open-source package PyBNesian for SPBNs with the additional bandwidth selection techniques and conducted extensive experimental analyses. Our results demonstrate that the proposed bandwidth selectors leverage increasing information more effectively than the normal rule, which, despite its robustness, stagnates with more data. In particular, unbiased cross-validation generally outperforms the normal rule, highlighting its advantage in high sample size scenarios.

Modern industrial systems are often subject to multiple failure modes, and their conditions are monitored by multiple sensors, generating multiple time-series signals. Additionally, time-to-failure data are commonly available. Accurately predicting a system's remaining useful life (RUL) requires effectively leveraging multi-sensor time-series data alongside multi-mode failure event data. In most existing models, failure modes and RUL prediction are performed independently, ignoring the inherent relationship between these two tasks. Some models integrate multiple failure modes and event prediction using black-box machine learning approaches, which lack statistical rigor and cannot characterize the inherent uncertainty in the model and data. This paper introduces a unified approach to jointly model the multi-sensor time-series data and failure time concerning multiple failure modes. This proposed model integrate a Cox proportional hazards model, a Convolved Multi-output Gaussian Process, and multinomial failure mode distributions in a hierarchical Bayesian framework with corresponding priors, enabling accurate prediction with robust uncertainty quantification. Posterior distributions are effectively obtained by Variational Bayes, and prediction is performed with Monte Carlo sampling. The advantages of the proposed model is validated through extensive numerical and case studies with jet-engine dataset.

Synchronization errors, such as insertions and deletions, present a fundamental challenge in DNA-based data storage systems, arising from both synthesis and sequencing noise. These channels are often modeled as insertion-deletion-substitution (IDS) channels, for which designing maximum-likelihood decoders is computationally expensive. In this work, we propose a data-driven approach based on neural polar decoders (NPDs) to design low-complexity decoders for channels with synchronization errors. The proposed architecture enables decoding over IDS channels with reduced complexity $O(AN log N )$, where $A$ is a tunable parameter independent of the channel. NPDs require only sample access to the channel and can be trained without an explicit channel model. Additionally, NPDs provide mutual information (MI) estimates that can be used to optimize input distributions and code design. We demonstrate the effectiveness of NPDs on both synthetic deletion and IDS channels. For deletion channels, we show that NPDs achieve near-optimal decoding performance and accurate MI estimation, with significantly lower complexity than trellis-based decoders. We also provide numerical estimates of the channel capacity for the deletion channel. We extend our evaluation to realistic DNA storage settings, including channels with multiple noisy reads and real-world Nanopore sequencing data. Our results show that NPDs match or surpass the performance of existing methods while using significantly fewer parameters than the state-of-the-art. These findings highlight the promise of NPDs for robust and efficient decoding in DNA data storage systems.

Causal discovery from observational data typically assumes full access to data and availability of domain experts. In practice, data often arrive in batches, and expert knowledge is scarce. Language Models (LMs) offer a surrogate but come with their own issues-hallucinations, inconsistencies, and bias. We present BLANCE (Bayesian LM-Augmented Causal Estimation)-a hybrid Bayesian framework that bridges these gaps by adaptively integrating sequential batch data with LM-derived noisy, expert knowledge while accounting for both data-induced and LM-induced biases. Our proposed representation shift from Directed Acyclic Graph (DAG) to Partial Ancestral Graph (PAG) accommodates ambiguities within a coherent Bayesian framework, allowing grounding the global LM knowledge in local observational data. To guide LM interaction, we use a sequential optimization scheme that adaptively queries the most informative edges. Across varied datasets, BLANCE outperforms prior work in structural accuracy and extends to Bayesian parameter estimation, showing robustness to LM noise.

The crisis of epistemic overload in modern scientific inquiry has exposed a critical deficiency in how truth claims are assessed, validated, and integrated across time and domain. The exponential growth in peer-reviewed publications, accompanied by inconsistent replication rates, entrenched citation biases, and the sociological entanglements of scientific authorship, has rendered traditional mechanisms of epistemic filtering increasingly obsolete. Simultaneously, artificial intelligence--while having demonstrated capacity in data correlation and language generation--remains fundamentally ill-equipped to perform rigorous epistemic reasoning. This gap is not merely technical but conceptual: current AI systems lack any principled framework for evaluating the truth-promoting value of claims, discerning authoritative sources, or understanding belief as a structured probabilistic relation between agents, claims, and contexts. The present work introduces a formal architecture--Bayesian Epistemology with Weighted Authority (BEW A)--which systematically encodes the logic of belief formation, update, and decay, guided by the core axioms of Bayesian rationality, tempered by structural mechanisms for authority weighting, replication scoring, and temporal reassessment.

We propose co-creative learning as a novel paradigm where humans and AI, i.e., biological and artificial agents, mutually integrate their partial perceptual information and knowledge to construct shared external representations, a process we interpret as symbol emergence. Unlike traditional AI teaching based on unilateral knowledge transfer, this addresses the challenge of integrating information from inherently different modalities. We empirically test this framework using a human-AI interaction model based on the Metropolis-Hastings naming game (MHNG), a decentralized Bayesian inference mechanism. In an online experiment, 69 participants played a joint attention naming game (JA-NG) with one of three computer agent types (MH-based, always-accept, or always-reject) under partial observability. Results show that human-AI pairs with an MH-based agent significantly improved categorization accuracy through interaction and achieved stronger convergence toward a shared sign system. Furthermore, human acceptance behavior aligned closely with the MH-derived acceptance probability. These findings provide the first empirical evidence for co-creative learning emerging in human-AI dyads via MHNG-based interaction. This suggests a promising path toward symbiotic AI systems that learn with humans, rather than from them, by dynamically aligning perceptual experiences, opening a new venue for symbiotic AI alignment.

Ferry quays experience rapid deterioration due to their exposure to harsh maritime environments and ferry impacts. Vibration-based structural health monitoring offers a valuable approach to assessing structural integrity and understanding the structural implications of these impacts. However, practical limitations often restrict sensor placement at critical locations. Consequently, virtual sensing techniques become essential for establishing a Digital Twin and estimating the structural response. This study investigates the application of the Gaussian Process Latent Force Model (GPLFM) for virtual sensing on the Magerholm ferry quay, combining in-operation experimental data collected during a ferry impact with a detailed physics-based model. The proposed Physics-Encoded Machine Learning model integrates a reduced-order structural model with a data-driven GPLFM representing the unknown impact forces via their modal contributions. Significant challenges are addressed for the development of the Digital Twin of the ferry quay, including unknown impact characteristics (location, direction, intensity), time-varying boundary conditions, and sparse sensor configurations. Results show that the GPLFM provides accurate acceleration response estimates at most locations, even under simplifying modeling assumptions such as linear time-invariant behavior during the impact phase. Lower accuracy was observed at locations in the impact zone. A numerical study was conducted to explore an optimal real-world sensor placement strategy using a Backward Sequential Sensor Placement approach. Sensitivity analyses were conducted to examine the influence of sensor types, sampling frequencies, and incorrectly assumed damping ratios. The results suggest that the GP latent forces can help accommodate modeling and measurement uncertainties, maintaining acceptable estimation accuracy across scenarios.