This is an implementation of the algorithm described in Section 3 of Hosszejni and Frühwirth-Schnatter (2022) <doi:10.48550/arXiv.2211.00671>. The algorithm is used to verify that the counting rule CR(r,1) holds for the sparsity pattern of the transpose of a factor loading matrix. As detailed in Section 2 of the same paper, if CR(r,1) holds, then the idiosyncratic variances are generically identified. If CR(r,1) does not hold, then we do not know whether the idiosyncratic variances are identified or not.

The Stratified-Petersen Analysis System (SPAS) is designed
    to estimate abundance in two-sample capture-recapture experiments 
    where the capture and recaptures are stratified. This is a generalization
    of the simple Lincoln-Petersen estimator.
    Strata may be defined in time or in space or both, 
    and the s strata in which marking takes place 
    may differ from the t strata in which recoveries take place.
    When s=t, SPAS reduces to the method described by 
    Darroch (1961) <doi:10.2307/2332748>.
    When s<t, SPAS implements the methods described in
    Plante, Rivest, and Tremblay (1988) <doi:10.2307/2533994>.
    Schwarz and Taylor (1998) <doi:10.1139/f97-238> describe
    the use of SPAS in estimating return of salmon stratified by
    time and geography. 
    A related package, BTSPAS, deals with temporal stratification where 
    a spline is used to model the distribution of the population 
    over time as it passes the second capture location.
    This is the R-version of the (now obsolete) standalone Windows 
    program available at <https://home.cs.umanitoba.ca/~popan/spas/spas_home.html>.

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.