Inference Procedures Research Articles

Efficient sparsity-promoting MAP estimation for Bayesian linear inverse problems

Abstract Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed linear inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown augmented by a generalized gamma hyper-prior model for the variance hyper-parameters. This investigation generalizes such models and their efficient maximum a posterior estimation using the iterative alternating sequential algorithm in two ways: (1) general sparsifying transforms: diverging from conventional methods, our approach permits use of sparsifying transformations with nontrivial kernels; (2) unknown noise variances: the noise variance is treated as a random variable to be estimated during the inference procedure. This is important in applications where the noise estimate cannot be accurately estimated a priori. Remarkably, these augmentations neither significantly burden the computational expense of the algorithm nor compromise its efficacy. We include convexity and convergence analysis and demonstrate our method’s efficacy in several numerical experiments.

U-Statistic Reduction: Higher-Order Accurate Risk Control and Statistical-Computational Trade-Off

U-statistics play central roles in many statistical learning tools but face the haunting issue of scalability. Despite extensive research on accelerating computation by U-statistic reduction, existing results almost exclusively focused on power analysis. Little work addresses risk control accuracy, which requires distinct and much more challenging techniques. In this paper, we establish the first statistical inference procedure with provably higher-order accurate risk control for incomplete U-statistics. The sharpness of our new result enables us to reveal how risk control accuracy also trades off with speed, for the first time in literature, which complements the well-known variance-speed trade-off. Our general framework converts the challenging and case-by-case analysis for many different designs into a surprisingly principled and routine computation. We conducted comprehensive numerical studies and observed results that validate our theory’s sharpness. Our method also demonstrates effectiveness on real-world data applications.

Distribution-on-scalar Single-index Quantile Regression Model for Handling Tumor Heterogeneity

This paper develops a distribution-on-scalar single-index quantile regression modeling framework to investigate the relationship between cancer imaging responses and scalar covariates of interest while tackling tumor heterogeneity. Conventional association analysis methods typically assume that the imaging responses are well-aligned after some preprocessing steps. However, this assumption is often violated in practice due to imaging heterogeneity. Although some distribution-based approaches are developed to deal with this heterogeneity, major challenges have been posted due to the nonlinear subspace formed by the distributional responses, the unknown nonlinear association structure, and the lack of statistical inference. Our method can successfully address all the challenges. We establish both estimation and inference procedures for the unknown functions in our model. The asymptotic properties of both estimation and inference procedures are systematically investigated. The finite-sample performance of our proposed method is assessed by using both Monte Carlo simulations and a real data example on brain cancer images from TCIA-GBM collection.

A class of semiparametric models for bivariate survival data.

We propose a new class of bivariate survival models based on the family of Archimedean copulas with margins modeled by the Yang and Prentice (YP) model. The Ali-Mikhail-Haq (AMH), Clayton, Frank, Gumbel-Hougaard (GH), and Joe copulas are employed to accommodate the dependency among marginal distributions. Baseline distributions are modeled semiparametrically by the Piecewise Exponential (PE) distribution and the Bernstein polynomials (BP). Inference procedures for the proposed class of models are based on the maximum likelihood (ML) approach. The new class of models possesses some attractive features: i) the ability to take into account survival data with crossing survival curves; ii) the inclusion of the well-known proportional hazards (PH) and proportional odds (PO) models as particular cases; iii) greater flexibility provided by the semiparametric modeling of the marginal baseline distributions; iv) the availability of closed-form expressions for the likelihood functions, leading to more straightforward inferential procedures. The properties of the proposed class are numerically investigated through an extensive simulation study. Finally, we demonstrate the versatility of our new class of models through the analysis of survival data involving patients diagnosed with ovarian cancer.

Non-Gaussian Stochastic Volatility models

Stochastic volatility models are fundamental tools in finance for accurately estimating and managing risks due to their ability to accommodate a time-varying volatility structure. However, a relevant constraint within these models is the reliance on Gaussian processes to model the latent (log-)variance, which can limit their ability to effectively capture events such as sudden jumps or spikes in the latent volatility. To address this limitation, we propose in this short paper a non-Gaussian SV model utilizing an inference procedure that combines Laplace and Variational Bayes approximations. Our study showcases the advantages of this correction in modeling the conditional variance of Bitcoin's return series.

Interval prediction of order statistics based on records by employing inter-record times

In this note, we propose a parametric inferential procedure for predicting future order statistics, based on record values, which takes inter-record times into account. We utilize the additional information contained in inter-record times for predicting future order statistics on the basis of observed record values from an independent sample. The two parameter exponential distribution is assumed to be the underlying distribution.

Using Hierarchical Bayesian Modeling to Enhance Statistical Inference on Contrast Sensitivity.

The purpose of this study is to introduce a nonparametric hierarchical Bayesian model (HBM) that enables advanced statistical inference on contrast sensitivity (CS) both at individual spatial frequencies (SFs) and across multiple SFs in clinical trials, where CS measurements are crucial for assessing safety and efficacy. The HBM computes the joint posterior distribution of CS at six Food and Drug Administration-designated SFs across the population, individual, and test levels. It incorporates covariances at both population and individual levels to capture the relationship between CSs across SFs. A Bayesian inference procedure (BIP) is also used to estimate the posterior distribution of CS at each SF independently. Both methods are applied to a quantitative CSF (qCSF) dataset of 112 subjects and compared in terms of precision, test-retest reliability of CS estimates, sensitivity, accuracy, and statistical power in detecting CS changes. The HBM reveals correlations between CSs in pairs of SFs and provides significantly more precise estimates and higher test-retest reliability compared to the BIP. Additionally, it improves the average sensitivity and accuracy in detecting CS changes for individual subjects, as well as statistical power for detecting group-level CS changes at individual and combinations of multiple SFs between luminance conditions. The HBM establishes a comprehensive framework to enhance sensitivity, accuracy, and statistical power for detecting CS changes in hierarchical experimental designs. The HBM presents a valuable tool for advancing CS assessments in the clinic and clinical trials, potentially improving the evaluation of treatment efficacy and patient outcomes.

Fast-iTPN: Integrally Pre-Trained Transformer Pyramid Network With Token Migration.

We propose integrally pre-trained transformer pyramid network (iTPN), towards jointly optimizing the network backbone and the neck, so that transfer gap between representation models and downstream tasks is minimal. iTPN is born with two elaborated designs: 1) The first pre-trained feature pyramid upon vision transformer (ViT). 2) Multi-stage supervision to the feature pyramid using masked feature modeling (MFM). iTPN is updated to Fast-iTPN, reducing computational memory overhead and accelerating inference through two flexible designs. 1) Token migration: dropping redundant tokens of the backbone while replenishing them in the feature pyramid without attention operations. 2) Token gathering: reducing computation cost caused by global attention by introducing few gathering tokens. The base/large-level Fast-iTPN achieve 88.75%/89.5% top-1 accuracy on ImageNet-1 K. With 1× training schedule using DINO, the base/large-level Fast-iTPN achieves 58.4%/58.8% box AP on COCO object detection, and a 57.5%/58.7% mIoU on ADE20 K semantic segmentation using MaskDINO. Fast-iTPN can accelerate the inference procedure by up to 70%, with negligible performance loss, demonstrating the potential to be a powerful backbone for downstream vision tasks.

Inference with Non-Homogeneous Lognormal Diffusion Processes Conditioned on Nearest Neighbor

In this work, we approach the forecast problem for a general non-homogeneous diffusion process over time with a different perspective from the classical one. We study the main characteristic functions as mean, mode, and α-quantiles conditioned on a future time, not conditioned on the past (as is normally the case), and we observe the specific formula in some interesting particular cases, such as Gompertz, logistic, or Bertalanffy diffusion processes, among others. This study aims to enhance classical inference methods when we need to impute data based on available information, past or future. We develop a simulation and obtain a dataset that is closer to reality, where there is no regularity in the number or timing of observations, to extend the traditional inference method. For such data, we propose using characteristic functions conditioned on the past or the future, depending on the closest point at which we aim to perform the imputation. The proposed inference procedure greatly reduces imputation errors in the simulated dataset.

Kajian Pemahaman Mahasiswa tentang Pengumpulan dan Analisis Data melalui Evaluasi Hasil Penelitian Skripsi

A deep understanding of data collection and analysis techniques is an essential competence for students to produce valid and high-quality research. This study employed a quantitative descriptive approach with 22 students as subjects who had studied these techniques. Each student was tasked with evaluating two quantitative theses relevant to the learning model, published within the last five years. The evaluation used a rubric covering seven key components: Data Identification and Classification, Frequency Distribution, Measures of Central Tendency and Data Variation, Coefficient of Variation, Standard Values, Inferential Statistical Procedures, and Data Integration and Synthesis. The study results revealed varying levels of student understanding across the components. Most students achieved high competence in Data Identification and Classification (95.45%) and Inferential Statistical Procedures (95.45%). However, comprehension of more complex components, such as Coefficient of Variation and Standard Values, remained weak, with only 54.55% of students fully competent. This study highlights the need for more structured teaching methods and intensive practical exercises, particularly in advanced statistical analysis and data visualization. The implications suggest that improving these areas can strengthen students' research skills, supporting better mastery of data analysis techniques in the future.

Varextropy of k-record values and its applications

. In this article, the varextropy measure based on k-record values is considered. The expressions for the varextropy measure for the nth upper and lower k-record values have been established. Additionally, we establish the varextropy measure of residual and past lifetimes based on k-record values. We also consider the problem of estimation of the varextropy measure for a two-parameter Weibull distribution based on the upper k-record values. Maximum likelihood estimation and Bayes estimation for varextropy measure have been considered based on upper k-record values. Bayes estimators are obtained using the Markov Chain Monte Carlo (MCMC) method. A simulation study is performed to determine the performance of the estimators developed in this article. Inferential procedures developed in this article have also been illustrated using real data.

Bayesian hierarchical hypothesis testing in large-scale genome-wide association analysis.

Variable selection and large-scale hypothesis testing are techniques commonly used to analyze high-dimensional genomic data. Despite recent advances in theory and methodology, variable selection and inference with highly collinear features remain challenging. For instance, collinearity poses a great challenge in genome-wide association studies involving millions of variants, many of which may be in high linkage disequilibrium. In such settings, collinearity can significantly reduce the power of variable selection methods to identify individual variants associated with an outcome. To address such challenges, we developed a Bayesian hierarchical hypothesis testing (BHHT)-a novel multiresolution testing procedure that offers high power with adequate error control and fine-mapping resolution. We demonstrate through simulations that the proposed methodology has a power-FDR performance that is competitive with (and in many scenarios better than) state-of-the-art methods. Finally, we demonstrate the feasibility of using BHHT with large sample size (n∼ 300,000) and ultra dimensional genotypes (∼ 15 million single-nucleotide polymorphisms or SNPs) by applying it to eight complex traits using data from the UK-Biobank. Our results show that the proposed methodology leads to many more discoveries than those obtained using traditional SNP-centered inference procedures. The article is accompanied by open-source software that implements the methods described in this study using algorithms that scale to biobank-size ultra-high-dimensional data.

Anatomical prior-based vertebral landmark detection for spinal disorder diagnosis

As one of fundamental ways to interpret spine images, detection of vertebral landmarks is an informative prerequisite for further diagnosis and management of spine disorders such as scoliosis and fractures. Most existing machine learning-based methods for automatic vertebral landmark detection suffer from overlapping landmarks or abnormally long distances between nearby landmarks against anatomical priors, and thus lack sufficient reliability and interpretability. To tackle the problem, this paper systematically utilizes anatomical prior knowledge in vertebral landmark detection. We explicitly formulate anatomical priors of the spine, related to distances among vertebrae and spatial order within the spine, and integrate these geometrical constraints within training loss, inference procedure, and evaluation metrics. First, we introduce an anatomy-constraint loss to regularize the training process with the aforementioned contextual priors explicitly. Second, we propose a simple-yet-effective anatomy-aided inference procedure by employing sequential prediction rather than a parallel counterpart. Third, we provide novel anatomy-related metrics to quantitatively evaluate to which extent landmark predictions follow the anatomical priors, as is not reflected within the widely-used landmark localization error metric. We employ the localization framework on 1410 anterior–posterior radiographic images. Compared with competitive baseline models, we achieve superior landmark localization accuracy and comparable Cobb angle estimation for scoliosis assessment. Ablation studies demonstrate the effectiveness of designed components on the decrease of localization error and improvement of anatomical plausibility. Additionally, we exhibit effective generalization performance by transferring our detection method onto sagittal 2-D slices of CT scans and boost the performance of downstream compression fracture classification at vertebra-level.

Shape Mediation Analysis in Alzheimer's Disease Studies.

As a crucial tool in neuroscience, mediation analysis has been developed and widely adopted to elucidate the role of intermediary variables derived from neuroimaging data. Typically, structural equation models (SEMs) are employed to investigate the influences of exposures on outcomes, with model coefficients being interpreted as causal effects. While existing SEMs have proven to be effective tools for mediation analysis involving various neuroimaging-related mediators, limited research has explored scenarios where these mediators are derived from the shape space. In addition, the linear relationship assumption adopted in existing SEMs may lead to substantial efficiency losses and decreased predictive accuracy in real-world applications. To address these challenges, we introduce a novel framework for shape mediation analysis, designed to explore the causal relationships between genetic exposures and clinical outcomes, whether mediated or unmediated by shape-related factors while accounting for potential confounding variables. Within our framework, we apply the square-root velocity function to extract elastic shape representations, which reside within the linear Hilbert space of square-integrable functions. Subsequently, we introduce a two-layer shape regression model to characterize the relationships among neurocognitive outcomes, elastic shape mediators, genetic exposures, and clinical confounders. Both estimation and inference procedures are established for unknown parameters along with the corresponding causal estimands. The asymptotic properties of estimated quantities are investigated as well. Both simulated studies and real-data analyses demonstrate the superior performance of our proposed method in terms of estimation accuracy and robustness when compared to existing approaches for estimating causal estimands.

Score test for marks in Hawkes processes

AbstractA score statistic for detecting the impact of marks in a linear Hawkes self-exciting point process is proposed, with its asymptotic properties, finite sample performance, power properties using simulation and application to real data presented. A major advantage of the proposed inference procedure is that the Hawkes process can be fitted under the null hypothesis that marks do not impact the intensity process. Hence, for a given record of a point process, the intensity process is estimated once only and then assessed against any number of potential marks without refitting the joint likelihood each time. Marks can be multivariate and serially dependent. The score function for any given set of marks is easily constructed as the covariance of functions of future intensities fits the unmarked process with functions of the marks under assessment. The asymptotic distribution of the score statistic is a Chi-squared distribution, with degrees of freedom equal to the number of parameters required to specify the boost function. Model-based or nonparametric estimation of required features of the mark’s marginal moments and serial dependence can be used. Using sample moments of the marks in the test statistic construction does not impact the size and power properties.

Birge ratio method for modeling dark uncertainty in multivariate meta-analyses and inter-laboratory studies

In the paper, we introduce a new approach for combining multivariate measurements obtained in individual studies. The procedure extends the Birge ratio method, a commonly used approach in physics in the univariate case, such as for the determination of physical constants, to multivariate observations. Statistical inference procedures are derived for the parameters of the multivariate location-scale model, which is related to the multivariate Birge ratio method. The new approach provides an alternative to the methods based on the application of the multivariate random effects model, which is commonly used for multivariate meta-analyses and inter-laboratory comparisons. In two empirical illustrations, we show that the introduced multivariate Birge ratio approach yields confidence intervals for the elements of the overall mean vector that are considerably narrower than those obtained by the methods derived under the multivariate random effects model.

Adaptive randomization methods for sequential multiple assignment randomized trials (smarts) via thompson sampling.

Response-adaptive randomization (RAR) has been studied extensively in conventional, single-stage clinical trials, where it has been shown to yield ethical and statistical benefits, especially in trials with many treatment arms. However, RAR and its potential benefits are understudied in sequential multiple assignment randomized trials (SMARTs), which are the gold-standard trial design for evaluation of multi-stage treatment regimes. We propose a suite of RAR algorithms for SMARTs based on Thompson Sampling (TS), a widely used RAR method in single-stage trials in which treatment randomization probabilities are aligned with the estimated probability that the treatment is optimal. We focus on two common objectives in SMARTs: (1) comparison of the regimes embedded in the trial and (2) estimation of an optimal embedded regime. We develop valid post-study inferential procedures for treatment regimes under the proposed algorithms. This is nontrivial, as even in single-stage settings standard estimators of an average treatment effect can have nonnormal asymptotic behavior under RAR. Our algorithms are the first for RAR in multi-stage trials that account for non-standard limiting behavior due to RAR. Empirical studies based on real-world SMARTs show that TS can improve in-trial subject outcomes without sacrificing efficiency for post-trial comparisons.

Detecting bubbles via FDR and FNR based on calibrated p-values

Detecting bubbles in asset prices is still an open question that has attracted considerable attention in recent years. This paper improves the bubble detection and dating approaches developed in recent years by Phillips and co-authors, proposing to assess the plausibility of its outcomes via the false discovery rate (FDR) and the false non-discovery rate (FNR) based on calibrated p-values. Calibrating p-values of unit root tests, applied sequentially to detect bubbles, allows recovery of their super-uniformity property, which is crucial for a valid implementation of the inferential procedure. The paper also develops original self-calibrated versions of both FDR and FNR for the specific problem of bubble testing. Calibrated p-values are implemented in an online false discovery-based approach which monitors bubbles in real time. The effectiveness of the proposed methods is investigated via a simulation study and an empirical application.

Assessment of Behavioral Problems among Children with Speech Difficulties

Abstract: Behavioral problems can present differently for many children with speech difficulties, some common ones outbursts or tantrums, unwillingness to follow directions, being angry or irritable, purposefully annoying others and physical aggression toward others, such as hitting, kicking, or scratching, some children may show one of these behaviors, while other children may have many. Objectives: to assess sociodemographic characteristics, behavioral problems and speech difficulties among children with speech difficulties. Methodology: A descriptive cross-sectional study design was carried out in Baghdad Teaching Hospital. A non- probability (purposive) study sample of (300) child, who attended Hearing and Speech Center. The data were analyzed using descriptive and inferential statistical procedure for data analysis. Results: The study results reveal that (41.7%) of children with age group 6-less than 8 years (73%) of them were males and remaining (27%) were females, second born among (41%) of them while (28.7%) of them were not registered and (36.7%) of children having stuttering; speech sound disorders were prevalent among (39.7%); childhood apraxia of speech prevalent among (19.7%). Conclusion: The children experience mild behavioral problems regarding somatic complaints, thought problems, and rule-breaking behaviors, and experience moderate behavioral problems regarding anxious/depressed problems, withdrawal, social problems, and aggressive behavior, while experiencing severe behavioral problems regarding attention and hyperactivity. Recommendations: the child with speech difficulties to be seen by a speech language pathologist (SLP) to assess the child to obtain a clear idea of the child’s strengths and weaknesses in speech and language.

Scheduling as a Constraint Satisfaction Problem (Using the Example of Open-Pit Minе Production Scheduling Problem)

The research described in the work is aimed at developing methods for Scheduling. The fundamental disadvantage of the existing methods of Mixed-Integer Linear Programming in application to the problems under consideration is the fact that they are too demanding on the amount of RAM. The difficulty of applying local search procedures to such high-dimensional problems is to develop an effective way to find an acceptable initial approximation and determine the neighboring state transition function, which would allow achieving the optimum fast enough. In the Operations Research Theory, adding additional conditions to a problem can lead to a fundamental change in the problem-solving scheme. The methods proposed in the study are implemented within the framework of the Constraint Programming Paradigm which makes it possible to represent the subject domain dependencies saving RAM, as well as to provide the ability to step-by-step take into account heterogeneous problem conditions without essentially changing the scheme of finding solutions. A significant part of the research deals with methods of logical inference on constraints to reduce the search space and speed up the computational process. The approach to scheduling is illustrated by the Open-Pit Mine Production Scheduling Problem, which was first proposed to be solved as a Constraint Satisfaction Problem. In order to find the first feasible solution, a «greedy» search method is proposed, the result of which can be improved using the developed hybrid method. Both methods rely on original procedures of inference on constraints. The proposed approach has proven its efficiency for block models with sizes of tens and hundreds of thousands of blocks.