Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming

Riutort-Mayol, Gabriel; Bürkner, Paul‐Christian; Andersen, Michael Riis; Solin, Arno; Vehtari, Aki

doi:10.48550/arxiv.2004.11408

Cited by 12 publications

(12 citation statements)

References 27 publications

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“…where µ(u) is the mean vector and K(u, u ) is the covariance matrix. The latter encompasses all our prior beliefs about the functional association between x and y, including continuity, smoothness, periodicity and scale properties (Riutort-Mayol et al, 2020). For notational simplicity, we set µ(u) = 0, though it is not necessary.…”

Section: Finite Population Bayesian Bootstrapping For Modelingmentioning

confidence: 99%

“…The problem becomes even more severe when the joint posterior distribution of (π A i , y i ) has to be simulated. we propose to use a low-ranked sparse GP based on the Laplace eigenvectors approximation (Riutort-Mayol et al, 2020;Solin and Särkkä, 2020). Such a method reduces the computational complexity up to O(n A l 2 ) where l << n A is the reduced rank of the covariance matrix.…”

Section: Finite Population Bayesian Bootstrapping For Modelingmentioning

confidence: 99%

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Robust and Efficient Bayesian Inference for Non-Probability Samples

Rafei¹,

Elliott²,

Flannagan³

2022

Preprint

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The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian outcomes and may perform poorly in presence of influential pseudo-weights. Furthermore, their variance estimator lacks a unified framework and rely often on asymptotic theory. To address these gaps, we propose an alternative Bayesian approach using a partially linear Gaussian process regression that utilizes a prediction model with a flexible function of the pseudo-inclusion probabilities to impute the outcome variable for the reference survey. By efficiency, we mean not only computational scalability but also superiority with respect to variance. We also show that Gaussian process regression behaves as a kernel matching technique based on the estimated propensity scores, which yields double robustness and lowers sensitivity to influential pseudo-weights. Using the simulated posterior predictive distribution, one can directly quantify the uncertainty of the proposed estimator and derive associated 95% credible intervals. We assess the repeated sampling properties of our method in two simulation studies. The application of this study deals with modeling count data with varying exposures under a non-probability sample setting.

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Section: Finite Population Bayesian Bootstrapping For Modelingmentioning

confidence: 99%

Section: Finite Population Bayesian Bootstrapping For Modelingmentioning

confidence: 99%

Robust and Efficient Bayesian Inference for Non-Probability Samples

Rafei¹,

Elliott²,

Flannagan³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For low-dimensional data with simple covariance functions such as the squared exponential, the differences between a spline GAM and a GP can be small in interpolation (see, e.g. Riutort-Mayol et al, 2020). However, the ability to add much richer structure to the covariance function (such as quasiperiodicity, non-stationarity, etc.)…”

Section: Advantages Of Gaussian Process Modellingmentioning

confidence: 99%

Predicting spatio‐temporal distributions of migratory populations using Gaussian process modelling

Piironen

Laaksonen

2022

Journal of Applied Ecology

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1. Knowledge concerning spatio-temporal distributions of populations is a prerequisite for successful conservation and management of migratory animals.Achieving cost-effective monitoring of large-scale movements is often difficult due to lack of effective and inexpensive methods.2. Taiga bean goose Anser fabalis fabalis and tundra bean goose A. f. rossicus offer an excellent example of a challenging management situation with harvested migratory populations. The subspecies have different conservation statuses and population trends. However, their distribution overlaps during migration to an unknown extent, which, together with their similar appearance, has created a conservation-management dilemma.3. Gaussian process (GP) models are widely adopted in the field of statistics and machine learning, but have seldom been applied in ecology so far. We introduce the R package gplite for GP modelling and use it in our case study together with birdwatcher observation data to study spatio-temporal differences between bean goose subspecies during migration in Finland in 2011-2019.4. We demonstrate that GP modelling offers a flexible and effective tool for analysing heterogeneous data collected by citizens. The analysis reveals spatial and temporal distribution differences between the two bean goose subspecies in Finland. Taiga bean goose migrates through the entire country, whereas tundra bean goose occurs only in a small area in south-eastern Finland and migrates later than taiga bean goose. Synthesis and applications.Within the studied bean goose populations, harvest can be targeted at abundant tundra bean goose by restricting hunting to southeastern Finland and to the end of the migration period. In general, our approach combining citizen science data with GP modelling can be applied to study spatiotemporal distributions of various populations and thus help in solving challenging management situations. The introduced R package gplite can be applied | 1147

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“…Evaluating a full-rank, Gaussian process with differentiable trajectories on the entirety of the mesh would be prohibitively expensive due to the O(n 3 ) computational complexity. Instead, we work with a low-rank representation of C(t) based on the framework introduced in [31]. This leads to the representation of the low-rank projection of C(t), denoted by Ĉ(t)…”

Section: Bayesian Inferencementioning

confidence: 99%

Estimating the fitness cost and benefit of antimicrobial resistance from pathogen genomic data

Helekal

Keeling

Grad

et al. 2022

Preprint

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Increasing levels of antibiotic resistance in many bacterial pathogen populations is a major threat to public health. Resistance to an antibiotic provides a fitness benefit when the bacteria is exposed to this antibiotic, but resistance also often comes at a cost to the resistant pathogen relative to susceptible counterparts. We lack a good understanding of these benefits and costs of resistance for many bacterial pathogens and antibiotics, but estimating them could lead to better use of antibiotics in a way that reduces or prevents the spread of resistance. Here, we propose a new model for the joint epidemiology of susceptible and resistant variants, which includes explicit parameters for the cost and benefit of resistance. We show how Bayesian inference can be performed under this model using phylogenetic data from susceptible and resistant lineages and that by combining data from both we are able to disentangle and estimate the resistance cost and benefit parameters separately. We applied our inferential methodology to several simulated datasets to demonstrate good scalability and accuracy. We analysed a dataset of Neisseria gonorrhoeae genomes collected between 2000 and 2013 in the USA. We found that two unrelated lineages resistant to fluoroquinolones shared similar epidemic dynamics and resistance parameters. Fluoroquinolones were abandoned for the treatment of gonorrhoea due to increasing levels of resistance, but our results suggest that they could be used to treat a minority of around 10% of cases without causing resistance to grow again.

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Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming

Cited by 12 publications

References 27 publications

Robust and Efficient Bayesian Inference for Non-Probability Samples

Robust and Efficient Bayesian Inference for Non-Probability Samples

Predicting spatio‐temporal distributions of migratory populations using Gaussian process modelling

Estimating the fitness cost and benefit of antimicrobial resistance from pathogen genomic data

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