Resources on spatial models

Abstract

A compliation of links to resources which I’ve found useful while working on beyond-borders.

GMRFs

• Lecture 4: Numerical methods for sparse matrices

Cross-validation

• Spatial leave-one-out blog post
• mlr3spatiotempcv package
• Cross-validation of CAR models cannot be done with stratified folds
• An R package in support of publication, “Spatial Autoregressive Models for Statistical Inference from Ecological Data.”
• Efficient LOO-CV, the loo package
• Approximate cross‐validatory predictive checks in disease mapping models
• When LOO and other cross-validation approaches are valid
• I am the supercargo
• Comments on Limitations of Bayesian Leave-One-Out Cross-Validation for Model Selection
• Bayesian leave-one-out cross-validation for large data

INLA

• Bayesian inference with INLA
• The R-INLA package, David Bolin
• Haakon Bakka
• Posterior predictive
  • Posterior Predictive in INLA
  • Julian Faraway
  • Obtain summary of posterior predictive distribution, R-INLA Google group
• Defining a latent model in R: The rgeneric model

Jeff’s notebooks

• INLA sandbox

Stan

• Exact sparse CAR models in Stan
• Spatial Models in Stan: Intrinsic Auto-Regressive Models for Areal Data
• Spatial Smoothing in Stan: Conditional Auto-Regressive Models
• Fast CAR: Two weird tricks for fast conditional autoregressive models in Stan
• feature/car in rstanarm
• Writing Stan programs for use with the loo package

Gaussian processes in Stan

• Add more Gaussian process kernels in brms
• Multilevel Gaussian Proccess with spectral mixture kernel
• Basis function approximation to Gaussian processes in brms
• Adding Gaussian Process Covariance Functions
• Approximate GPs with Spectral Stuff
• Approximate GP prediction question

Hilbert space methods

• Hilbert Space Methods for Reduced-Rank Gaussian Process Regression
• Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming
• stancode_BF_1dim.stan

Non-stationarity

• BayesNSGP: Bayesian Analysis of Non-Stationary Gaussian Process Models
• Bayesian inference for high-dimensional nonstationary Gaussian processes

R packages

• Both TMB and Stan working in an R package
  • Guidelines for including TMB c++ code in an R package
  • TMB C++ code in R package and CRAN checks
  • Best practices for distributing TMB and R code
• Formatting Rd files
  • (R)Markdown support
• Getting a Linux R package to work on Windows
  • Making R package work in both Windows and Linux
  • Building and checking R source packages for Windows
  • Building R Binary Packages for Linux
• R Packages (2e)

Neighbourhood weights

• Bayesian spatial models with a mixture neighborhood structure
• Evaluating the effect of neighbourhood weight matrices on smoothing properties of Conditional Autoregressive (CAR) models
• Spatial smoothing in Bayesian models: a comparison of weights matrix specifications and their impact on inference
• Spatial weights objects as sparse matrices and graphs

Model comparison

• Model selection tutorials and talks
• Does coverage matter?
• Simulation-based calibration
• A random interval \((L(X), U(X))\) has \(100(1 * \alpha)\)% frequentist coverage for \(\theta\) if, before the data are gathered \(P(L(X) < \theta < U(X) | \theta) = 1 * \alpha\)
• DIC: Deviance Information Criteria

Coresets

• Coresets for automated, scalable Bayesian inference
• Coreset (Wikipedia)
• Automated Scalable Bayesian Inference via Hilbert Coresets

Modifiable areal unit problem

• Flowerdew slides
• The modifiable areal unit problem (MAUP) in physical geography
• Neighbourhood effects on health: does it matter where you draw the boundaries?
• Spatio-Temporal Change of Support Modeling with R
• Spatial change-of-support and misalignment problems
• Change of support / moving average /kernel smoothing INLA Google group

Log scoring

• Predictive Inference Based on Markov Chain Monte Carlo Output

Variograms

• Optimal interpolation and isarithmic mapping of soil properties: I The semi‐variogram and punctual kriging
• Quantifying the scale effect in geospatial big data using semi-variograms
• gstat package
• Implementing variograms in R
• R Variograms & Kriging

“Some software for geostatistical analysis uses an empirical variogram to fit the parameters of the correlation function. However, this option does not make any assumptions about a likelihood function for the data or uses a multivariate Gaussian distribution for the spatially structured random effect. A good description of these techniques is available in Cressie (1993).”

Chosing MCMC sample sizes

• MCMC Output Analysis with R package mcmcse
  • See the function mcmcse::minESS

Survey weights

• Design Effects and Effective Sample Size

Non-integer pseduo-likelihoods

• Non-integer counts due to the use of survey weights. Could use round but this is an unsatisfying solution
• In stan and TMB a custom continuous version of the likelihood could be implemented
• In R-INLA there are xbinomial and xpoisson functions for non-integer counts
  • Be warned that these may make the marginal likelihood not interpretable as it is not clear what to do with the normalising constant
• Keywords to investigate
  • Bayesian pseudo likelihood
• Continuous generalization of the negative binomial distribution
• R-INLA Google group links
  • Non-integer counts for binomial model
  • what is binomial distribution doing with non-integer data

Compact support kernels

• Empty so far!

Multiple instance learning

• Multiple Instance Learning with Bag Dissimilarities
• Gaussian Processes Multiple Instance Learning
• Variational Bayesian Multiple Instance Learning with Gaussian Processes

Graph Laplacians

• A Short Tutorial on Graph Laplacians, Laplacian Embedding, and Spectral Clustering

Aggregated Gaussian processes

• Variational Learning on Aggregate Outputs with Gaussian Processes
• Multi-resolution Multi-task Gaussian Processes

Misc.

• Developing a Cancer Atlas using Bayesian Methods: A Practical Guide for Application and Interpretation
  • Investigation of Bayesian spatial models
• A quick refresher on the coordinate reference system
• A Case Study Competition Among Methods for Analyzing Large Spatial Data
• A spatial regression model for the disaggregation of areal unit based data to high-resolution grids with application to vaccination coverage mapping
• Generalized spatial fusion model framework for joint analysis of point and areal data
• SUMMER: Bayesian Small Area Estimation using Complex Survey Data
• Generalised inverse
• Hierarchical Bayesian species distribution models with the hSDMR Package
• [R-sig-Geo] Choosing the right nb2listw-style
• The Effect of Bias, Variance Estimation, Skewness and Kurtosis of the Empirical Logit on Weighted Least Squares Analyses on JSTOR
• Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under-and over-smoothingg