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Ensemble sampler for infinite-dimensional inverse problems
We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our new sampler is based on the affine...
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Estimation, Model Diagnosis, and Process Control Under the Normal Model
This chapter introduces statistical methods for copula-based Markov models under the normal margin. First, the data structures and the idea of...
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Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models
Cross-validation can be used to measure a model’s predictive accuracy for the purpose of model comparison, averaging, or selection. Standard...
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Special Matrices and Operations Useful in Modeling and Data Science
In previous chapters, we encountered a number of special matrices, such as symmetric matrices, banded matrices, elementary operator matrices, and so...
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Prior specification for binary Markov mesh models
We propose prior distributions for all parts of the specification of a Markov mesh model. In the formulation, we define priors for the sequential...
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Graphical Modeling of Multiple Biological Pathways in Genomic Studies
Complex diseases are associated with a variety of genomic factors. Identifying such risk factors can help us to better understand the pathogenesis of...
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Continuous-Time Discrete-State Modeling for Deep Whale Dives
Understanding unexposed/baseline behavior of marine mammals is required to assess the effects of increasing levels of anthropogenic noise exposure in...
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Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value...
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Geometric ergodicity of a Metropolis-Hastings algorithm for Bayesian inference of phylogenetic branch lengths
This manuscript extends the work of Spade et al. (Math Biosci 268:9–21, 2015) to an examination of a fully-updating version of a Metropolis-Hastings...
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Stationary Processes and Their Information Rate
This chapter briefly introduces the necessary concepts from the theory of stochastic processes (see for example Lamperti 1977; Doob 1953) that are...
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Variance Bounding of Delayed-Acceptance Kernels
A delayed-acceptance version of a Metropolis–Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to...
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Multivariate Gaussian processes: definitions, examples and applications
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong...
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Importance Resampling
ResamplingResampling is the action of drawing randomly from a weighted sample, so as to obtain an unweighted sample. Resampling may be viewed as a...
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Liapunov and Related Systems
We consider here algorithms which cannot be cast as stochastic gradient schemes, but have associated with their limiting (d-dimensional) o.d.e.
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A modeler’s guide to extreme value software
This review paper surveys recent development in software implementations for extreme value analyses since the publication of Stephenson and Gilleland...
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Robustly Fitting Gaussian Graphical Models—the R Package robFitConGraph
This chapter gives a tutorial-style introduction to the R package robFitConGraph, which provides a robust goodness-of-fit test for Gaussian graphical...
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A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation
This article considers a modeling problem of integer-valued time series of bounded counts in which the binomial index of dispersion of the...
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Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the...
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Bayesian Latent Gaussian Models for High-Dimensional Spatial Extremes
In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings,...
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Limit theorems for branching processes with immigration in a random environment
We investigate branching processes with immigration in a random environment. Using Goldie’s implicit renewal theory we prove that under a generalized...