arXiv subjects

Matias Quiroz

Publications and source records attributed to Matias Quiroz.

At least 19 recordsLinked to original sources

arXiv2026

How does academic performance affect self-efficacy? Interpretable modelling through latent academic achievement

There is increasing evidence of a directional relationship from academic performance to self-efficacy. We develop a Bayesian model for investigating this relationship when academic performance is measured on an ordinal scale and self-efficacy on a continuous scale. The model allows latent academic achievement to enter the self-efficacy regression as a predictor, while Bayesian variable selection identifies factors associated with either response. The resulting conditional formulation yields an interpretable regression characterisation of how latent academic achievement relates to self-efficacy. Furthermore, it enables a tailored partially collapsed Gibbs sampler that analytically integrates out the regression coefficients when updating the variable inclusion indicators. Simulation studies demonstrate that the proposed conditional formulation and tailored sampler improve sampling efficiency and variable-selection performance relative to a recent, more general joint Gaussian copula regression formulation. We apply the methodology to data from the longitudinal study of Australian children, a landmark national cohort study covering children's education, social and emotional wellbeing, health and family circumstances. The model and analysis shed light on how latent academic achievement relates to self-efficacy in Australian children, and reveal that the two outcomes differ markedly in the range of covariates associated with each outcome.

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arXiv2026

Spectral subsampling MCMC for L\'evy-driven continuous-time ARMA models with expensive likelihood contributions

Subsampling-based Markov chain Monte Carlo (MCMC) algorithms aim to accelerate Bayesian inference by evaluating the likelihood using only a subset of the data at each iteration. However, in many standard tall-data applications, individual likelihood contributions are inexpensive to evaluate and the resulting reductions in actual computing time are often substantially smaller than the nominal reduction in data size due to computational overhead. We study a different computational regime arising in frequency-domain inference for continuous-time processes observed at equally spaced discrete time points. This gives rise to aliasing, whereby each contribution to the Whittle likelihood requires summation over shifted frequency components, unlike standard discrete-time spectral settings where spectral evaluations do not require such summation. We demonstrate that this structure makes subsampling MCMC, a subsampling-based MCMC approach that estimates the log-likelihood using data subsampling and efficient control variates, particularly effective for reducing computational cost. We illustrate the approach for Bayesian frequency-domain inference in discretely observed continuous-time autoregressive moving average models driven by finite second-moment L\'evy processes.

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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.

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arXiv2026

Analysing symbolic data by pseudo-marginal methods

Symbolic data analysis (SDA) aggregates large individual-level datasets into a small number of distributional summaries, such as random rectangles or random histograms. The inference is carried out using these summaries in place of the original dataset, resulting in computational gains at the loss of some information. In likelihood-based SDA, the likelihood function is characterised by an integral with a large exponent, which limits the method's utility as for typical models the integral is unavailable in closed form. In addition, the likelihood function is known to produce biased parameter estimates in some circumstances. Our article develops a Bayesian framework for SDA methods in these settings that resolves the issues resulting from integral intractability and biased parameter estimation using pseudo-marginal Markov chain Monte Carlo methods. We develop an exact but computationally expensive method based on path sampling and the Poisson estimator, and a much faster, but approximate, method based on a Taylor expansion. Through simulation and real-data examples we demonstrate the performance of the developed methods, showing large reductions in computation time compared to the full-data analysis, with only a small loss of information.

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arXiv2026

Dynamic linear regression models for forecasting time series with semi long memory errors

Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to follow a stationary autoregressive integrated moving average (ARIMA) model, or its seasonal variants, which are unable to capture a long-range dependence structure (long memory) of the error process. We propose a novel dynamic linear regression model that incorporates the long-range dependence feature of the errors and show that the proposed error process may: (i) have a significant impact on the posterior uncertainty of the estimated regression parameters and (ii) improve the model's forecasting ability. We develop a Markov chain Monte Carlo method to fit general dynamic linear regression models based on a frequency domain approach that enables fast, asymptotically exact Bayesian inference for large datasets. We demonstrate that our approximate algorithm is faster than the traditional time domain approaches, such as the Kalman filter and the multivariate Gaussian likelihood, while producing a highly accurate approximation to the posterior. The method is illustrated in simulated examples and two energy forecasting applications, showing that it outperforms approaches that do not account for semi-long memory, as well as a state-of-the-art neural-network-based forecasting procedure.

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arXiv2025

A correlated pseudo-marginal approach to doubly intractable problems

Doubly intractable models are encountered in a number of fields, e.g. social networks, ecology and epidemiology. Inference for such models requires the evaluation of a likelihood function, whose normalising factor depends on the model parameters and is assumed to be computationally intractable. The normalising constant of the posterior distribution and the additional normalising factor of the likelihood function result in a so-called doubly intractable posterior, for which it is difficult to directly apply Markov chain Monte Carlo methods. We propose a signed pseudo-marginal Metropolis-Hastings algorithm with an unbiased block-Poisson estimator to sample from the posterior distribution of doubly intractable models. As the estimator can be negative, the algorithm targets the absolute value of the estimated posterior and uses an importance sampling estimator to ensure simulation-consistent estimates of the posterior mean of a function of the parameters. The importance sampling estimator can perform poorly when its denominator is close to zero. We derive a finite-sample concentration inequality that ensures, with high probability, that this pathological case does not occur. Our estimator for doubly intractable problems has three advantages over existing estimators. First, the estimator is well-suited for efficient parallelisation and vectorisation. Second, its structure is ideal for correlated pseudo-marginal methods, which are well known to dramatically increase sampling efficiency. Third, the estimator enables the derivation of heuristic guidelines for tuning its hyperparameters under simplifying assumptions. We demonstrate the superior performance of our method in the standard benchmark example that models correlated spatial data using the Ising model, as well as the Kent distribution model for spherical data.

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arXiv2025

Calibrated Bayesian inference for random fields on large irregular domains using the debiased spatial Whittle likelihood

Bayesian inference for stationary random fields is computationally demanding. Whittle-type likelihoods in the frequency domain based on the fast Fourier Transform (FFT) have several appealing features: i) low computational complexity of only $\mathcal{O}(n \log n)$, where $n$ is the number of spatial locations, ii) robustness to assumptions of the data-generating process, iii) ability to handle missing data and irregularly spaced domains, and iv) flexibility in modelling the covariance function via the spectral density directly in the spectral domain. It is well known, however, that the Whittle likelihood suffers from bias and low efficiency for spatial data. The debiased Whittle likelihood is a recently proposed alternative with better frequentist properties. We propose a methodology for Bayesian inference for stationary random fields using the debiased spatial Whittle likelihood, with an adjustment from the composite likelihood literature. The adjustment is shown to give a well-calibrated Bayesian posterior as measured by coverage properties of credible sets, without sacrificing the quasi-linear computation time. We apply the method to simulated data and two real datasets.

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arXiv2025

A Scalable Gradient-Based Optimization Framework for Sparse Minimum-Variance Portfolio Selection

Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality constraint: only $k$ assets from a universe of $p$ may be included. The standard approach models this problem as a mixed-integer quadratic program and relies on commercial solvers to find the optimal solution. However, the computational costs of such methods increase exponentially with $k$ and $p$, making them too slow for problems of even moderate size. We propose a fast and scalable gradient-based approach that transforms the combinatorial sparse selection problem into a constrained continuous optimization task via Boolean relaxation, while preserving equivalence with the original problem on the set of binary points. Our algorithm employs a tunable parameter that transmutes the auxiliary objective from a convex to a concave function. This allows a stable convex starting point, followed by a controlled path toward a sparse binary solution as the tuning parameter increases and the objective moves toward concavity. In practice, our method matches commercial solvers in asset selection for most instances and, in rare instances, the solution differs by a few assets whilst showing a negligible error in portfolio variance.

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arXiv2024

Forecasting realized covariances using HAR-type models

We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First, modeling the logs of the marginal volatilities is strongly preferred over direct modeling of marginal volatility. Thus, our proposed model that accounts for attenuation bias (for the log-response) provides superior one-step-ahead forecasts over existing multivariate realized covariance approaches. Second, accounting for measurement errors in marginal realized variances generally improves multivariate forecasting performance, but to a lesser degree than previously found in the literature. Third, time-varying parameter models based on state-space models perform almost equally well. Fourth, statistical and economic criteria for comparing the forecasting performance lead to some differences in the models' rankings, which can partially be explained by the turbulent post-pandemic data in our out-of-sample validation dataset using sub-sample analyses.

econ.EM↗

arXiv2024

Perturbations of Markov Chains

This chapter surveys progress on three related topics in perturbations of Markov chains: the motivating question of when and how "perturbed" MCMC chains are developed, the theoretical problem of how perturbation theory can be used to analyze such chains, and finally the question of how the theoretical analyses can lead to practical advice.

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arXiv2022

Spectral Subsampling MCMC for Stationary Multivariate Time Series with Applications to Vector ARTFIMA Processes

Spectral subsampling MCMC was recently proposed to speed up Markov chain Monte Carlo (MCMC) for long stationary univariate time series by subsampling periodogram observations in the frequency domain. This article extends the approach to multivariate time series using a multivariate generalisation of the Whittle likelihood. To assess the computational gains from spectral subsampling in challenging problems, a multivariate generalisation of the autoregressive tempered fractionally integrated moving average model (ARTFIMA) is introduced and some of its properties derived. Bayesian inference based on the Whittle likelihood is demonstrated to be a fast and accurate alternative to the exact time domain likelihood. Spectral subsampling is shown to provide up to two orders of magnitude additional speed-up, while retaining MCMC sampling efficiency and accuracy, compared to spectral methods using the full dataset. Keywords: Bayesian, Markov chain Monte Carlo, Semi-long memory, Spectral analysis, Whittle likelihood.

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arXiv2020

The block-Poisson estimator for optimally tuned exact subsampling MCMC

Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favourably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature.

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arXiv2020

Subsampling Sequential Monte Carlo for Static Bayesian Models

We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is an advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. A Hamiltonian Monte Carlo update makes distant moves for the model parameters, and a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate both the usefulness and limitations of the methodology for estimating four generalized linear models and a generalized additive model with large datasets.

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arXiv2020

Gaussian variational approximation for high-dimensional state space models

Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The number of parameters in the covariance matrix grows as the square of the number of model parameters, so it is necessary to find simple yet effective parameterizations of the covariance structure when the number of model parameters is large. We approximate the joint posterior distribution over the high-dimensional state vectors by a dynamic factor model, having Markovian time dependence and a factor covariance structure for the states. This gives a reduced description of the dependence structure for the states, as well as a temporal conditional independence structure similar to that in the true posterior. The usefulness of the approach is illustrated for prediction in two high-dimensional applications that are challenging for Markov chain Monte Carlo sampling. The first is a spatio-temporal model for the spread of the Eurasian Collared-Dove across North America; the second is a Wishart-based multivariate stochastic volatility model for financial returns.

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arXiv2020

Spectral Subsampling MCMC for Stationary Time Series

Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of independence. We propose a novel technique for speeding up MCMC for time series data by efficient data subsampling in the frequency domain. For several challenging time series models, we demonstrate a speedup of up to two orders of magnitude while incurring negligible bias compared to MCMC on the full dataset. We also propose alternative control variates for variance reduction based on data grouping and coreset constructions.

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arXiv2019

Hamiltonian Monte Carlo with Energy Conserving Subsampling

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC computationally costly, especially in problems with large datasets, since it is necessary to compute posterior densities and their derivatives with respect to the parameters. Naively computing the Hamiltonian dynamics on a subset of the data causes HMC to lose its key ability to generate distant parameter proposals with high acceptance probability. The key insight in our article is that efficient subsampling HMC for the parameters is possible if both the dynamics and the acceptance probability are computed from the same data subsample in each complete HMC iteration. We show that this is possible to do in a principled way in a HMC-within-Gibbs framework where the subsample is updated using a pseudo marginal MH step and the parameters are then updated using an HMC step, based on the current subsample. We show that our subsampling methods are fast and compare favorably to two popular sampling algorithms that utilize gradient estimates from data subsampling. We also explore the current limitations of subsampling HMC algorithms by varying the quality of the variance reducing control variates used in the estimators of the posterior density and its gradients.

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arXiv2018

Variance reduction properties of the reparameterization trick

The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is overwhelming empirical evidence in the literature showing its success, there is relatively little research exploring why the reparameterization trick is so effective. We explore this under the idealized assumptions that the variational approximation is a mean-field Gaussian density and that the log of the joint density of the model parameters and the data is a quadratic function that depends on the variational mean. From this, we show that the marginal variances of the reparameterization gradient estimator are smaller than those of the score function gradient estimator. We apply the result of our idealized analysis to real-world examples.

stat.ML↗

arXiv2018

Subsampling MCMC - An introduction for the survey statistician

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called pseudo-marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.

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