arXiv subjects

Bao Anh Vu

Publications and source records attributed to Bao Anh Vu.

3 recordsLinked to original sources

arXiv2025

Neural posterior inference with state-space models for calibrating ice sheet simulators

Ice sheet models are routinely used to quantify and project an ice sheet's contribution to sea level rise. In order for an ice sheet model to generate realistic projections, its parameters must first be calibrated using observational data; this is challenging due to the nonlinearity of the model equations, the high dimensionality of the underlying parameters, and limited data availability for validation. This study leverages the emerging field of neural posterior approximation for efficiently calibrating ice sheet model parameters and boundary conditions. We make use of a one-dimensional (flowline) Shallow-Shelf Approximation model in a state-space framework. A neural network is trained to infer the underlying parameters, namely the bedrock elevation and basal friction coefficient along the flowline, based on observations of ice velocity and ice surface elevation. Samples from the approximate posterior distribution of the parameters are then used within an ensemble Kalman filter to infer latent model states, namely the ice thickness along the flowline. We show through a simulation study that our approach yields more accurate estimates of the parameters and states than a state-augmented ensemble Kalman filter, which is the current state-of-the-art. We apply our approach to infer the bed elevation and basal friction along a flowline in Thwaites Glacier, Antarctica.

stat.AP↗

arXiv2025

Recursive variational Gaussian approximation with the Whittle likelihood for linear non-Gaussian state space models

Parameter inference for linear and non-Gaussian state space models is challenging because the likelihood function contains an intractable integral over the latent state variables. While Markov chain Monte Carlo (MCMC) methods provide exact samples from the posterior distribution as the number of samples goes to infinity, they tend to have high computational cost, particularly for observations of a long time series. When inference with MCMC methods is computationally expensive, variational Bayes (VB) methods are a useful alternative. VB methods approximate the posterior density of the parameters with a simple and tractable distribution found through optimisation. This work proposes a novel sequential VB approach that makes use of the Whittle likelihood for computationally efficient parameter inference in linear, non-Gaussian state space models. Our algorithm, called Recursive Variational Gaussian Approximation with the Whittle Likelihood (R-VGA-Whittle), updates the variational parameters by processing data in the frequency domain. At each iteration, R-VGA-Whittle requires the gradient and Hessian of the Whittle log-likelihood, which are available in closed form. Through several examples involving a linear Gaussian state space model; a univariate/bivariate stochastic volatility model; and a state space model with Student's t measurement error, where the latent states follow an autoregressive fractionally integrated moving average (ARFIMA) model, we show that R-VGA-Whittle provides good approximations to posterior distributions of the parameters, and that it is very computationally efficient when compared to asymptotically exact methods such as Hamiltonian Monte Carlo.

stat.CO↗

arXiv2024

R-VGAL: A Sequential Variational Bayes Algorithm for Generalised Linear Mixed Models

Models with random effects, such as generalised linear mixed models (GLMMs), are often used for analysing clustered data. Parameter inference with these models is difficult because of the presence of cluster-specific random effects, which must be integrated out when evaluating the likelihood function. Here, we propose a sequential variational Bayes algorithm, called Recursive Variational Gaussian Approximation for Latent variable models (R-VGAL), for estimating parameters in GLMMs. The R-VGAL algorithm operates on the data sequentially, requires only a single pass through the data, and can provide parameter updates as new data are collected without the need of re-processing the previous data. At each update, the R-VGAL algorithm requires the gradient and Hessian of a "partial" log-likelihood function evaluated at the new observation, which are generally not available in closed form for GLMMs. To circumvent this issue, we propose using an importance-sampling-based approach for estimating the gradient and Hessian via Fisher's and Louis' identities. We find that R-VGAL can be unstable when traversing the first few data points, but that this issue can be mitigated by using a variant of variational tempering in the initial steps of the algorithm. Through illustrations on both simulated and real datasets, we show that R-VGAL provides good approximations to the exact posterior distributions, that it can be made robust through tempering, and that it is computationally efficient.

stat.CO↗