arXiv subjects

Abhranil Das

Publications and source records attributed to Abhranil Das.

3 recordsLinked to original sources

arXiv2024

New methods to compute the generalized chi-square distribution

We present four new mathematical methods, two exact and two approximate, along with open-source software, to compute the cdf, pdf and inverse cdf of the generalized chi-square distribution. Some methods are geared for speed, while others are designed to be accurate far into the tails, using which we can also measure large values of the discriminability index $d'$ between multivariate normal distributions. We compare the accuracy and speed of these and previous methods, characterize their advantages and limitations, and identify the best methods to use in different cases.

stat.CO↗

arXiv2020

Methods to integrate multinormals and compute classification measures

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases, there exist no general analytical expressions, standard numerical methods or software for these integrals. Here we present mathematical results and open-source software that provide (i) the probability in any domain of a normal in any dimensions with any parameters, (ii) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector, (iii) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index and relation to the operating characteristic, (iv) ways to scale the discriminability of two distributions, (v) dimension reduction and visualizations for such problems, and (vi) tests for how reliably these methods may be used on given data. We demonstrate these tools with vision research applications of detecting occluding objects in natural scenes, and detecting camouflage.

stat.ML↗

arXiv2015

Transient dynamics in the thermal ratchets transport model

The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet model in response to periodic switching. Transient aperiodic behavior is observed that converges asymptotically to the period of the switching. We study measures of the transport rate, the transient lifetime, and an equivalent of `amplitude', then investigate their dependence on various properties of the system, along with other features of the transient and asymptotic dynamics.

cond-mat.stat-mech↗