Sample size estimation and blinded sample size reestimation in Adaptive Study Design.

Functionality for spatio-temporal modeling of large data sets is provided. A Gaussian process in space and time is defined through a stochastic partial differential equation (SPDE). The SPDE is solved in the spectral space, and after discretizing in time and space, a linear Gaussian state space model is obtained. When doing inference, the main computational difficulty consists in evaluating the likelihood and in sampling from the full conditional of the spectral coefficients, or equivalently, the latent space-time process. In comparison to the traditional approach of using a spatio-temporal covariance function, the spectral SPDE approach is computationally advantageous. See Sigrist, Kuensch, and Stahel (2015) <doi:10.1111/rssb.12061> for more information on the methodology. This package aims at providing tools for two different modeling approaches. First, the SPDE based spatio-temporal model can be used as a component in a customized hierarchical Bayesian model (HBM). The functions of the package then provide parameterizations of the process part of the model as well as computationally efficient algorithms needed for doing inference with the HBM. Alternatively, the adaptive MCMC algorithm implemented in the package can be used as an algorithm for doing inference without any additional modeling. The MCMC algorithm supports data that follow a Gaussian or a censored distribution with point mass at zero. Covariates can be included in the model through a regression term.

The heterogeneity of spatial data presenting a finite number of categories can be measured via computation of spatial entropy. Functions are available for the computation of the main entropy and spatial entropy measures in the literature. They include the traditional version of Shannon's entropy (Shannon, 1948 <doi:10.1002/j.1538-7305.1948.tb01338.x>), Batty's spatial entropy (Batty, 1974 <doi:10.1111/j.1538-4632.1974.tb01014.x>), O'Neill's entropy (O'Neill et al., 1998 <doi:10.1007/BF00162741>), Li and Reynolds' contagion index (Li and Reynolds, 1993 <doi:10.1007/BF00125347>), Karlstrom and Ceccato's entropy (Karlstrom and Ceccato, 2002 <https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-61351>), Leibovici's entropy (Leibovici, 2009 <doi:10.1007/978-3-642-03832-7_24>), Parresol and Edwards' entropy (Parresol and Edwards, 2014 <doi:10.3390/e16041842>) and Altieri's entropy (Altieri et al., 2018, <doi:10.1007/s10651-017-0383-1>). Full references for all measures can be found under the topic 'SpatEntropy'. The package is able to work with lattice and point data. The updated version works with the updated 'spatstat' package (>= 3.0-2).