Statistical Principles Research Articles

Computational processes of simultaneous learning of stochasticity and volatility in humans

Making adaptive decisions requires predicting outcomes, and this in turn requires adapting to uncertain environments. This study explores computational challenges in distinguishing two types of noise influencing predictions: volatility and stochasticity. Volatility refers to diffusion noise in latent causes, requiring a higher learning rate, while stochasticity introduces moment-to-moment observation noise and reduces learning rate. Dissociating these effects is challenging as both increase the variance of observations. Previous research examined these factors mostly separately, but it remains unclear whether and how humans dissociate them when they are played off against one another. In two large-scale experiments, through a behavioral prediction task and computational modeling, we report evidence of humans dissociating volatility and stochasticity solely based on their observations. We observed contrasting effects of volatility and stochasticity on learning rates, consistent with statistical principles. These results are consistent with a computational model that estimates volatility and stochasticity by balancing their dueling effects.

Modeling nonlinear stress-strain model for sulfate dry-wet cycle erosion of concrete: considerations for the initial compaction stage

Sulfate dry-wet cycle erosion significantly affects the mechanical properties of concrete. Investigating the uniaxial compressive stress-strain relationship under these conditions is essential for developing accurate constitutive models. This study analyzes the uniaxial stress-strain curves of concrete subjected to dry-wet cycles in 5% and 15% sulfate solutions. The results show that the initial compaction phase in the stress-strain relationship is particularly pronounced under increasing sulfate concentrations and cycle counts. The concrete experiences an extended compaction phase, which accounts for up to 35.71% of the total strain process. This finding challenge traditional constitutive models, which struggle to accurately describe this phase. To address this issue, the study develops a nonlinear stress-strain model for concrete, incorporating the initial damage caused by sulfate dry-wet cycle erosion, based on Weibull statistical damage mechanics principles. The research indicates that the effects of sulfate concentration and cycle count are predominantly reflected in the pronounced nonlinearity of the skeleton strain function’s opening size (a) and shape characteristics (b), modeled using a fourth-degree polynomial. The model demonstrates an excellent fit to experimental data with an R2 value of 0.99989, showing that the proposed nonlinear stress-strain relationship effectively captures the uniaxial mechanical behavior of concrete under sulfate dry-wet cycle erosion and provides a robust framework for developing constitutive models in such environments.

Machine Learning Monte Carlo Approaches and Statistical Physics Notions to Characterize Bacterial Species in Human Microbiota

Recent studies have shown correlations between the microbiota’s composition and various health conditions. Machine learning (ML) techniques are essential for analyzing complex biological data, particularly in microbiome research. ML methods help analyze large datasets to uncover microbiota patterns and understand how these patterns affect human health. This study introduces a novel approach combining statistical physics with the Monte Carlo (MC) methods to characterize bacterial species in the human microbiota. We assess the significance of bacterial species in different age groups by using notions of statistical distances to evaluate species prevalence and abundance across age groups and employing MC simulations based on statistical mechanics principles. Our findings show that the microbiota composition experiences a significant transition from early childhood to adulthood. Species such as Bifidobacterium breve and Veillonella parvula decrease with age, while others like Agathobaculum butyriciproducens and Eubacterium rectale increase. Additionally, low-prevalence species may hold significant importance in characterizing age groups. Finally, we propose an overall species ranking by integrating the methods proposed here in a multicriteria classification strategy. Our research provides a comprehensive tool for microbiota analysis using statistical notions, ML techniques, and MC simulations.

Which is the better polyp detection metric: adenomas per colonoscopy or adenoma detection rate? A simulation modelling study

Background We compared the ability of ADR and APC to assess an endoscopist’s detection ability using statistical principles and simulations. Methods We simulated a population of endoscopists and patients to compare the ability of ADR versus APC for capturing the true endoscopist ability (TEA). We compared these rates with and without adjustment for patient and exam factors using multivariable models, and adjustment for imprecision due to low volume using empirical Bayes (shrinkage). Power calculations were used to compare the ability of ADR and APC to distinguish higher from lower rates over two time periods for an endoscopist. Results APC and ADR had similar discriminatory ability for assessing TEA. This increased with higher volumes and after adjusting for risk factors and low volume using shrinkage. Higher APC and ADRs had higher power for comparing an endoscopist’s detection over two time periods, but APC was superior to ADR. For example, there was 29% power to distinguish (n=200 colonoscopies) APCs:0.10 from 0.15, similar to the power (28%) to distinguish corresponding ADRs:10% and 14%. However, at same volume (n=200), the power to distinguish higher APC rates (0.50vs.0.75) was greater (89%) than the power (78%) for corresponding ADRs (39%vs.53%). Conclusions Adjusting for patient and exam factors and/or using shrinkage techniques for lower volume endoscopists can increase the correlation between TEA for both ADR and APC. For higher detection rates, APC offers more power than ADR in distinguishing differences in the detection ability.

Using a Multivariate Virtual Experiment for Uncertainty Evaluation with Unknown Variance

Virtual experiments are a digital representation of a real measurement and play a crucial role in modern measurement sciences and metrology. Beyond their common usage as a modeling and validation tool, a virtual experiment may also be employed to perform a parameter sensitivity analysis or to carry out a measurement uncertainty evaluation. For the latter to be compliant with statistical principles and metrological guidelines, the procedure to obtain an estimate and a corresponding measurement uncertainty requires careful consideration. We employ a Monte Carlo sampling procedure using a virtual experiment that allows one to perform a measurement uncertainty evaluation according to the Monte Carlo approach of JCGM-101 and JCGM-102, two widely applied guidelines for uncertainty evaluation in metrology. We extend and formalize a previously published approach for simple additive models to account for a large class of non-linear virtual experiments and measurement models for multidimensionality of the data and output quantities, and for the case of unknown variance of repeated measurements. With the algorithm developed here, a simple procedure for the evaluation of measurement uncertainty is provided that may be applied in various applications that admit a certain structure for their virtual experiment. Moreover, the measurement model commonly employed for uncertainty evaluation according to JCGM-101 and JCGM-102 is not required for this algorithm, and only evaluations of the virtual experiment are performed to obtain an estimate and an associated uncertainty of the measurand. We demonstrate the efficacy of the developed approach and the effect of the underlying assumptions for a generic polynomial regression example and an example of a simplified coordinate measuring machine and its virtual representation. The results of this work highlight that considerable effort, diligence, and statistical considerations need to be invested to make use of a virtual experiment for uncertainty evaluation in a way that ensures equivalence with the accepted guidelines.

Study design: think 'scientific value' not 'p-values'.

Statistically based experimental designs have been available for over a century. However, many preclinical researchers are completely unaware of these methods, and the success of experiments is usually equated only with 'p < 0.05'. By contrast, a well-thought-out experimental design strategy provides data with evidentiary and scientific value. A value-based strategy requires implementation of statistical design principles coupled with basic project management techniques. This article outlines the three phases of a value-based design strategy: proper framing of the research question, statistically based operationalisation through careful selection and structuring of appropriate inputs, and incorporation of methods that minimise bias and process variation. Appropriate study design increases study validity and the evidentiary strength of the results, reduces animal numbers, and reduces waste from noninformative experiments. Statistically based experimental design is thus a key component of the 'Reduction' pillar of the 3R (Replacement, Reduction, Refinement) principles for ethical animal research.

A mathematical primer to classical deep learning

This manuscript synthesizes the statistical foundations of classical deep learning by integrating insights from eight seminal works. It covers matrix calculus, neuron layers, weight and bias indexing, cost functions, differentiation of neuron operations, activation functions, bias functions, gradient descent, and backpropagation algorithms. The synthesis aims to provide a comprehensive understanding of the mathematical and statistical principles underpinning deep learning models, facilitating their application and further development in various domains.

Enhanced framework for solving general energy equations based on metropolis-hasting Markov chain Monte Carlo

Due to the widespread presence of heat and mass transfer phenomena in industrial applications, numerous studies have been devoted to the accurate solution of energy equations, providing a foundation for the analysis of heat and mass transfer processes in practical applications. In this study, a Green's Function Markov Superposition Monte Carlo (GMSMC) for solving general energy equations has been developed based on probability and statistical principles owing to its advantageous features of insensitivity towards dimension and geometric complexity as well as the capability to handle multiple integrals in complex domains. The energy equation is first decomposed, and corresponding probability models are established for each component, considering their interrelationships. Subsequently, a solution framework for solving the general energy equation is constructed by integrating these probability models based on a Markov chain structure. The mathematical principles and formulae of the proposed method are derived in detail. The performance of the proposed method is validated by several heat transfer systems with different combinations of boundary conditions and features, which mainly include the distribution of the internal heat source and whether the convection or transient term is included. Results of the validation show that the temperatures obtained by the proposed method are in good agreement with the FEM based on a fine grid, no matter whether the calculation is for a single point or a distribution.

Constrains for attending District Early Intervention Centre (DEIC) of Purba Bardhaman district, West Bengal: Perspectives of both service providers and caregivers of the beneficiaries, a Mixed-Method Study.

This study was conducted to assess the clinicosocial profile characteristics of the beneficiaries attending DEIC and to explore the challenges faced by both the caregivers and service providers. A facility-based, mixed-method study with phenomenological approach was conducted in Burdwan Medical College of Purba Bardhaman district, West Bengal, from January 2023 to April 2023. For quantitative part, record analysis was conducted involving all children enrolled at DEIC from January 2022 to December 2022, and for qualitative part, caregivers and service providers were selected purposively and interviewed using the in-depth-interview (IDI) guide. Inductive thematic analysis was conducted simultaneously till data saturation was achieved. The principles of descriptive statistics were applied to organize and present the quantitative data in tables and diagrams. Qualitative data were transcribed into verbatim and analyzed thematically with inductive approach. Out of 3332 children enrolled, 58.4% were males, and 44.2% were aged between 0 and 1 month. 59.3% of them had developmental delays, 7.9% had defects, 42.9% had diseases, and 21.3% had some deficiencies. Major hindering factors in service provision among service providers were resource deficiency, inadequate capacity building, administrative bottlenecks, limited supportive supervision, inadequate advocacy, and awareness deficit. No major constraints were found from caregivers' perspective in accessing healthcare. DEIC is running with shortage of proper infrastructure and adequate supervision. Periodic training, appropriate awareness building, and continuous flow of logistics are needed to ensure a better quality of life among beneficiaries.

Dynamic deformation measurement with 2-frame phase-shifting speckle interferometry based on speckle statistics and wavefront multiplexing.

Phase-shifting speckle interferometry could achieve full-field deformation measurement of rough surfaces. To meet the dynamic requirement and further improve the accuracy, a two-step synchronous phase-shifting measurement system is established based on the polarization-sensitive phase modulation ability of a liquid crystal spatial light modulator; by multiplexing the reference wavefront, an accurate phase shift is generated between two independent recording channels, and a common-path self-reference vortex interference structure is built for precise spatial registration. Meanwhile, according to the speckle statistical principle, a novel two-frame phase-shifting algorithm as well as a two-step spatial registration strategy is presented to strengthen the robustness of intensity and position differences caused by spatial-multiplexing; thereby, accurate transient deformation can be directly obtained from phase-shifting speckle interferograms recorded before and after deformation. The effectiveness and accuracy of the proposal are validated from the out-of-plane deformation measurement experiment by comparing with the traditional two-step and four-step phase-shifting methods. The dynamic ability is exhibited through reconstructing mechanical and thermal deformations across various application scenarios.

The Importance of Statistics in Medical Healthcare

Abstract: Statistical principles play a fundamental role in shaping the landscape of medical science by providing a structured framework for analyzing data, drawing conclusions, and making informed decisions in healthcare settings. In the realm of medical research, statistical principles are crucial for designing experiments, interpreting results, and ensuring the reliability and validity of findings. Key statistical concepts like hypothesis testing, confidence intervals, regression analysis, and survival analysis are extensively utilized in medical studies to assess the effectiveness of treatments, understand disease patterns, and evaluate healthcare interventions. These principles enable healthcare professionals to make evidence-based decisions, tailor treatments to individual patient needs, and continuously improve the quality of care provided to patients. The role of statistics in medical research starts at the planning stage of a clinical trial or laboratory experiment to establish the design and size of an experiment that will ensure a good prospect of detecting effects of clinical or scientific interest. Statistics is again used during the analysis of data (sample data) to make inferences valid in a wider population. In simple situations computation of simple quantities such as P-values, confidence intervals, standard deviations, standard errors or application of some standard parametric or nonparametric tests may suffice.

Statistical uncertainty principle in Markov kinetics

A reciprocality between the statistical variance of observables of a thermodynamic state and that of their conjugate variables, as entropic forces, originates from the thermodynamic conjugacy with respect to an entropy function. This thermodynamic uncertainty principle in equilibrium can be derived from the Maximum Entropy principle and is independent upon underlying mechanistic details. We present, based on the Maximum Caliber principle as the dynamic generalization of Maximum Entropy, the formalism of the uncertainty principle in kinetics in time homogeneous Markov processes between transitional observables and their conjugate path entropic forces. A stochastic biophysical model for molecular motors is used as an illustrating example. The present work generalizes the phenomenological thermodynamics of uncertainties/fluctuations and is applicable to data ad infinitum.

An accurate measurement method of irregular coal gangue volume based on adaptive image restoration and error compensation

To improve the accuracy of volume measurement for irregularly shaped coal gangue, defects in the depth image and various errors in volume measurement are analyzed. The gray difference similarity (Gds) is proposed for pre-classifying defects, and the depth and RGB information are used interactively for adaptive repair. To minimize the impact of abnormal gray distribution and irrelevant information on the repair process, the areas to be repaired are divided into abnormal regions or layers based on gray and distance weights. Taking into account parameters like geometric morphology (GeMo), volume (Ve), and GeMo × Ve, the influence of wrong imaging and gaps is fully considered. The reverse compensation of errors is achieved by applying the principles of mathematical statistics and the nonlinear surface fitting algorithm. The results show that compared with other algorithms, the proposed algorithm has the smallest measurement error of 6.614 % and is not easily affected by external factors.

A Theoretical Review of Modern Robust Statistics

Robust statistics is a fairly mature field that dates back to the early 1960s, with many foundational concepts having been developed in the ensuing decades. However, the field has drawn a new surge of attention in the past decade, largely due to a desire to recast robust statistical principles in the context of high-dimensional statistics. In this article, we begin by reviewing some of the central ideas in classical robust statistics. We then discuss the need for new theory in high dimensions, using recent work in high-dimensional M-estimation as an illustrative example. Next, we highlight a variety of interesting recent topics that have drawn a flurry of research activity from both statisticians and theoretical computer scientists, demonstrating the need for further research in robust estimation that embraces new estimation and contamination settings, as well as a greater emphasis on computational tractability in high dimensions.

Synthetic lidar point cloud generation using deep generative models for improved driving scene object recognition

The imbalanced distribution of different object categories poses a challenge for training accurate object recognition models in driving scenes. Supervised machine learning models trained on imbalanced data are biased and easily overfit the majority classes, such as vehicles and pedestrians, which appear more frequently in driving scenes. We propose a novel data augmentation approach for object recognition in lidar point cloud of driving scenes, which leverages probabilistic generative models to produce synthetic point clouds for the minority classes and complement the original imbalanced dataset. We evaluate five generative models based on different statistical principles, including Gaussian mixture model, variational autoencoder, generative adversarial network, adversarial autoencoder and the diffusion model. Experiments with a real-world autonomous driving dataset show that the synthetic point clouds generated for the minority classes by the Latent Generative Adversarial Network result in significant improvement of object recognition performance for both minority and majority classes. The codes are available at https://github.com/AAAALEX-XIANG/Synthetic-Lidar-Generation.

The randomness and determinacy of wall pressure fluctuations in incompressible flow

Wall pressure fluctuations caused by turbulent boundary layers have a significant impact on aircraft structural vibration and cabin noise. This study aims to investigate the mechanism of turbulence-induced pressure fluctuations by focusing on the randomness of wall pressure fluctuations, analyzed in both the time–frequency and spatial-wavenumber domains using measured data obtained from a phase array in a wind tunnel. Three roughness elements were designed and installed upstream of the plate to manipulate the turbulent boundary layer at a specific Mach number. The results of the investigation demonstrate that the disturbance strength induced by the roughness element influences the randomness of wall pressure fluctuations, in addition to the parameters utilized for data analysis. Generally, stronger turbulence fluctuations tend to decrease the randomness of pressure fluctuations. Moreover, wall pressure fluctuations also exhibit certain statistical principles that cannot be precisely calculated using mathematical expressions, highlighting their inherent randomness. Further investigation into randomness in the spatial-wavenumber domain revealed the hydrodynamic modes of turbulence fluctuations with varying convection velocity analyzed through wavenumber maps computed using the beamforming algorithm. These modes with variable convective speed significantly contribute to the generation of randomness in wall pressure fluctuations. Both the time–frequency domain and the spatial-wavenumber domain affect the randomness characteristics of wall pressure fluctuations. However, such effects are not easily discernible through a rudimentary analysis of the space–time correlation of turbulence fluctuations.

Catastrophic cost and coping strategies of tuberculosis patients in a block of Purba Bardhaman District, West Bengal: A crossectional study

BackgroundThe elevated expenses associated with tuberculosis (TB), can hinder access to treatment and adherence. ObjectivesThis study was done to find out catastrophic cost (defined as 20% of the total annual income) resulting from treatment and diagnosis of TB, factors associated with it and delineated the coping mechanisms employed by the affected individuals and their families. Materials and methodsA cross sectional study was conducted for a period of 6 months, September 2023 to February 2024, among 146 patients registered in the Tuberculosis Unit (TU) of Bhatar block, Purba Bardhaman District,West Bengal. A pre validated questionnaire was used for interviewing the patients. Data was analysed using the principles of descriptive statistics, organised and presented in the form of tables. ResultsOut of 146 tuberculosis (TB) patients, the study revealed mean total cost incurred for TB-related services amounted to Rs 30,046 ± Rs 9406 with direct cost of Rs 2964.26 ± Rs 990.3 and indirect cost of Rs 27,406 ± Rs 9,351.54(36.9%) of the study population reported that their families faced catastrophic costs. Coping strategies like taking loan emerged as the most prevalent means, with 45(30.8%) patients reporting it followed by selling livestock which was prevalent among 14(9.6%) of them. ConclusionsIn spite of the implementation of Universal Health Coverage, TB-affected households still faces the risk of catastrophic total costs. A cost-mitigation policy and financial protection should be provided additionally along with better health care facility to all patients.

Unifying approaches to understanding capacity in change detection.

To navigate changes within a highly dynamic and complex environment, it is crucial to compare current visual representations of a scene to previously formed representations stored in memory. This process of mental comparison requires integrating information from multiple sources to inform decisions about changes within the environment. In the present article, we combine a novel systems factorial technology change detection task (Blunden et al., 2022) with a set size manipulation. Participants were required to detect 0, 1, or 2 changes of low and high detectability between a memory and probe array of 1-4 spatially separated luminance discs. Analyses using systems factorial technology indicated that the processing architecture was consistent across set sizes but that capacity was always limited and decreased as the number of distractors increased. We developed a novel model of change detection based on the statistical principles of basic sampling theory (Palmer, 1990; Sewell et al., 2014). The sample size model, instantiated parametrically, predicts the architecture and capacity results a priori and quantitatively accounted for several key results observed in the data: (a) increasing set size acted to decrease sensitivity (d') in proportion to the square root of the number of items in the display; (b) the effect of redundancy benefited performance by a factor of the square root of the number of changes; and (c) the effect of change detectability was separable and independent of the sample size costs and redundancy benefits. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A quality improvement project on reducing antibiotic use duration in very low birth weight preterm infants in the neonatal intensive care unit

To develop effective measures to reduce antibiotic use duration in very low birth weight (VLBW) preterm infants in the neonatal intensive care unit through quality improvement methods. The study population consisted of hospitalized VLBW preterm infants, with the percentage of hospitalization time during which antibiotics were used from November 2020 to June 2021 serving as the baseline. The specific quality improvement goal was to reduce the duration of antibiotic use. Factors affecting antibiotic use duration in preterm infants were analyzed using Pareto charts. Key drivers were identified, and specific interventions were formulated based on the stages of antibiotic use. Changes in the percentage of antibiotic use duration were monitored with run charts until the quality improvement target was achieved. From November 2020 to June 2021, the baseline antibiotic use duration percentage was 49%, with a quality improvement target to reduce this by 10% within 12 months. The Pareto analysis indicated that major factors influencing antibiotic duration included non-standard antibiotic use; delayed cessation of antibiotics when no infection evidence was present; prolonged central venous catheter placement; insufficient application of kangaroo care; and delayed progress in enteral nutrition. The interventions implemented included: (1) establishing sepsis evaluation and management standards; (2) educating medical staff on the rational use of antibiotics for preterm infants; (3) supervising the enforcement of antibiotic use standards during ward rounds; (4) for those without clear signs of infection and with negative blood cultures, discontinued the use of antibiotics 36 hours after initiation; (5) reducing the duration of central venous catheterization and parenteral nutrition to lower the risk of infection in preterm infants. The control chart showed that with continuous implementation of interventions, the percentage of antibiotic use duration was reduced from 49% to 32%, a statistically significant decrease. The application of quality improvement tools based on statistical principles and process control may significantly reduce the antibiotic use duration in VLBW preterm infants. Citation:Chinese Journal of Contemporary Pediatrics, 2024, 26(7): 736-742.

A mathematical theory of relational generalization in transitive inference

Humans and animals routinely infer relations between different items or events and generalize these relations to novel combinations of items. This allows them to respond appropriately to radically novel circumstances and is fundamental to advanced cognition. However, how learning systems (including the brain) can implement the necessary inductive biases has been unclear. We investigated transitive inference (TI), a classic relational task paradigm in which subjects must learn a relation ([Formula: see text] and [Formula: see text]) and generalize it to new combinations of items ([Formula: see text]). Through mathematical analysis, we found that a broad range of biologically relevant learning models (e.g. gradient flow or ridge regression) perform TI successfully and recapitulate signature behavioral patterns long observed in living subjects. First, we found that models with item-wise additive representations automatically encode transitive relations. Second, for more general representations, a single scalar "conjunctivity factor" determines model behavior on TI and, further, the principle of norm minimization (a standard statistical inductive bias) enables models with fixed, partly conjunctive representations to generalize transitively. Finally, neural networks in the "rich regime," which enables representation learning and improves generalization on many tasks, unexpectedly show poor generalization and anomalous behavior on TI. We find that such networks implement a form of norm minimization (over hidden weights) that yields a local encoding mechanism lacking transitivity. Our findings show how minimal statistical learning principles give rise to a classical relational inductive bias (transitivity), explain empirically observed behaviors, and establish a formal approach to understanding the neural basis of relational abstraction.