arXiv subjects

Aishwarya Bhaskaran

Publications and source records attributed to Aishwarya Bhaskaran.

5 recordsLinked to original sources

arXiv2026

Stabilised weighted data subsampling for accelerated inference in models with recursive likelihoods

Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased estimator of the log-likelihood. By assigning higher sampling probabilities to early observations, the method reduces the effective depth of recursive likelihood evaluations and hence computational cost. However, sampling probabilities that decay too slowly yield limited savings, while overly aggressive decay can substantially inflate estimator variance. We develop a stabilisation framework, supported by theory, that restricts the decay to avoid both computational and variance pathologies through principled hyperparameter tuning. We also derive an unbiased subsampling estimator of the log-likelihood gradient, enabling gradient-based inference. The methodology can be embedded within a range of inferential frameworks. We illustrate its use in variational Bayes and subsampling Markov chain Monte Carlo for conditional volatility models, including leverage effects. Empirical results show substantial computational speed-ups relative to full-data methods while maintaining inferential accuracy. We also compare with recent stochastic gradient MCMC and divide-and-conquer MCMC methods for temporally dependent data, observing favourable empirical performance.

stat.ME↗

arXiv2024

A maximum penalised likelihood approach for semiparametric accelerated failure time models with time-varying covariates and partly interval censoring

Accelerated failure time (AFT) models are frequently used to model survival data, providing a direct quantification of the relationship between event times and covariates. These models allow for the acceleration or deceleration of failure times through a multiplicative factor that accounts for the effect of covariates. While existing literature provides numerous methods for fitting AFT models with time-fixed covariates, adapting these approaches to scenarios involving both time-varying covariates and partly interval-censored data remains challenging. Motivated by a randomised clinical trial dataset on advanced melanoma patients, we propose a maximum penalised likelihood approach for fitting a semiparametric AFT model to survival data with partly interval-censored failure times. This method also accommodates both time-fixed and time-varying covariates. We utilise Gaussian basis functions to construct a smooth approximation of the non-parametric baseline hazard and fit the model using a constrained optimisation approach. The effectiveness of our method is demonstrated through extensive simulations. Finally, we illustrate the relevance of our approach by applying it to a dataset from a randomised clinical trial involving patients with advanced melanoma.

stat.ME↗

arXiv2023

Second Term Improvement to Generalised Linear Mixed Model Asymptotics

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average within-group sample size then the asymptotic variances have orders $m^{-1}$ and $(mn)^{-1}$, depending on the parameter. We extend this theory to provide explicit forms of the $(mn)^{-1}$ second terms of the asymptotically harder-to-estimate parameters. Improved accuracy of studentised confidence intervals is one consequence of our theory.

math.ST↗

arXiv2022

Dispersion Parameter Extension of Precise Generalized Linear Mixed Model Asymptotics

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically normal distributions with asymptotic mutual independence between fixed effects, random effects covariance and dispersion parameters. The dispersion parameter maximum likelihood estimator has a particularly simple asymptotic distribution which enables straightforward valid likelihood-based inference.

math.ST↗

arXiv2019

Conditionally structured variational Gaussian approximation with importance weights

We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of variational approximations that exploit this partitioning and go beyond Gaussian variational approximation. This approximation is motivated by the fact that in many hierarchical models, there are global variance parameters which determine the scale of local latent variables in their posterior conditional on the global parameters. We also consider parsimonious parametrizations by using conditional independence structure, and improved estimation of the log marginal likelihood and variational density using importance weights. These methods are shown to improve significantly on Gaussian variational approximation methods for a similar computational cost. Application of the methodology is illustrated using generalized linear mixed models and state space models.

stat.CO↗