arXiv subjects

Buddhananda Banerjee

Publications and source records attributed to Buddhananda Banerjee.

14 recordsLinked to original sources

arXiv2026

Phonon anomalies and critical scaling in the spin-$1/2$ trimer chain Na$_2$Cu$_3$Ge$_4$O$_{12}$

Low-dimensional quantum magnets provide an ideal platform to explore spin-lattice coupling-mediated quantum correlations, which give rise to emergent quasiparticle excitations. The antiferromagnetically coupled spin-1/2 trimer chain of copper ions in Na$_2$Cu$_3$Ge$_4$O$_{12}$ (NCGO) hosts high-energy spin excitations of different species, whose energy scales overlap with those of lattice vibrations. Here, we report a comprehensive temperature-dependent Raman spectroscopic study performed between 80 and 400 K. The dynamic spin susceptibility, as obtained from the analysis of the broad spectral background, reveals the emergence of quasiparticle excitations below 170 K. We further identify an unusual crossover of phonon dynamics when the material transits from a normal paramagnetic state to a correlated quantum magnetic state. A power law dependence of the integrated Raman susceptibility of the phonon modes, $I_{\chi^{\prime\prime}}^{i}\sim|T-T_{c}|^\beta$, is observed with the critical temperature $T_c$=167$\pm$1 K, and critical exponent $\beta = 0.24\pm 0.02$. The combined results obtained from the broad spectral background and sharp phonon peaks further indicate that the phonon renormalization observed across the crossover is driven by dynamic spin states. Additionally, statistical correlations among phonon energy eigenvalues, quantified through matrix-norm and power-test analyses of 200 spectra recorded at 80 K, reveal an unexpected linear correlation among phonon modes, also indicating that the collective lattice response is governed by spin correlations. These findings establish NCGO as a model system for investigating cooperative spin-lattice coupling and critical scaling behavior of phonon dynamics in low-dimensional magnetic materials.

cond-mat.str-el↗

arXiv2026

Distribution-Free test for Changepoint Detection in Angular Mean Direction: Application in Finance

In this paper, we propose a distribution-free test for detecting changepoint in the mean direction of angular data. The uncertainty in angular measurements is quantified through the \textit{square of an angle}, derived from the intrinsic geometry of the torus. It is established that, under the null hypothesis, the test statistic distributionally converges to the Kolmogorov distribution, while under the alternative hypothesis, both the consistency of the test and the asymptotic properties of the changepoint estimator are established. Through extensive simulations, we compare the empirical performance of the proposed method with two existing approaches for angular data and further benchmark it against a test based on the circular arc length distance. Finally, we demonstrate the practical utility of our approach by analyzing the timestamps of extreme events in Bitcoin, Ethereum, and Gold price datasets, where the continuous, high-frequency nature of the data is modeled in the circular framework.

stat.ME↗

arXiv2026

Hyperbolic statistical inference for Treatment Effects with Circular biomarker of astigmatism

Circular biomarkers arise naturally in many biomedical applications, particularly in ophthalmology, where angular measurements such as astigmatism are routinely recorded. Similar directional variables also occur in the study of human body rotations, including movements of the hand, waist, neck, and lower limbs. Motivated by a clinical dataset comprising angular measurements of astigmatism induced by two cataract surgery procedures, we propose a novel two-sample testing framework for circular data grounded in hyperbolic geometry. Assuming von Mises distributions with either common or group-specific concentration parameters, we embed the corresponding parameter spaces into the Poincar\'e disk, an open unit disk endowed with the Poincar\'e metric.Under this construction, each von Mises distribution is mapped uniquely to a point in the Poincar\'e disk, yielding a continuous geometric representation that preserves the intrinsic structure of the parameter space. This embedding enables direct comparison of group distributions via hyperbolic distances, leading to natural and interpretable test statistics. We develop permutation-based tests for the common concentration case and bootstrap-based procedures for unequal concentrations. Extensive simulation studies demonstrate stable empirical size, strong consistency, and superior asymptotic power compared with existing competing methods. The proposed methodology is illustrated through a detailed analysis of the cataract surgery dataset, including a clinically informed restructuring of the original observations. The results highlight the practical advantages of incorporating hyperbolic geometry into the analysis of circular biomedical data and underscore the potential of geometry-aware inference for directional biomarkers.

stat.ME↗

arXiv2025

A Semi-Parametric Torus-to-Torus Regression Model with Geometric Loss: Application to Cyclone Data

This study introduces a novel torus-to-torus regression framework to improve the analysis and prediction of cyclone-driven wind-wave directional dynamics. This research, to our knowledge, establishes a mathematical framework for modeling the regression between bivariate angular predictors and bivariate angular responses for the first time in the literature. The proposed approach enhances the capacity to model coupled directional processes commonly observed in extreme coastal cyclones. The proposed model makes use of generalized M\"{o}bius transformation and differential geometry for model building. A new loss function, derived from the intrinsic geometry of the torus, is introduced to facilitate effective semi-parametric estimation without requiring any specific distributional assumptions on the angular error. The prediction error is measured as an angular loss on the surface of the torus and also the angular deflection along normal directions on the unit sphere transported from the torus. Additionally, a new visualization technique for circular data is introduced. The practical relevance of the model is illustrated through its application to wind-wave directional datasets from two major cyclonic events, Amphan and Biparjoy, that impacted the eastern and western coastlines of India, respectively.

stat.ME↗

arXiv2025

Change-point problem: Direct estimation using a geometry inspired identifiable reparameterization

Estimation of mean shift in a temporally ordered sequence of random variables with a possible existence of change-point is an important problem in many disciplines. In the available literature of more than fifty years the estimation methods of the mean shift is usually dealt as a two-step problem. A test for the existence of a change-point is followed by an estimation process of the mean shift, which is known as testimator. The problem suffers from over parametrization. When viewed as an estimation problem, we establish that the maximum likelihood estimator (MLE) always gives a false alarm indicting an existence of a change-point in the given sequence even though there is no change-point at all. After modelling the parameter space as a modified horn torus. We introduce a new method of estimation of the parameters. The newly introduced estimation method of the mean shift is assessed with a proper Riemannian metric on that conic manifold. It is seen that its performance is superior compared to that of the MLE. The proposed method is implemented on Bitcoin data and compared its performance with the performance of the MLE.

stat.ME↗

arXiv2024

Semi-parametric least-area linear-circular regression through M\"{o}bius transformation

This paper introduces a novel regression model designed for angular response variables with linear predictors, utilizing a generalized M\"{o}bius transformation to define the regression curve. By mapping the real axis to the circle, the model effectively captures the relationship between linear and angular components. A key innovation is the introduction of an area-based loss function, inspired by the geometry of a curved torus, for efficient parameter estimation. The semi-parametric nature of the model eliminates the need for specific distributional assumptions about the angular error, enhancing its versatility. Extensive simulation studies, incorporating von Mises and wrapped Cauchy distributions, highlight the robustness of the framework. The model's practical utility is demonstrated through real-world data analysis of Bitcoin and Ethereum, showcasing its ability to derive meaningful insights from complex data structures.

stat.ME↗

arXiv2024

Intrinsic Geometry-Based Angular Covariance: A Novel Framework for Nonparametric Changepoint Detection in Meteorological Data

In many temporal datasets, the parameters of the underlying distribution may change abruptly at unknown times. Detecting such changepoints is crucial for numerous applications. Although such a problem has been extensively studied for linear data, there has been notably less research on bivariate angular data. To the best of our knowledge, this paper presents the first attempt to address the changepoint detection problem for the mean direction of toroidal and spherical data. By defining the ``square of an angle'' through intrinsic geometry, we construct a curved dispersion matrix for bivariate angular data, analogous to the linear dispersion matrix in Euclidean space. Using the analogous measure of the ``Mahalanobis distance,'' we develop two new non-parametric tests to identify changes in the mean direction parameters for toroidal and spherical distributions. The pivotal distributions of the test statistics are shown to follow the Kolmogorov distribution under the null hypothesis. Under the alternative hypothesis, we establish the consistency of the proposed tests. We also apply the proposed methods to detect changes in mean direction for hourly wind-wave direction (toroidal) measurements and the path (spherical) of the cyclonic storm ``Biporjoy,'' which occurred between 6th and 19th June 2023 over the Arabian Sea, western coast of India.

stat.ME↗

arXiv2024

Intrinsic geometry-inspired dependent toroidal distribution: Application to regression model for astigmatism data

This paper introduces a dependent toroidal distribution, to analyze astigmatism data following cataract surgery. Rather than utilizing the flat torus, we opt to represent the bivariate angular data on the surface of a curved torus, which naturally offers smooth edge identifiability and accommodates a variety of curvatures: positive, negative, and zero. Beginning with the area-uniform toroidal distribution on this curved surface, we develop a five-parameter-dependent toroidal distribution that harnesses its intrinsic geometry via the area element to model the distribution of two dependent circular random variables. We show that both marginal distributions are Cardioid, with one of the conditional variables also following a Cardioid distribution. This key feature enables us to propose a circular-circular regression model based on conditional expectations derived from circular moments. To address the high rejection rate (approximately 50%) in existing acceptance-rejection sampling methods for Cardioid distributions, we introduce an exact sampling method based on a probabilistic transformation. Additionally, we generate random samples from the proposed dependent toroidal distribution through suitable conditioning. This bivariate distribution and the regression model are applied to analyze astigmatism data arising in the follow-up of one and three months due to cataract surgery.

stat.AP↗

arXiv2024

An Efficient Sampling from Circular Distributions and its Extension to Toroidal Distributions

Sampling from circular distributions is a fundamental task in directional statistics. A key challenge in acceptance-rejection methods lies in selecting an efficient envelope density, as poor choices can lead to low acceptance rates and increased computational cost, especially in large-scale simulations. To address this, we propose a new sampling framework that utilizes the idea of upper Riemann sums to construct a piecewise envelope. This method ensures validity for any Riemann-integrable target density on a bounded interval. This method exhibits enhanced efficacy relative to the present sampling method for the von Mises distribution. Additionally, we introduce a flexible family of distributions defined on the surface of a curved torus, using its area element. The proposed sampling method is then employed to generate samples from the toroidal model. We explore the maximum entropy characterization and other theoretical properties of one of the marginal distributions arising from this construction for the von Mises distribution. To illustrate the practical utility of our framework, we apply the model to a real dataset on wind direction.

stat.ME↗

arXiv2024

A geometric approach in non-parametric Changepoint detection in circular data

In many temporally ordered data sets, it is observed that the parameters of the underlying distribution change abruptly at unknown times. The detection of such changepoints is important for many applications. While this problem has been studied substantially in the linear data setup, not much work has been done for angular data. In this article, we utilize the intrinsic geometry of a torus to propose new non-parametric tests. First, we propose new tests for the existence of changepoint(s) in the concentration, and second, a test to detect mean direction and/or concentration. The limiting distributions of the test statistics are derived, and their powers are obtained using extensive simulation. It is seen that the tests have better power than the corresponding existing tests. The proposed methods have been implemented on three real-life data sets, revealing interesting insights. In particular, our method, when used to detect simultaneous changes in mean direction and concentration for hourly wind direction measurements of the cyclonic storm "Amphan," identified changepoints that could be associated with important meteorological events.

stat.ME↗

arXiv2023

Sampling from the surface of a curved torus: A new genesis

The distributions of toroidal data, often viewed as an extension of circular distributions, do not consider the intrinsic geometry of a curved torus. For the first time, Diaconis et al. (2013)[Diaconis, P., Holmes, S., & Shahshahani, M. (2013). Sampling from a manifold. Advances in modern statistical theory and applications: a Festschrift in honor of Morris L. Eaton, 10, 102-125.] introduce uniform distribution on the surface of a curved torus with respect to its surface area. But the suggested acceptance-rejection method of sampling from it rejects approximately half of the data. We propose a probabilistic transformation for sampling from the same distribution without losing data. In addition, we introduce a new genesis of random samples from some popular circular distributions using histogram-based acceptance-rejection sampling that uses a very thin envelope. The idea leads to generalizing for sampling from distributions on the surface of a curved torus with a high acceptance rate.Apart from reducing computational cost in the inferential study of different toroidal distributions, uniform sampling from the surface of a curve torus will be helpful to understand any unknown distribution on it.

stat.ME↗

arXiv2022

MDAS: A Diagnostic Approach to Assess the Quality of Data Splitting in Machine Learning

In the field of machine learning, model performance is usually assessed by randomly splitting data into training and test sets. Different random splits, however, can yield markedly different performance estimates, so a genuinely good model may be discarded or a poor one selected purely due to an unlucky partition. This motivates a principled way to diagnose the quality of a given data split. We propose a diagnostic framework based on a new discrepancy measure, the Mahalanobis Distribution Alignment Score (MDAS). MDAS is a symmetric dissimilarity measure between two multivariate samples, rather than a strict metric. MDAS captures both mean and covariance differences and is affine invariant. Building on this, we construct a Monte Carlo test that evaluates whether an observed split is statistically compatible with typical random splits, yielding an interpretable p-value for split quality. Using several real data sets, we study the relationship between MDAS and model robustness, including its association with the normalized Akaike information criterion. Finally, we apply MDAS to compare existing state-of-the-art deterministic data-splitting strategies with standard random splitting. The experimental results show that MDAS provides a simple, model-agnostic tool for auditing data splits and improving the reliability of empirical model evaluation.

stat.CO↗

arXiv2020

A model for the spread of an epidemic from local to global: A case study of COVID-19 in India

In this paper we propose an epidemiological model for the spread of COVID-19. The dynamics of the spread is based on four fundamental categories of people in a population: Tested and infected, Non-Tested but infected, Tested but not infected, and non-Tested and not infected. The model is based on two levels of dynamics of spread in the population: at local level and at the global level. The local level growth is described with data and parameters which include testing statistics for COVID-19, preventive measures such as nationwide lockdown, and the migration of people across neighboring locations. In the context of India, the local locations are considered as districts and migration or traffic flow across districts are defined by normalized edge weight of the metapopulation network of districts which are infected with COVID-19. Based on this local growth, state level predictions for number of people tested with COVID-19 positive are made. Further, considering the local locations as states, prediction is made for the country level. The values of the model parameters are determined using grid search and minimizing an error function while training the model with real data. The predictions are made based on the present statistics of testing, and certain linear and log-linear growth of testing at state and country level. Finally, it is shown that the spread can be contained if number of testing can be increased linearly or log-linearly by certain factors along with the preventive measures in near future. This is also necessary to prevent the sharp growth in the count of infected and to get rid of the second wave of pandemic.

physics.soc-ph↗

arXiv2015

On existence of a change in mean of functional data

Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes, it is crucial to know about the existence of change point in a given sequence of functional data before doing any further statistical inference. We develop a new methodology to provide a test for detecting a change in the mean function of the corresponding data. To obtain the test statistic we provide an alternative estimator of the covariance kernel. The proposed estimator is asymptotically unbiased under the null hypothesis and, at the same time, has smaller amount of bias than that of the existing estimator. We show here that under the null hypothesis the proposed test statistic is pivotal asymptotically. Moreover, it is shown that under alternative hypothesis the test is consistent for large enough sample size. It is also found that the proposed test is more powerful than the available test procedure in the literature. From the extensive simulation studies we observe that the proposed test outperforms the existing one with a wide margin in power for moderate sample size. The developed methodology performs satisfactorily for the average daily temperature of central England and monthly global average anomaly of temperatures.

stat.ME↗