Publications (45)
Asynchronous Gibbs Sampling
Alexander Terenin, Daniel Simpson, David Draper
Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their…
On the convergence of the Escalator Boxcar Train
à ke Brännström, Linus Carlsson, Daniel Simpson
The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to investigate the dynamics of physiologically structured population models, i.e.,…
Non-stationary Spatial Modelling with Applications to Spatial Prediction of Precipitation
Geir-Arne Fuglstad, Daniel Simpson, Finn Lindgren +1
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structur…
Multivariate Gaussian Random Fields with Oscillating Covariance Functions using Systems of Stochastic Partial Differential Equations
Xiangping Hu, Finn Lindgren, Daniel Simpson +1
In this paper we propose a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) with oscillating covariance functions through systems of stochastic parti…
Treatment effect estimation with Multilevel Regression and Poststratification
Yuxiang Gao, Lauren Kennedy, Daniel Simpson
Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Traditionally, MRP studie…
Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation: Bayesian inference for latent Gaussian models and beyond
Charles C. Margossian, Aki Vehtari, Daniel Simpson +1
Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as…
Pareto Smoothed Importance Sampling
Aki Vehtari, Daniel Simpson, Andrew Gelman +2
Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the…
Spatial Modeling, with Application to Complex Survey Data: Discussion of "Model-based Geostatistics for Prevalence Mapping in Low-Resource Settings", by Diggle and Giorgi
Jon Wakefield, Daniel Simpson, Jessica Godwin
Prevalence mapping in low resource settings is an increasingly important endeavor to guide policy making and to spatially and temporally characterize the burden of disease. We will…
Discussion of "Geodesic Monte Carlo on Embedded Manifolds"
Simon Byrne, Mark Girolami, Persi Diaconis +9
Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)
Spatial Modelling of Temperature and Humidity using Systems of Stochastic Partial Differential Equations
Xiangping Hu, Ingelin Steinsland, Daniel Simpson +2
This work is motivated by constructing a weather simulator for precipitation. Temperature and humidity are two of the most important driving forces of precipitation, and the strate…
Explainable Deep Learning Models for Dynamic and Online Malware Classification
Quincy Card, Daniel Simpson, Kshitiz Aryal +2
In recent years, there has been a significant surge in malware attacks, necessitating more advanced preventive measures and remedial strategies. While several successful AI-based m…
Computationally efficient spatial modeling of annual maximum 24 hour precipitation. An application to data from Iceland
Ãli Páll Geirsson, Birgir Hrafnkelsson, Daniel Simpson
We propose a computationally efficient statistical method to obtain distributional properties of annual maximum 24 hour precipitation on a 1 km by 1 km regular grid over Iceland. A…
Discussion of "Sequential Quasi-Monte Carlo" by Mathieu Gerber and Nicolas Chopin
Chris. J. Oates, Daniel Simpson, Mark Girolami
A discussion on the possibility of reducing the variance of quasi-Monte Carlo estimators in applications. Further details are provided in the accompanying paper "Variance Reduction…
The use of systems of stochastic PDEs as priors for multivariate models with discrete structures
Erlend Aune, Daniel Simpson
A challenge in multivariate problems with discrete structures is the inclusion of prior information that may differ in each separate structure. A particular example of this is seis…
Using stacking to average Bayesian predictive distributions
Yuling Yao, Aki Vehtari, Daniel Simpson +1
The widely recommended procedure of Bayesian model averaging is flawed in the M-open setting in which the true data-generating process is not one of the candidate models being fit.…
The experiment is just as important as the likelihood in understanding the prior: A cautionary note on robust cognitive modelling
Lauren Kennedy, Daniel Simpson, Andrew Gelman
Cognitive modelling shares many features with statistical modelling, making it seem trivial to borrow from the practices of robust Bayesian statistics to protect the practice of ro…
The MCMC split sampler: A block Gibbs sampling scheme for latent Gaussian models
Ãli Páll Geirsson, Birgir Hrafnkelsson, Daniel Simpson +1
A novel computationally efficient Markov chain Monte Carlo (MCMC) scheme for latent Gaussian models (LGMs) is proposed in this paper. The sampling scheme is a two block Gibbs sampl…
Fast approximate inference with INLA: the past, the present and the future
Daniel Simpson, Finn Lindgren, HÃ¥vard Rue
Latent Gaussian models are an extremely popular, flexible class of models. Bayesian inference for these models is, however, tricky and time consuming. Recently, Rue, Martino and Ch…
Using sex and gender in survey adjustment
Lauren Kennedy, Katharine Khanna, Daniel Simpson +3
Accounting for sex and gender is a challenge in social science research. While other methodology papers consider issues surrounding appropriate measurement, we consider the problem…
Think continuous: Markovian Gaussian models in spatial statistics
Daniel Simpson, Finn Lindgren, HÃ¥vard Rue
Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRF…
Improving multilevel regression and poststratification with structured priors
Yuxiang Gao, Lauren Kennedy, Daniel Simpson +1
A central theme in the field of survey statistics is estimating population-level quantities through data coming from potentially non-representative samples of the population. Multi…
Multivariate Gaussian Random Fields Using Systems of Stochastic Partial Differential Equations
Xiangping Hu, Daniel Simpson, Finn Lindgren +1
In this paper a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduc…
Scalable Bayesian Learning with posteriors
Samuel Duffield, Kaelan Donatella, Johnathan Chiu +2
Although theoretically compelling, Bayesian learning with modern machine learning models is computationally challenging since it requires approximating a high dimensional posterior…
Assessment of fiducial motion in CBCT projections of the abdominal tumor using template matching and sequential stereo triangulation
Oluwaseyi M. Oderinde, Hassan Mostafavi, Daniel Simpson +3
Purpose: To assess the fiducial motion in abdominal stereotactic body radiotherapy (SBRT) using the cone-beam computed tomography (CBCT) projections acquired for pre-treatment pati…
The prior can generally only be understood in the context of the likelihood
Andrew Gelman, Daniel Simpson, Michael Betancourt
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, refe…
Going off grid: Computationally efficient inference for log-Gaussian Cox processes
Daniel Simpson, Janine Illian, Finn Lindgren +2
This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuous…
The Integrated Nested Laplace Approximation for fitting Dirichlet regression models
JoaquÃn MartÃnez-Minaya, Finn Lindgren, Antonio López-QuÃlez +2
This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness…
On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
Anne-Marie Lyne, Mark Girolami, Yves Atchadé +2
A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal…
Specifying Gaussian Markov Random Fields with Incomplete Orthogonal Factorization using Givens Rotations
Xiangping Hu, Daniel Simpson, HÃ¥vard Rue
In this paper an approach for finding a sparse incomplete Cholesky factor through an incomplete orthogonal factorization with Givens rotations is discussed and applied to Gaussian…
Bayesian Adaptive Smoothing Spline using Stochastic Differential Equations
Yu Ryan Yue, Daniel Simpson, Finn Lindgren +1
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathemati…
Data integration for high-resolution, continental-scale estimation of air pollution concentrations
Matthew L. Thomas, Gavin Shaddick, Daniel Simpson +2
Air pollution constitutes the highest environmental risk factor in relation to heath. In order to provide the evidence required for health impact analyses, to inform policy and to…
Non-stationary Gaussian models with physical barriers
Haakon Bakka, Jarno Vanhatalo, Janine Illian +2
The classical tools in spatial statistics are stationary models, like the Matérn field. However, in some applications there are boundaries, holes, or physical barriers in the stud…
Validating Bayesian Inference Algorithms with Simulation-Based Calibration
Sean Talts, Michael Betancourt, Daniel Simpson +2
Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model imple…
Beyond the Valley of the Covariance Function
Daniel Simpson, Finn Lindgren, HÃ¥vard Rue
Discussion of "Cross-Covariance Functions for Multivariate Geostatistics" by Genton and Kleiber [arXiv:1507.08017].
Spatial modelling with R-INLA: A review
Haakon Bakka, HÃ¥vard Rue, Geir-Arne Fuglstad +5
Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realist…
Constructing Priors that Penalize the Complexity of Gaussian Random Fields
Geir-Arne Fuglstad, Daniel Simpson, Finn Lindgren +1
Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides…
Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy
Geir-Arne Fuglstad, Finn Lindgren, Daniel Simpson +1
Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is t…
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Aki Vehtari, Andrew Gelman, Daniel Simpson +2
Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this pape…
Visualization in Bayesian workflow
Jonah Gabry, Daniel Simpson, Aki Vehtari +2
Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian da…
Does non-stationary spatial data always require non-stationary random fields?
Geir-Arne Fuglstad, Daniel Simpson, Finn Lindgren +1
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stati…
Bayesian Workflow
Andrew Gelman, Aki Vehtari, Daniel Simpson +7
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilis…
Thermodynamic Linear Algebra
Maxwell Aifer, Kaelan Donatella, Max Hunter Gordon +5
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardw…
Yes, but Did It Work?: Evaluating Variational Inference
Yuling Yao, Aki Vehtari, Daniel Simpson +1
While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. We propose two diag…
An intuitive Bayesian spatial model for disease mapping that accounts for scaling
Andrea Riebler, Sigrunn H. Sørbye, Daniel Simpson +1
In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulat…
Bayesian computing with INLA: new features
Thiago G. Martins, Daniel Simpson, Finn Lindgren +1
The INLA approach for approximate Bayesian inference for latent Gaussian models has been shown to give fast and accurate estimates of posterior marginals and also to be a valuable…