arXiv subjects

Sujit K. Ghosh

Publications and source records attributed to Sujit K. Ghosh.

23 records · Page 2Linked to original sources

arXiv2019

Assessing Biosimilarity using Functional Metrics

In recent years there have been a lot of interest to test for similarity between biological drug products, commonly known as biologics. Biologics are large and complex molecule drugs that are produced by living cells and hence these are sensitive to the environmental changes. In addition, biologics usually induce antibodies which raises the safety and efficacy issues. The manufacturing process is also much more complicated and often costlier than the small-molecule generic drugs. Because of these complexities and inherent variability of the biologics, the testing paradigm of the traditional generic drugs cannot be directly used to test for biosimilarity. Taking into account some of these concerns we propose a functional distance based methodology that takes into consideration the entire time course of the study and is based on a class of flexible semi-parametric models. The empirical results show that the proposed approach is more sensitive than the classical equivalence tests approach which are usually based on arbitrarily chosen time point. Bootstrap based methodologies are also presented for statistical inference.

stat.ME↗

arXiv2018

How proper are Bayesian models in the astronomical literature?

The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure) such as an unbounded uniform prior is used. Improper priors are often used in the astronomical literature to reflect a lack of prior knowledge, but checking whether the resulting posterior is a probability distribution is sometimes neglected. It turns out that 23 articles out of 75 articles (30.7%) published online in two renowned astronomy journals (ApJ and MNRAS) between Jan 1, 2017 and Oct 15, 2017 make use of Bayesian analyses without rigorously establishing posterior propriety. A disturbing aspect is that a Gibbs-type Markov chain Monte Carlo (MCMC) method can produce a seemingly reasonable posterior sample even when the posterior is not a probability distribution (Hobert and Casella, 1996). In such cases, researchers may erroneously make probabilistic inferences without noticing that the MCMC sample is from a non-existing probability distribution. We review why checking posterior propriety is fundamental in Bayesian analyses, and discuss how to set up scientifically motivated proper priors.

astro-ph.IM↗

arXiv2018

Robust and Accurate Inference via a Mixture of Gaussian and Student's t Errors

A Gaussian measurement error assumption, i.e., an assumption that the data are observed up to Gaussian noise, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t distribution helps reduce the bias. However, it may be less efficient in estimating parameters if the heavy tailed assumption is uniformly applied to all of the data when most of them are normally observed. We propose a mixture error assumption that selectively converts Gaussian errors into Student's t errors according to latent outlier indicators, leveraging the best of the Gaussian and Student's t errors; a parameter estimation can be not only robust but also accurate. Using simulated hospital profiling data and astronomical time series of brightness data, we demonstrate the potential for the proposed mixture error assumption to estimate parameters accurately in the presence of outliers.

stat.ME↗

arXiv2017

Disentangling Time Series Spectra with Gaussian Processes: Applications to Radial Velocity Analysis

Measurements of radial velocity variations from the spectroscopic monitoring of stars and their companions are essential for a broad swath of astrophysics, providing access to the fundamental physical properties that dictate all phases of stellar evolution and facilitating the quantitative study of planetary systems. The conversion of those measurements into both constraints on the orbital architecture and individual component spectra can be a serious challenge, however, especially for extreme flux ratio systems and observations with relatively low sensitivity. Gaussian processes define sampling distributions of flexible, continuous functions that are well-motivated for modeling stellar spectra, enabling proficient search for companion lines in time-series spectra. We introduce a new technique for spectral disentangling, where the posterior distributions of the orbital parameters and intrinsic, rest-frame stellar spectra are explored simultaneously without needing to invoke cross-correlation templates. To demonstrate its potential, this technique is deployed on red-optical time-series spectra of the mid-M dwarf binary LP661-13. We report orbital parameters with improved precision compared to traditional radial velocity analysis and successfully reconstruct the primary and secondary spectra. We discuss potential applications for other stellar and exoplanet radial velocity techniques and extensions to time-variable spectra. The code used in this analysis is freely available as an open source Python package.

astro-ph.SR↗

arXiv2014

Fast Hamiltonian Monte Carlo Using GPU Computing

In recent years, the Hamiltonian Monte Carlo (HMC) algorithm has been found to work more efficiently compared to other popular Markov Chain Monte Carlo (MCMC) methods (such as random walk Metropolis-Hastings) in generating samples from a posterior distribution. A general framework for HMC based on the use of graphical processing units (GPUs) is shown to greatly reduce the computing time needed for Bayesian inference. The most expensive computational tasks in HMC are the evaluation of the posterior kernel and computing its gradient with respect to the parameters of interest. One of primary goals of this article to show that by expressing each of these tasks in terms of simple matrix or element-wise operations and maintaining persistent objects in GPU memory, the computational time can be drastically reduced. By using GPU objects to perform the entire HMC simulation, most of the latency penalties associated with transferring data from main to GPU memory can be avoided. Thus, the proposed computational framework is conceptually very simple, but also is general enough to be applied to most problems that use HMC sampling. For clarity of exposition, the effectiveness of the proposed approach is demonstrated in the high-dimensional setting on a standard statistical model - multinomial regression. Using GPUs, analyses of data sets that were previously intractable for fully Bayesian approaches due to the prohibitively high computational cost are now feasible.

stat.CO↗