Functional Data Analysis for Density Functions by Transformation to a Hilbert Space

An implementation of the methodology described in Petersen and Mueller (2016) for the functional data analysis of samples of density functions. Densities are first transformed to their corresponding log quantile densities, followed by ordinary Functional Principal Components Analysis (FPCA). Transformation modes of variation yield improved interpretation of the variability in the data as compared to FPCA on the densities themselves. The standard fraction of variance explained (FVE) criterion commonly used for functional data is adapted to the transformation setting, also allowing for an alternative quantification of variability for density data through the Wasserstein metric of optimal transport.

Solve Generalized Estimating Equations for Clustered Data

Estimation of generalized linear models with correlated/clustered observations by use of generalized estimating equations (GEE). See e.g. Halekoh and Højsgaard, (2005, ), for details. Several types of clustering are supported, including exchangeable variance structures, AR1 structures, M-dependent, user-specified variance structures and more. The model fitting computations are performed using modified code from the 'geeM' package, while the interface and output objects have been written to resemble the 'geepack' package. The package also contains additional tools for working with and inspecting results from the 'geepack' package, e.g. a 'confint' method for 'geeglm' objects from 'geepack'.

Processes Calcium Imaging Data

Identifies the locations of neurons, and estimates their calcium concentrations over time using the SCALPEL method proposed in Petersen, Ashley; Simon, Noah; Witten, Daniela. SCALPEL: Extracting neurons from calcium imaging data. Ann. Appl. Stat. 12 (2018), no. 4, 2430--2456. . < https://projecteuclid.org/euclid.aoas/1542078051>.

Estimate Time Varying Reproduction Numbers from Epidemic Curves

Tools to quantify transmissibility throughout an epidemic from the analysis of time series of incidence as described in Cori et al. (2013) and Wallinga and Teunis (2004) .

Fits Piecewise Constant Models with Data-Adaptive Knots

Implements the fused lasso additive model as proposed in Petersen, A., Witten, D., and Simon, N. (2016). Fused Lasso Additive Model. Journal of Computational and Graphical Statistics, 25(4): 1005-1025.

Partial Separability and Functional Gaussian Graphical Models

Estimates a functional graphical model and a partially separable Karhunen-Loève decomposition for a multivariate Gaussian process. See Zapata J., Oh S. and Petersen A. (2019) .

Wasserstein Regression and Inference

Implementation of the methodologies described in 1) Alexander Petersen, Xi Liu and Afshin A. Divani (2021) , including global F tests, partial F tests, intrinsic Wasserstein-infinity bands and Wasserstein density bands, and 2) Chao Zhang, Piotr Kokoszka and Alexander Petersen (2022) , including estimation, prediction, and inference of the Wasserstein autoregressive models.

Warping Landmark Configurations

Compute bending energies, principal warps, partial warp scores, and the non-affine component of shape variation for 2D landmark configurations, as well as Mardia-Dryden distributions and self-similar distributions of landmarks, as described in Mitteroecker et al. (2020) . Working examples to decompose shape variation into small-scale and large-scale components, and to decompose the total shape variation into outline and residual shape components are provided. Two landmark datasets are provided, that quantify skull morphology in humans and papionin primates, respectively from Mitteroecker et al. (2020) and Grunstra et al. (2020) .

'Trial Sequential Analysis' for Error Control and Inference in Sequential Meta-Analyses

Frequentist sequential meta-analysis based on 'Trial Sequential Analysis' (TSA) in programmed in Java by the Copenhagen Trial Unit (CTU). The primary function is the calculation of group sequential designs for meta-analysis to be used for planning and analysis of both prospective and retrospective sequential meta-analyses to preserve type-I-error control under sequential testing. 'RTSA' includes tools for sample size and trial size calculation for meta-analysis and core meta-analyses methods such as fixed-effect and random-effects models and forest plots. TSA is described in Wetterslev et. al (2008) . The methods for deriving the group sequential designs are based on Jennison and Turnbull (1999, ISBN:9780849303166).

Discrete Distribution Approximations

Creates discretised versions of continuous distribution functions by mapping continuous values to an underlying discrete grid, based on a (uniform) frequency of discretisation, a valid discretisation point, and an integration range. For a review of discretisation methods, see Chakraborty (2015) .