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.

Modeling spatial dependencies in dependent variables, extending traditional spatial regression approaches. It allows for the joint modeling of both the mean and the variance of the dependent variable, incorporating semiparametric effects in both models. Based on generalized additive models (GAM), the package enables the inclusion of non-parametric terms while maintaining the classical theoretical framework of spatial regression. Additionally, it implements the Generalized Spatial Autoregression (GSAR) model, which extends classical methods like logistic Spatial Autoregresive Models (SAR), probit Spatial Autoregresive Models (SAR), and Poisson Spatial Autoregresive Models (SAR), offering greater flexibility in modeling spatial dependencies and significantly improving computational efficiency and the statistical properties of the estimators. Related work includes: a) J.D. Toloza-Delgado, Melo O.O., Cruz N.A. (2024). "Joint spatial modeling of mean and non-homogeneous variance combining semiparametric SAR and GAMLSS models for hedonic prices". <doi:10.1016/j.spasta.2024.100864>. b) Cruz, N. A., Toloza-Delgado, J. D., Melo, O. O. (2024). "Generalized spatial autoregressive model". <doi:10.48550/arXiv.2412.00945>.