Weak Consistency Research Articles

Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model

Abstract We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a $\gamma$ fraction of the vertices classified correctly, where $\gamma \in (0.5,1)$ depends on the signal-to-noise ratio (SNR) of the model. When the SNR grows slowly as the number of vertices goes to infinity, our algorithm achieves weak consistency, which improves the previous results in Ghoshdastidar and Dukkipati ((2017) Ann. Stat.45(1) 289–315.) for non-uniform HSBMs. Our spectral algorithm consists of three major steps: (1) Hyperedge selection: select hyperedges of certain sizes to provide the maximal signal-to-noise ratio for the induced sub-hypergraph; (2) Spectral partition: construct a regularised adjacency matrix and obtain an approximate partition based on singular vectors; (3) Correction and merging: incorporate the hyperedge information from adjacency tensors to upgrade the error rate guarantee. The theoretical analysis of our algorithm relies on the concentration and regularisation of the adjacency matrix for sparse non-uniform random hypergraphs, which can be of independent interest.

Asymptotic properties for generalized edge frequency polygon of nonparametric density estimation

This article pays attention to the generalized edge frequency polygon. By taking weighted averages of the heights in the neighbouring 2 k ( k ≥ 1 ) bins, we can reduce the asymptotic mean integrated squared error than that of the frequency polygon estimator. As a density estimator based on histogram technique, the generalized edge frequency polygon has the advantage of computational simplicity and has been widely used in many fields. The purpose of this article is to investigate the weak consistency, the uniformly weak consistency and the rate of the uniformly weak consistency for generalized edge frequency polygon of density function under α-mixing samples, which improve and extend those of frequency polygon in the literature. In particular, the simulation study and real data analysis based on finite samples are performed to verify the validity of the theoretical results.

Dual-consistency guidance semi-supervised medical image segmentation with low-level detail feature augmentation

In deep-learning-based medical image segmentation tasks, semi-supervised learning can greatly reduce the dependence of the model on labeled data. However, existing semi-supervised medical image segmentation methods face the challenges of object boundary ambiguity and a small amount of available data, which limit the application of segmentation models in clinical practice. To solve these problems, we propose a novel semi-supervised medical image segmentation network based on dual-consistency guidance, which can extract reliable semantic information from unlabeled data over a large spatial and dimensional range in a simple and effective manner. This serves to improve the contribution of unlabeled data to the model accuracy. Specifically, we construct a split weak and strong consistency constraint strategy to capture data-level and feature-level consistencies from unlabeled data to improve the learning efficiency of the model. Furthermore, we design a simple multi-scale low-level detail feature enhancement module to improve the extraction of low-level detail contextual information, which is crucial to accurately locate object contours and avoid omitting small objects in semi-supervised medical image dense prediction tasks. Quantitative and qualitative evaluations on six challenging datasets demonstrate that our model outperforms other semi-supervised segmentation models in terms of segmentation accuracy and presents advantages in terms of generalizability. Code is available at https://github.com/0Jmyy0/SSMIS-DC.

Maternal modifiable factors and risk of congenital heart defects: systematic review and causality assessment

ObjectivePrimary prevention strategies are critical to reduce the global burden of congenital heart defects (CHDs); this requires robust knowledge of causal agents. We aimed to review associations between CHDs and...

Kernel density estimation for a stochastic process with values in a Riemannian manifold

This paper is related to the issue of the density estimation of observations with values in a Riemannian submanifold. In this context, Henry and Rodriguez ((2009), ‘Kernel Density Estimation on Riemannian Manifolds: Asymptotic Results’, Journal of Mathematical Imaging and Vision, 34, 235–239) proposed a kernel density estimator for independent data. We investigate here the behaviour of Pelletier's estimator when the observations are generated from a strictly stationary α-mixing process with values in this submanifold. Our study encompasses both pointwise and uniform analyses of the weak and strong consistency of the estimator. Specifically, we give the rate of convergence in terms of mean square error, probability, and almost sure convergence (a.s.). We also give a central-limit theorem and illustrate our proposal through some simulations and a real data application.

Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier–Stokes equations as a paradigm

Abstract This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein contraction rates for the approximating dynamics bears on long time accuracy estimates. In particular, our approach yields weak consistency bounds on ${\mathbb{R}}^{+}$ while providing a means to sidestepping a commonly occurring situation where certain higher order moment bounds are unavailable for the approximating dynamics. Additionally, to facilitate the analytical core of our approach, we develop a refinement of certain ‘weak Harris theorems’. This extension expands the scope of applicability of such Wasserstein contraction estimates to a variety of interesting stochastic partial differential equation examples involving weaker dissipation or stronger nonlinearity than would be covered by the existing literature. As a guiding and paradigmatic example, we apply our formalism to the stochastic 2D Navier–Stokes equations and to a semi-implicit in time and spectral Galerkin in space numerical approximation of this system. In the case of a numerical approximation, we establish quantitative estimates on the approximation of invariant measures as well as prove weak consistency on ${\mathbb{R}}^{+}$. To develop these numerical analysis results, we provide a refinement of $L^{2}_{x}$ accuracy bounds in comparison to the existing literature, which are results of independent interest.

Household earthquake readiness: Conceptualization and measurement

Decades of research have been dedicated to understanding and measuring the capacity of households to face and deal with earthquakes. A reflective-measure model equating household earthquake readiness to preparedness has been adopted assuming the presence of a common factor. However, using instruments with unknown psychometric properties is prevalent, instruments with known psychometric properties are unaligned with the construct, and information on the source of items is missing. This study proposes an alternative theoretical framework based on a causal indicator model equating household earthquake readiness to hazard adjustments applied to earthquakes; investigates the presence of a common factor; and, suggests a new measure constructed following the literature guidelines and based on prior research on household earthquake readiness: Earthquake Adjustments Checklist (EAC). Factor Analysis was used to analyze the data from 921 residents in the Azores, a Portuguese archipelago vulnerable to seismic risk. The final version of the EAC contains 13 items derived from the literature that are congruent with Portuguese household earthquake recommendations and with the supporting construct. These items were formulated to be applicable elsewhere. A four-factor solution was obtained differing from the three postulated dimensions of hazard adjustments. The results showed weak correlations, low commonalities and internal consistency pointing to a common factor that is nonexistent or at least insufficient to explain the variability in the adoption of household earthquake adjustments. Moreover, a weak correlation was found between two factors. These findings have implications for the understanding and measuring of household earthquake readiness and practice.

Perception of diagnosis by family caregivers in severe brain injury patients in China

ObjectivesSurrogate decision-making by family caregivers for patients with severe brain injury is influenced by the availability and understanding of relevant information and expectations for future rehabilitation. We aimed to compare the consistency of family caregivers’ perceptions with clinical diagnoses and to inform their expectation of prognosis in the future.MethodsThe Coma Recovery Scale-Revised was used to assess the diagnosis of inpatients with severe brain injury between February 2019 and February 2020. A main family caregiver was included per patient. The family caregiver’s perception of the patient’s consciousness and expectations of future recovery were collected through questionnaires and compared consistently with the clinical diagnosis.ResultsThe final sample included 101 main family caregivers of patients (57 UWS, unresponsive wakefulness syndrome, 37 MCS, minimally conscious state, 7 EMCS, emergence from MCS) with severe brain injury. Only 57 family caregivers correctly assessed the level of consciousness as indicated by the CRS-R, showing weak consistency (Kappa = 0.217, P = 0.002). Family caregivers’ demographic characteristics and CRS-R diagnosis influenced the consistency between perception and clinical diagnosis. Family caregivers who provided hands-on care to patients showed higher levels of consistent perception (AOR = 12.24, 95% CI = 2.06-73.00, P = 0.006). Compared to UWS, the family caregivers of MCS patients were more likely to have a correct perception (OR = 7.68, 95% CI = 1.34–44.06). Family caregivers had positive expectations for patients’ recovery in terms of both communication and returning to normal life.ConclusionNearly half of family caregivers have inadequate understanding of their relative’s level of consciousness, and most of them report overly optimistic expectations that do not align with clinical diagnosis. Providing more medical information to family caregivers to support their surrogate decision-making process is essential.

A fine-grained self-adapting prompt learning approach for few-shot learning with pre-trained language models

Pre-trained language models have demonstrated remarkable performance in few-shot learning through the emergence of “prompt-based learning” methods, where the performance of these tasks highly rely on the quality of prompts. Existing prompt learning methods typically customize a single prompt to each few-shot learning task and all the examples in the task share the universal prompt. However, a fine-grained prompt design can enhance the performance of few-shot learning task by leveraging more diverse information hidden in the set of examples. In light of this motivation, this paper introduce an example-specific prompt learning method to embody fine-grained self-adapting prompts for few-shot learning with pre-trained models. Specifically, we introduce the concept of the “weak consistency assumption”, to trade-off the task-specific consistent and example-specific diversity. Based on this assumption, a novel method called Self-adapting Continuous Prompt Learning (SP-learning) to learn example-specific prompts is proposed. It employs a cross-attention prompt generator that considers the characteristics of input samples and utilizes a diversity calibration technique to adjust the prompt generator accordingly. By personalizing prompts for each example, SP-learning aims to improve few-shot learning performance. We perform a systematic evaluation on 10 public benchmark tasks and our method outperforms 8 of those tasks. Our research sheds light on the importance of personalized prompts and opens up new possibilities for improving few-shot learning tasks.

The Development and Challenges of Digital Government in the Intelligent Era

With the advent of the intelligent era, there is a need to leverage the empowering effects of data and construct a digital government governance system. Currently, driven by a reform mindset, innovative concepts, robust resource integration and implementation capabilities, as well as complementary technological advancements and innovative practices, the digital government exhibits governance characteristics of infrastructure cloudification, full-touchpoint digitization, online business processes, and data-driven operations. Its transformation logic reflects the interactive philosophy of flat communication, collaborative sharing of government data, optimization of precise service delivery, and the effective output of scientific decision-making. Despite its powerful governance effectiveness, digital government governance still faces challenges such as slow response to departmental needs, data silos, poor service collaboration, and weak business consistency. A comprehensive deepening of government digital transformation in the future requires innovative concepts, transitioning from information dissemination to intelligent applications, data innovation transitioning from data silos to data circulation and sharing, service innovation transitioning from function-driven to demand-driven by society, and decision-making innovation transitioning from unilateral decisions to collaborative, participatory, and shared decision-making. This will ultimately enhance the governance effectiveness of digital government.

Artificial intelligence enhances whole-slide interpretation ofPD-L1 CPS in triple-negative breast cancer: Amulti-institutional ring study.

Evaluation of the programmed cell death ligand-1 (PD-L1) combined positive score (CPS) is vital to predict the efficacy of the immunotherapy in triple-negative breast cancer (TNBC), but pathologists show substantial variability in the consistency and accuracy of the interpretation. It is of great importance to establish an objective and effective method which is highly repeatable. We proposed a model in a deep learning-based framework, which at the patch level incorporated cell analysis and tissue region analysis, followed by the whole-slide level fusion of patch results. Three rounds of ring studies (RSs) were conducted. Twenty-one pathologists of different levels from four institutions evaluated the PD-L1 CPS in TNBC specimens as continuous scores by visual assessment and our artificial intelligence (AI)-assisted method. In the visual assessment, the interpretation results of PD-L1 (Dako 22C3) CPS by different levels of pathologists have significant differences and showed weak consistency. Using AI-assisted interpretation, there were no significant differences between all pathologists (P = 0.43), and the intraclass correlation coefficient (ICC) value was increased from 0.618 [95% confidence interval (CI) = 0.524-0.719] to 0.931 (95% CI = 0.902-0.955). The accuracy of interpretation result is further improved to 0.919 (95% CI = 0.886-0.947). Acceptance of AI results by junior pathologists was the highest among all levels, and 80% of the AI results were accepted overall. With the help of the AI-assisted diagnostic method, different levels of pathologists achieved excellent consistency and repeatability in the interpretation of PD-L1 (Dako 22C3) CPS. Our AI-assisted diagnostic approach was proved to strengthen the consistency and repeatability in clinical practice.

Key factors in the future of oral and dental health in Iran using scenario writing approach

BackgroundOral and dental health can significantly impact individuals’ quality of life. The World Health Organization introduces oral health as one of the essential priorities of public health worldwide. Given the lack of studies on the future of oral and dental health in Iran, this study used a futures studies approach to identify the factors in oral and dental health in Iran through scenario writing.MethodsThis study was conducted in three stages including the scenario writing approach, qualitative methods, and exploratory future research. First, potential variables affecting future oral and dental health systems were extracted through interviews. The focus group discussion determined the uncertainty and importance of the variables. Then, the cross-impact balance matrix was imported into the Scenario Wizard software to identify the different states of the scenario generator variables and compatible scenarios were extracted.ResultsSeventy variables were extracted as key variables affecting the future of oral and dental health. Regarding the importance and uncertainty, seventeen variables scored higher and fell into policy and governance, economy and financing, social, service delivery, and technology, serving as five categories of scenario generators. Fifteen scenarios with weak consistency and three with strong consistency were obtained using the Cross-Impact Balance matrix in Scenario Wizard software.ConclusionThe probability of a pessimistic scenario where all five categories of the scenarios were in the worst possible state was higher due to its consistency. The government’s support policies and commitment to oral and dental health were two key factors in the future. Achieving an optimistic and favorable scenario for the future of the country’s oral and dental health system depends on the government and policymakers in the health sector adopting a positive attitude towards the role of oral and dental health services in improving societal health. In this scenario, the five categories of the scenario generators were in the best condition.

Efficient inference of parent-of-origin effect using case-control mother–child genotype data

Parent-of-origin effect plays an important role in mammal development and disorder. Case-control mother–child pair genotype data can be used to detect parent-of-origin effect and is often convenient to collect in practice. Most existing methods for assessing parent-of-origin effect do not incorporate any covariates, which may be required to control for confounding factors. We propose to model the parent-of-origin effect through a logistic regression model, with predictors including maternal and child genotypes, parental origins, and covariates. The parental origins may not be fully inferred from genotypes of a target genetic marker, so we propose to use genotypes of markers tightly linked to the target marker to increase inference efficiency. A robust statistical inference procedure is developed based on a modified profile log-likelihood in a retrospective way. A computationally feasible expectation–maximization algorithm is devised to estimate all unknown parameters involved in the modified profile log-likelihood. This algorithm differs from the conventional expectation–maximization algorithm in the sense that it is based on a modified instead of the original profile log-likelihood function. The convergence of the algorithm is established under some mild regularity conditions. This expectation–maximization algorithm also allows convenient handling of missing child genotypes. Large sample properties, including weak consistency, asymptotic normality, and asymptotic efficiency, are established for the proposed estimator under some mild regularity conditions. Finite sample properties are evaluated through extensive simulation studies and the application to a real dataset.

The weighted sum of powers in mean for estimating a change point in linear processes with random coefficients

The weighted sum of powers in mean for estimating a change point in linear processes with random coefficients

FINITE APPROXIMATION OF NONCOOPERATIVE 2-PERSON GAMES PLAYED IN STAIRCASE-FUNCTION CONTINUOUS SPACES

V. Romanuke Finite approximation of noncooperative 2-person games played in staircase-function continuous spaces Background. There is a known method of approximating continuous noncooperative 2-person games, wherein an approximate solution (an equilibrium situation) is considered acceptable if it changes minimally by changing the sampling step minimally. However, the method cannot be applied straightforwardly to a 2-person game played with staircase-function strategies. Besides, the independence of the player’s sampling step selection should be taken into account. Objective. The objective is to develop a method of finite approximation of 2-person games played in staircase-function continuous spaces by taking into account that the players are likely to independently sample their pure strategy sets. Methods. To achieve the said objective, a 2-person game, in which the players’ strategies are staircase functions of time, is formalized. In such a game, the set of the player’s pure strategies is a continuum of staircase functions of time, and the time is thought of as it is discrete. The conditions of sampling the set of possible values of the player’s pure strategy are stated so that the game becomes defined on a product of staircase-function finite spaces. In general, the sampling step is different at each player and the distribution of the sampled points (function-strategy values) is non-uniform. Results. A method of finite approximation of 2-person games played in staircase-function continuous spaces is presented. The method consists in irregularly sampling the player’s pure strategy value set, finding the best equilibria in “smaller” bimatrix games, each defined on a subinterval where the pure strategy value is constant, and stacking the equilibrium situations if they are consistent. The stack of the “smaller” bimatrix game equilibria is an approximate equilibrium in the initial staircase game. The (weak) consistency of the approximate equilibrium is studied by how much the payoff and equilibrium situation change as the sampling density minimally increases by the three ways of the sampling increment: only the first player’s increment, only the second player’s increment, both the players’ increment. The consistency is decomposed into the payoff, equilibrium strategy support cardinality, equilibrium strategy sampling density, and support probability consistency. It is practically reasonable to consider a relaxed payoff consistency. Conclusions. The suggested method of finite approximation of staircase 2-person games consists in the independent samplings, solving “smaller” bimatrix games in a reasonable time span, and stacking their solutions if they are consistent. The finite approximation is regarded appropriate if at least the respective approximate (stacked) equilibrium is -payoff consistent.

MamlFormer: Priori-experience guiding transformer network via manifold adversarial multi-modal learning for laryngeal histopathological grading

Pathologic grading of laryngeal squamous cell carcinoma (LSCC) plays a crucial role in diagnosis, prognosis, and migration. However, the grading performance and interpretability of the intelligent grading model based on LSCC low magnification images are poor. This is because it lacks the delicate nuclear information and information more relevant to grading contained in the high magnification images labeled by pathologists. Yet, low magnification images have information such as tissue texture and contours. Thus, we proposed an end-to-end transformer network with manifold adversarial multi-modal learning (MamlFormer). It effectively fuses and learns LSCC high and low magnification pathology image modalities. Firstly, we demonstrate the feasibility and sufficient conditions for modal fusion of LSCC high and low magnification images from Hoeffding's inequality and multimodal co-regularization. Secondly, we design a new manifold block. It constructs the manifold subspace by some principles. Those principles are divisibility, recoverability, and local distance closest of the feature matrix before and after the mapping of the LSCC each magnification image modalities. Meanwhile it can well solve the problems of redundant feature matrix information and weak modal semantic consistency after multimodal learning. Thirdly, we utilize the encoder and the adversarial loss function to implement adversarial block. It can adaptively learn the latent metrics of the modal distributions of LSCC high and low magnification images. Therefore, it also enhances the complementarity of LSCC high and low magnification image modalities. Then, numerous experiments show that MamlFormer outperforms other SOTA models in both grading performance and interpretability. Finally, we also performed generalization experiments on highly prevalent cervix squamous cell carcinoma. The MamlFormer over is superior to other SOTA models in terms of grading performance and interpretability. This indicates its excellent generalization performance and clinical practicability.

Data-driven multinomial random forest: a new random forest variant with strong consistency

In this paper, we modify the proof methods of some previously weakly consistent variants of random forest into strongly consistent proof methods, and improve the data utilization of these variants in order to obtain better theoretical properties and experimental performance. In addition, we propose the Data-driven Multinomial Random Forest (DMRF) algorithm, which has the same complexity with BreimanRF (proposed by Breiman) while satisfying strong consistency with probability 1. It has better performance in classification and regression tasks than previous RF variants that only satisfy weak consistency, and in most cases even surpasses BreimanRF in classification tasks. To the best of our knowledge, DMRF is currently a low-complexity and high-performing variation of random forest that achieves strong consistency with probability 1.

Clinician Risk Tolerance and Rates of Admission From the Emergency Department

Much remains unknown about the extent of and factors that influence clinician-level variation in rates of admission from the emergency department (ED). In particular, emergency clinician risk tolerance is a potentially important attribute, but it is not well defined in terms of its association with the decision to admit. To further characterize this variation in rates of admission from the ED and to determine whether clinician risk attitudes are associated with the propensity to admit. In this observational cohort study, data were analyzed from the Massachusetts All Payer Claims Database to identify all ED visits from October 2015 through December 2017 with any form of commercial insurance or Medicaid. ED visits were then linked to treating clinicians and their risk tolerance scores obtained in a separate statewide survey to examine the association between risk tolerance and the decision to admit. Statistical analysis was performed from 2022 to 2023. The ratio between observed and projected admission rates was computed, controlling for hospital, and then plotted against the projected admission rates to find the extent of variation. Pearson correlation coefficients were then used to examine the association between the mean projected rate of admission and the difference between actual and projected rates of admission. The consistency of clinician admission practices across a range of the most common conditions resulting in admission were then assessed to understand whether admission decisions were consistent across different conditions. Finally, an assessment was made as to whether the extent of deviation from the expected admission rates at an individual level was associated with clinician risk tolerance. The study sample included 392 676 ED visits seen by 691 emergency clinicians. Among patients seen for ED visits, 221 077 (56.3%) were female, and 236 783 (60.3%) were 45 years of age or older; 178 890 visits (46.5%) were for patients insured by Medicaid, 96 947 (25.2%) were for those with commercial insurance, 71 171 (18.5%) were Medicare Part B or Medicare Advantage, and the remaining 37 702 (9.8%) were other insurance category. Of the 691 clinicians, 429 (62.6%) were male; mean (SD) age was 46.5 (9.8) years; and 72 (10.4%) were Asian, 13 (1.9%) were Black, 577 (83.5%) were White, and 29 (4.2%) were other race. Admission rates across the clinicians included ranged from 36.3% at the 25th percentile to 48.0% at the 75th percentile (median, 42.1%). Overall, there was substantial variation in admission rates across clinicians; physicians were just as likely to overadmit or underadmit across the range of projected rates of admission (Pearson correlation coefficient, 0.046 [P = .23]). There also was weak consistency in admission rates across the most common clinical conditions, with intraclass correlations ranging from 0.09 (95% CI, 0.02-0.17) for genitourinary/syncope to 0.48 (95% CI, 0.42-0.53) for cardiac/syncope. Greater clinician risk tolerance (as measured by the Risk Tolerance Scale) was associated with a statistically significant tendency to admit less than the projected admission rate (coefficient, -0.09 [P = .04]). The other scales studied revealed no significant associations. In this cohort study of ED visits from Massachusetts, there was statistically significant variation between ED clinicians in admission rates and little consistency in admission tendencies across different conditions. Admission tendencies were minimally associated with clinician innate risk tolerance as assessed by this study's measures; further research relying on a broad range of measures of risk tolerance is needed to better understand the role of clinician attitudes toward risk in explaining practice patterns and to identify additional factors that may be associated with variation at the clinician level.

Construction and evolutionary pattern of the coupling relationship network of regional sustainable development in China

Climate change poses a serious threat to the survival and development of humankind. Accordingly, sustainable socioeconomic transformation has become a major global concern. This study quantitatively assesses the process and speed of regional-level sustainable development in China, as well as the degree of coupling and the degree of coupling coordination among Sustainable Development Goals (SDGs). To this end, based on regional development and data monitoring in China, we construct a regional sustainable development assessment system containing 111 indicators, which combines existing sustainable development assessment indicators with the indicators of the 2030 Agenda for Sustainable Development. On that basis, using network topology construction and modal transformation, we propose a framework for analyzing the coupling relationships and evolutionary patterns of regional sustainable development. The study found that the score for SDGs at the national level increased from 50.80 in 2010 to 60.86 in 2020, showing a good development trend and the differences between provinces and regions was gradually reduced. The development speed of regional sustainable transformation shows a change from decreasing to increasing. In recent years, there is a significant change in the acceleration of regional sustainable development in China, with the vast majority of provinces having positive acceleration and only three provinces having negative acceleration. China's regional sustainable development shows that mutual coordination and promotion among provinces was higher in the eastern area than in the central region, which was higher than in the western area. The sustainable processes of each region and the coordination of sustainable development steadily increased toward a high level of coupling, all achieving coordinated development. The degree of coupling coordination and the SDG scores in each region were positively correlated with economic development, reflecting the role of economic development in the promotion of sustainability. However, this positive correlation showed a tendency of strengthening and then weakening. The correlation of the evolution patterns in the eastern–central, eastern–western, and central–western regions over time presented a trend of first weakening, then strengthening, and then weakening. Although the process of promoting sustainable development in western and central regions over time is weak synergistic consistency with that in eastern regions, overall, China's regional sustainable development presents a development model of multi-province linkage and multi-goal coordination.

Nonparametric Bayes multiresolution testing for high-dimensional rare events

In a variety of application areas, there is interest in assessing evidence of differences in the intensity of event realizations between groups. For example, in cancer genomic studies collecting data on rare variants, the focus is on assessing whether and how the variant profile changes with the disease subtype. Motivated by this application, we develop multiresolution nonparametric Bayes tests for differential mutation rates across groups. The multiresolution approach yields fast and accurate detection of spatial clusters of rare variants, and our nonparametric Bayes framework provides great flexibility for modelling the intensities of rare variants. Some theoretical properties are also assessed, including weak consistency of our Dirichlet Process-Poisson-Gamma mixture over multiple resolutions. Simulation studies illustrate excellent small sample properties relative to competitors, and we apply the method to detect rare variants related to common variable immunodeficiency from whole exome sequencing data on 215 patients and over 60,027 control subjects.