Specific Emitter Identification (SEI) distinguishes individual emitters by extracting subtle features from intercepted radio frequency signals. This process relies on the design and extraction of specific features. Current methods for selecting and characterizing radio frequency fingerprints vary by individual, and the extraction process is closely coupled with environmental conditions. As a result, the generality of such identification algorithms is often limited, particularly when the application environment does not match the premise of feature design, leading to rapid degradation or even failure of individual identification performance. This paper proposes a deep clustering model based on polarization feature learning for identifying individual communication emitters. The approach involves constructing a guided network to extract datasets of polarization features from communication signals and utilizing a contrastive representation learning network to extract dual-polarization features from I/Q data samples. Subsequently, a Bayesian nonparametric (BNP) class mixture model algorithm, capable of inferring an unknown number of clusters, is employed to build a multi-level clustering network for clustering analysis of the extracted features. Under 5 dB conditions, the method described in this paper achieves an average recognition accuracy of 87.5%.

Cancer survivors often experience multiple cooccurring symptoms such as insomnia, pain, fatigue, and anxiety; yet conventional analyses in symptom science typically analyze symptoms one at a time and thus overlook putative clusters of shared symptom experiences. We applied a novel machine learning approach to supporting tailored symptom management to cooccurring symptoms. Bayesian nonparametric (BNP) clustering was applied to discover unique subgroups of symptom profiles in cancer survivors diagnosed with insomnia (N = 160) and with cooccurring pain, fatigue, and anxiety, using secondary symptom data from a clinical trial (clinicaltrials.gov: NCT02356575) comparing cognitive-behavioral therapy for insomnia (CBT-I) and acupuncture. BNP identified survivor subgroups by recognizing shared features in symptoms that contributed to heterogeneous treatment responses at 8 weeks. Simulations evaluated sensitivity to model assumptions. BNP identified three patient subgroups: (1) "insomnia-predominant" (N = 84) with high severity insomnia alone; (2) "insomnia & pain" (n = 21) with high severity of both insomnia and pain; and (3) "high symptom burden" (n = 54) with high severity across all symptoms. CBT-I produced greater insomnia reduction among "insomnia-predominant" patients (posterior mean=-2.45, 95% Bayesian Highest Density Interval: -4.38, -0.35) and among "insomnia & pain" patients (-2.66, 80% HDI: -4.50, -0.50). However, acupuncture produced greater pain reduction among "insomnia & pain" patients (-1.47, 95% HDI: -2.79, -0.18). CBT-I and acupuncture were equally effective for all symptoms among the "high symptom burden" patients. Simulations showed that our main BNP settings accurately identified these subgroups. Unsupervised BNP learning supports interventions tailored to patients' symptom burden and their main concerns. If further validated, BNP learning provides a roadmap for precision symptom management for cancer survivors, and broadly applicable in behavioral medicine data analysis.

The automated collection of streaming observational data has become standard and defies most traditional analytic techniques. It is not just that models are hard to identify, there may not be any model that can be safely and usefully assumed. Indeed, frequently it is only predictions that can be made and assessed. Problems for this kind of data are often called M-Open and have motivated new statistical approaches and philosophies. This paper will review some of the most successful recent predictive methods for the M-Open problem class. Techniques include predictors from Bayesian nonparametrics such as Gaussian process priors, predictors using expert advice such as the Shtarkov solution, hash function based predictors such as the Count-Min sketch, conformal prediction, and neural nets including Long Short-Term Memory networks.

Predicting future insurance claims using observed covariates is essential for actuaries in setting appropriate insurance premiums. For this purpose, actuaries commonly employ parametric regression models, which assume the same functional form tying the response to the covariates across all data points. However, these models may lack the flexibility required to accurately capture, at the individual level, the relationship between covariates and claims frequency and severity. This limitation is particularly relevant as claims data are often multimodal, highly skewed, and heavy-tailed. In this paper, we explore the use of Bayesian nonparametric (BNP) regression models to predict claims frequency and severity based on covariates. Specifically, we model claims frequency as a mixture of Poisson regression and the logarithm of claims severity as a mixture of normal regression. We then employ Dirichlet process (DP) and Pitman-Yor process (PY) as priors for the mixing distribution over the regression parameters. Unlike parametric regression, such models allow each data point to have its own individual parameters, thereby making them highly flexible and resulting in improved prediction accuracy. We describe model fitting using Markov chain Monte Carlo (MCMC) methods and illustrate their applicability using two independent real-world insurance datasets. The proposed BNP models reduced the mean squared error for the French and Belgian claims frequency data by approximately 52% and 33%, respectively (relative to standard Poisson regression), and for the corresponding claims severity data by nearly 45% and 79%, respectively (relative to standard multiple linear regression).

ABSTRACT To address the challenges of ‘high‐density interference’ and ‘multi‐mode parameter agility’ in Radar Emitter Identification (REI) under complex electromagnetic environments, as well as the limitations of existing models‐pulse sequence models have weak anti‐noise capability, whereas statistical feature models are prone to multi‐mode parameter confusion‐this paper proposes an REI method based on Typical Parameter Sequences (TPS). First, a three‐level ‘operational mode‐beam dwell‐pulse group’ signal model is constructed to clarify the hierarchy of key radar features and lay a foundation for both the rationality of TPS and sliding windows design in TPS extraction. A Pulse Repetition Interval (PRI) probability model under pulse interference and loss is also established, providing a theoretical basis for noise suppression. Second, Hierarchical Bayesian Nonparametrics (HBNP) clustering and hierarchical denoising extract local typical parameters, which are concatenated into global TPS (retains temporal information, anti‐noise, data compression) via sliding windows. Finally, Long Short‐Term Memory (LSTM) realises emitter identification. Simulation experiments show that: In strong noise environments, the proposed model's accuracy is significantly higher than that of pulse sequence models after accumulating a limited number of beam dwells; in multi‐mode switching scenarios, its accuracy is much higher than that of statistical feature models, helping alleviate multi‐mode parameter confusion.

Left-censored observations due to limits of detection and/or quantification are common in clinical and epidemiologic research when continuous predictors are assessed from human specimens. In these settings, values below a certain threshold are not detectable in laboratory analysis and are reported as missing in the dataset. Classical imputation approaches have mostly relied on imputing the same number for all non-detected samples, thus compromising the continuous nature of the censored variables and affecting their variability and potential inclusion in regression modeling. Continuous imputations have been presented, but generally focusing on a single variable at the time. It is common, moreover, for the same human specimen to be used for the quantification of several biomarkers or exposures simultaneously, thus resulting in a complex set of multivariate and possibly correlated left-censored observations. To the best of our knowledge, there is no established framework that flexibly accounts for the real-world complexity of these data. We propose a Bayesian multiple imputation (MI) approach that relies on the introduction of multivariate latent variables to handle multivariate left-censored data. We present a general framework, accommodating both a parametric approach, assuming multivariate normality of the data, and a nonparametric approach, modeling observations by means of a location Dirichlet process mixture of multivariate normal kernels. Both approaches are implemented through a Gibbs sampling scheme. The performances of our approach are investigated with a simulation study based on environmental exposures, and illustrated by analyzing a real dataset on cardiovascular biomarkers.

Let ( X , F , μ ) (\mathcal {X},\mathcal {F},\mu ) and ( Y , G , ν ) (\mathcal {Y},\mathcal {G},\nu ) be probability spaces and ( Z n ) (Z_n) be a sequence of random variables with values in ( X × Y , F ⊗ G ) (\mathcal {X}\times \mathcal {Y},\,\mathcal {F}\otimes \mathcal {G}) . Let Γ ( μ , ν ) \Gamma (\mu ,\nu ) be the collection of all probability measures p p on F ⊗ G \mathcal {F}\otimes \mathcal {G} such that p ( A × Y ) = μ ( A ) and p ( X × B ) = ν ( B ) for all A ∈ F and B ∈ G . \begin{equation*} p\bigl (A\times \mathcal {Y}\bigr )=\mu (A)\quad \text {and}\quad p\bigl (\mathcal {X}\times B\bigr )=\nu (B)\quad \text {for all }A\in \mathcal {F}\text { and }B\in \mathcal {G}. \end{equation*} In this paper, we build some probability measures Π \Pi on Γ ( μ , ν ) \Gamma (\mu ,\nu ) . In addition, for each such Π \Pi , we assume that ( Z n ) (Z_n) is exchangeable with de Finetti’s measure Π \Pi and we evaluate the conditional distribution Π ( ⋅ ∣ Z 1 , … , Z n ) \Pi (\,\cdot \mid Z_1,\ldots ,Z_n) . In Bayesian nonparametrics, if ( Z 1 , … , Z n ) (Z_1,\ldots ,Z_n) are the available data, Π \Pi and Π ( ⋅ ∣ Z 1 , … , Z n ) \Pi (\,\cdot \mid Z_1,\ldots ,Z_n) can be regarded as the prior and the posterior, respectively. To support this interpretation, it suffices to think of a problem where the unknown probability distribution of some bivariate phenomenon is constrained to have marginals μ \mu and ν \nu . Finally, analogous results are obtained for the set Γ ( μ ) \Gamma (\mu ) of those probability measures on F ⊗ G \mathcal {F}\otimes \mathcal {G} with marginal μ \mu on F \mathcal {F} (but arbitrary marginal on G \mathcal {G} ). That is, we introduce some priors on Γ ( μ ) \Gamma (\mu ) and we evaluate the corresponding posteriors.

In educational research, comparison of the performances of students in the courses/subjects they offered may be done in order to compare the methods in which they were taught, understand the influence of knowledge of one course on another or to compare the cognitive knowledge of students in different disciplines. The purpose is often to understand how best the performances of the students can be improved upon. In this study, using a sample size of two hundred (200) students in each faculty, two statistical methods, the Mann Whitney U test and the Bayesian non-parametric (BNP) Mann Whitney U test were employed to investigate if there exist a significant statistical difference in performances (recorded as grades) of students in two faculties of a university. While the classical test yielded no statistically significant difference (p = 0.229), the Bayesian analysis provided moderate evidence favoring the null hypothesis with a Bayes’ factor (BF₁₀ = 0.284), though posterior estimates suggested a slight performance edge for Computing students. These findings underscore the ability of the Bayesian method to yield more informative conclusions and hence its use in educational research, especially when classical results are inconclusive.

The increasingly flexible decision-making process of modern cognitive radar (CR) systems has placed considerable challenges toward electronic reconnaissance systems or radar warning receivers, which must help to determine the appropriate countermeasure methods for these radar systems in modern complex electromagnetic environments. It is necessary to accurately predict CR's internal action policy according to the interaction observations between CR and receivers under non-cooperative scenarios. Such that useful adversarial information can be extracted by reconnaissance systems for afterward processing and analysis. From the perspective of the reconnaissance side, this work presents a unified CR action policy prediction framework that combines feature extraction and reward estimation processes without much prior knowledge about CR's decision-making process in terms of CR reward structure and components. Focusing on the CR performing continuous control tasks, a method based on Bayesian nonparametric (BNP) theory is designed for automatic feature extraction from observed demonstration trajectories that are collected in various CR tasks. The proposed BNP method can significantly improve the multi-dimensional information representation ability of features. Further, a deep inverse reinforcement learning (DIRL) method is designed to estimate CR's internal reward functions without the knowledge of function structures. The performance of the proposed method is evaluated and verified under simulated CR target tracking scenarios. Experimental results showed the superiority and effectiveness of the proposed method.

Förster resonance energy transfer (FRET) is a widely used tool to probe nanometer scale dynamics, projecting rich 3D biomolecular motion onto noisy 1D traces. However, interpretation of FRET traces remains challenging due to degeneracy—distinct structural states map to similar FRET efficiencies— and often suffers from under- and/or over-fitting due to the need to predefine the number of FRET states and noise characteristics. Here we provide a new software, Bayesian nonparametric FRET (BNP-FRET) for binned data obtained from integrative detectors, that eliminates user-dependent parameters and accurately incorporates all known noise sources, enabling the identification of distinct configurations from 1D traces in a plug-n-play manner. Using simulated and experimental data, we demonstrate that BNP-FRET eliminates logistical barrier of predetermining states for each FRET trace and permits high-throughput, simultaneous analysis of a large number of kinetically heterogeneous traces. Furthermore, working in the Bayesian paradigm, BNP-FRET naturally provides uncertainty estimates for all model parameters including the number of states, kinetic rates, and FRET efficiencies.

Rating procedure is crucial in many applied fields (e.g., educational, clinical, emergency). In these contexts, a rater (e.g., teacher, doctor) scores a subject (e.g., student, doctor) on a rating scale. Given raters’ variability, several statistical methods have been proposed for assessing and improving the quality of ratings. The analysis and the estimate of the Intraclass Correlation Coefficient (ICC) are major concerns in such cases. As evidenced by the literature, ICC might differ across different subgroups of raters and might be affected by contextual factors and subject heterogeneity. Model estimation in the presence of heterogeneity has been one of the recent challenges in this research line. Consequently, several methods have been proposed to address this issue under a parametric multilevel modelling framework, in which strong distributional assumptions are made. We propose a more flexible model under the Bayesian nonparametric (BNP) framework, in which most of those assumptions are relaxed. By eliciting hierarchical discrete nonparametric priors, the model accommodates clusters among raters and subjects, naturally accounts for heterogeneity, and improves estimates’ accuracy. We propose a general BNP heteroscedastic framework to analyze continuous and coarse rating data and possible latent differences among subjects and raters. The estimated densities are used to make inferences about the rating process and the quality of the ratings. By exploiting a stick-breaking representation of the discrete nonparametric priors, a general class of ICC indices might be derived for these models. Our method allows us to independently identify latent similarities between subjects and raters and can be applied in precise education to improve personalized teaching programs or interventions. Theoretical results about the ICC are provided together with computational strategies. Simulations and a real-world application are presented, and possible future directions are discussed.

We provide a novel statistical perspective on a classical problem at the intersection of computer science and information theory: recovering the empirical frequency of a symbol in a large discrete dataset using only a compressed representation, or sketch, obtained via random hashing. Departing from traditional algorithmic approaches, recent works have proposed Bayesian nonparametric (BNP) methods that can provide more informative frequency estimates by leveraging modeling assumptions about the distribution of the sketched data. In this article, we propose an alternative smoothed-Bayesian approach, inspired by existing BNP methods but designed to overcome their computational limitations when dealing with large-scale data from realistic distributions, including those with power-law tail behaviors. For sketches obtained with a single hash function, our approach is supported by precise theoretical guarantees, including unbiasedness and optimality under a Bayesian framework within an intuitive class of linear estimators. For sketches with multiple hash functions, we introduce an approach based on multi-view learning to construct computationally efficient frequency estimators. We validate our method on synthetic and real data, comparing its performance to that of existing alternatives. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Although exchangeable processes from Bayesian nonparametrics have been used as a generating mechanism for random partition models, we deviate from this paradigm to explicitly incorporate clustering information in the formulation of our random partition model. Our shrinkage partition distribution takes any partition distribution and shrinks its probability mass toward a specific anchor partition. We show how this provides a framework to model hierarchically-dependent and temporally-dependent random partitions. The shrinkage parameter controls the degree of dependence, accommodating at its extremes both independence and complete equality. Since prior knowledge of items may vary, our formulation allows the degree of shrinkage toward the anchor to be item-specific. Our random partition model has a tractable normalizing constant which allows for standard Markov chain Monte Carlo algorithms for posterior sampling. We prove intuitive theoretical properties for our distribution and compare it to related partition distributions. We show that our model provides better out-of-sample fit in a real data application. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Abstract The study of almost surely discrete random probability measures is an active line of research in Bayesian non-parametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant interest in the context of Bayesian mixture models. This allows the definition of priors that encourage well-separated and interpretable clusters. In this work, we provide a unified framework for the construction and the Bayesian analysis of random probability measures with interacting atoms, encompassing both repulsive and attractive behaviours. Specifically, we derive closed-form expressions for the posterior distribution, the marginal and predictive distributions, previously unavailable except for the case of measures with i.i.d. atoms. We show how these quantities are fundamental for both prior elicitation and developing new posterior simulation algorithms for hierarchical mixture models. Our results are obtained without any assumption on the finite point process governing the atoms of the random measure. Their proofs rely on analytical tools borrowed from Palm calculus theory, which might be of independent interest. We specialize our treatment to the classes of Poisson, Gibbs, and determinantal point processes, as well as in the case of shot-noise Cox processes. Finally, we illustrate different modelling strategies on simulated and real datasets.

Abstract: Small sample sizes and high-dimensional data present fundamental obstacles for statistical modeling, inference, and decision-making across a wide range of scientific and engineering disciplines. Traditional statistical techniques often break down under these regimes, yielding unstable or biased estimates. Adaptive Bayesian methods, with their intrinsic ability to incorporate prior information, update beliefs sequentially, and flexibly model complex structures, offer a powerful alternative. This paper synthesizes insights from cutting-edge studies on scalable inference, sequential Bayesian experimental design, and robust prior modeling for small-sample and high-dimensional settings. We provide critical evaluations of existing techniques, propose new adaptive frameworks for improved inference stability, and explore strategies to enhance both computational scalability and statistical robustness. Our findings underscore the pivotal role of adaptive Bayesian methods in navigating the challenges of complex, modern data environments. Keywords: Adaptive Bayesian Inference, Small Sample Challenges, High-Dimensional Data, Scalable Bayesian Methods, Sequential Design, Robust Priors, Hybrid Sampling, Bayesian Nonparametrics, Posterior Approximation, Experimental Design under Uncertainty

Molecular Dynamics (MD) simulations are a versatile tool to investigate the interactions of proteins within their environments, in particular, of membrane proteins with the surrounding lipids. However, quantitative analysis of lipid-protein binding kinetics has remained challenging due to considerable noise and low frequency of long binding events, even in hundreds of microseconds of simulation data. Here, we apply Bayesian nonparametrics to compute residue-resolved residence time distributions from MD trajectories. Such an analysis characterizes binding processes at different time scales (quantified by their kinetic off-rate) and assigns to each trajectory frame a probability of belonging to a specific process. In this way, we classify trajectory frames in an unsupervised manner and obtain, for example, different binding poses or molecular densities based on the time scale of the process. We demonstrate our approach by characterizing interactions of cholesterol with six different G-protein-coupled receptors (A2AAR, β2AR, CB1R, CB2R, CCK1R, and CCK2R) simulated with coarse-grained MD simulations with the MARTINI model. The nonparametric Bayesian analysis allows us to connect the coarse binding time series data to the underlying molecular picture and thus not only infers accurate binding kinetics with error distributions from MD simulations but also describes molecular events responsible for the broad range of kinetic rates.

Multivariate Item Response Theory (MIRT) is sought-after widely by applied researchers looking for interpretable (sparse) explanations underlying response patterns in questionnaire data. There is, however, an unmet demand for such sparsity discovery tools in practice. Our article develops a Bayesian platform for binary and ordinal item MIRT which requires minimal tuning and scales well on large datasets due to its parallelizable features. Bayesian methodology for MIRT models has traditionally relied on MCMC simulation, which cannot only be slow in practice, but also often renders exact sparsity recovery impossible without additional thresholding. In this work, we develop a scalable Bayesian EM algorithm to estimate sparse factor loadings from mixed continuous, binary, and ordinal item responses. We address the seemingly insurmountable problem of unknown latent factor dimensionality with tools from Bayesian nonparametrics which enable estimating the number of factors. Rotations to sparsity through parameter expansion further enhance convergence and interpretability without identifiability constraints. In our simulation study, we show that our method reliably recovers both the factor dimensionality as well as the latent structure on high-dimensional synthetic data even for small samples. We demonstrate the practical usefulness of our approach on three datasets: an educational assessment dataset, a quality-of-life measurement dataset, and a bio-behavioral dataset. All demonstrations show that our tool yields interpretable estimates, facilitating interesting discoveries that might otherwise go unnoticed under a pure confirmatory factor analysis setting. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Molecular Dynamics (MD) simulations are a versatile tool to investigate the interactions of proteins within their environments, in particular of membrane proteins with the surrounding lipids. However, quantitative analysis of lipid-protein binding kinetics has remained challenging due to considerable noise and low frequency of long binding events, even in hundreds of microseconds of simulation data. Here we apply Bayesian nonparametrics to compute residue-resolved residence time distributions from MD trajectories. Such an analysis characterizes binding processes at different timescales (quantified by their kinetic off-rate) and assigns to each trajectory frame a probability of belonging to a specific process. In this way, we classify trajectory frames in an unsupervised manner and obtain, for example, different binding poses or molecular densities based on the timescale of the process. We demonstrate our approach by characterizing interactions of cholesterol with six different G-protein coupled receptors ( , , , , , ) simulated with coarse-grained MD simulations with the MARTINI model. The nonparametric Bayesian analysis allows us to connect the coarse binding time series data to the underlying molecular picture and, thus, not only infers accurate binding kinetics with error distributions from MD simulations but also describes molecular events responsible for the broad range of kinetic rates.

ABSTRACT Satellite and aerial imagery is collected at a dizzying rate, but how to best distill this information is often unknown. Classifying images is the most popular approach but requires specifying groups a priori. This article introduces a method for fully unsupervised whole-image clustering, specifically designed for massive datasets of remote-sensing scenes with no labels. Our approach is tailored to the unique challenges of this domain and offers several key advantages: (1) We fine-tune a pretrained deep neural network (DINOv2) on a labelled source satellite imagery dataset, enabling broad applicability across diverse remote-sensing imagery with varying ground sample distances (GSDs), resolutions and image sizes. This fine-tuned model can effectively extract meaningful feature vectors from unseen remote-sensing datasets with minimal further adaptation, making it both scalable and robust for large-scale remote-sensing tasks. (2) We reduce the dimensionality of these deep features through manifold projection, mapping them into a low-dimensional Euclidean space to streamline downstream processing and enhance computational efficiency. (3) These low-dimensional features are then clustered using a computationally scalable Bayesian nonparametric (BNP) technique, which automatically infers both the number of clusters and their membership. Our extensive evaluation on the challenging SATellite ImageNet (SATIN) Land Use task, a benchmark that includes 10 overhead imagery datasets, highlights the robustness of our method in the remote-sensing domain, outperforming state-of-the-art zero-shot classification techniques on multiple datasets. Additionally, we provide a proof-of-concept demonstration on a leading computer vision benchmark, which showcases the competitiveness of our unsupervised approach against even supervised techniques. Our approach is highly relevant for future geospatial analysis since it can be further fine-tuned to specific downstream tasks, including those that incorporate data modalities beyond the visible spectrum, without the need for significant modifications.

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either restrictive modelling assumptions or involve intricate algorithms for posterior inference. We propose a flexible and computationally convenient approach for density regression based on a single-weights dependent Dirichlet process mixture of normal distributions model for univariate continuous responses. We assume an additive structure for the mean of each mixture component and incorporate the effects of continuous covariates through smooth functions. The key components of our modelling approach are penalised B-splines and their bivariate tensor product extension. Our method also seamlessly accommodates categorical covariates, linear effects of continuous covariates, varying coefficient terms, and random effects, which is why we refer our model as a Dirichlet process mixture of normal structured additive regression models. A notable feature of our method is the simplicity of posterior simulation using Gibbs sampling, as closed-form full conditional distributions for all model parameters are available. Results from a simulation study demonstrate that our approach successfully recovers the true conditional densities and other regression functionals in challenging scenarios. Applications to three real datasets further underpin the broad applicability of our method. An R package, DDPstar, implementing the proposed method is provided.