Estimating Local False Discovery Rates Using Empirical Bayes Methods

New empirical Bayes methods aiming at analyzing the association of single nucleotide polymorphisms (SNPs) to some particular disease are implemented in this package. The package uses local false discovery rate (LFDR) estimates of SNPs within a sample population defined as a "reference class" and discovers if SNPs are associated with the corresponding disease. Although SNPs are used throughout this document, other biological data such as protein data and other gene data can be used. Karimnezhad, Ali and Bickel, D. R. (2016) < http://hdl.handle.net/10393/34889>.

Small Area Estimation using Empirical Bayes without Auxiliary Variable

Estimates the parameter of small area in binary data without auxiliary variable using Empirical Bayes technique, mainly from Rao and Molina (2015,ISBN:9781118735787) with book entitled "Small Area Estimation Second Edition". This package provides another option of direct estimation using weight. This package also features alpha and beta parameter estimation on calculating process of small area. Those methods are Newton-Raphson and Moment which based on Wilcox (1979) and Kleinman (1973) .

Calculates Safety Stopping Boundaries for a Single-Arm Trial using Bayes

Computation of stopping boundaries for a single-arm trial using a Bayesian criterion. For each m<=n (n=total patient number of the trial) the smallest number of observed toxicities is calculated leading to the termination of the trial/accrual according to the specified criteria. The probabilities of stopping the trial/accrual at and up until (resp.) the m-th patient (m<=n) is also calculated. This design is more conservative than the frequentist approach (using Clopper Pearson CIs) which might be preferred as it concerns safety. See also Aamot et al. (2010) "Continuous monitoring of toxicity in clinical Trials - simulating the risk of stopping prematurely" .

Spatial Clustering with Hidden Markov Random Field using Empirical Bayes

Spatial clustering with hidden markov random field fitted via EM algorithm, details of which can be found in Yi Yang (2021) . It is not only computationally efficient and scalable to the sample size increment, but also is capable of choosing the smoothness parameter and the number of clusters as well.

Fitting Shared Atoms Nested Models via MCMC or Variational Bayes

An efficient tool for fitting nested mixture models based on a shared set of atoms via Markov Chain Monte Carlo and variational inference algorithms. Specifically, the package implements the common atoms model (Denti et al., 2023), its finite version (similar to D'Angelo et al., 2023), and a hybrid finite-infinite model (D'Angelo and Denti, 2026). All models implement univariate nested mixtures with Gaussian kernels equipped with a normal-inverse gamma prior distribution on the parameters. Additional functions are provided to help analyze the results of the fitting procedure. References: Denti, Camerlenghi, Guindani, Mira (2023) , D’Angelo, Canale, Yu, Guindani (2023) , D’Angelo, Denti (2026) .

Sparse High-Dimensional Linear Mixed Modeling with a Partitioned Empirical Bayes ECM Algorithm

Implements a partitioned Empirical Bayes Expectation Conditional Maximization (ECM) algorithm for sparse high-dimensional linear mixed modeling as described in Zgodic, Bai, Zhang, and McLain (2025) . The package provides efficient estimation and inference for mixed models with high-dimensional fixed effects.

Multiple Testing Approach using Average Power Function (APF) and Bayes FDR Robust Estimation

Implements a multiple testing approach to the choice of a threshold gamma on the p-values using the Average Power Function (APF) and Bayes False Discovery Rate (FDR) robust estimation. Function apf_fdr() estimates both quantities from either raw data or p-values. Function apf_plot() produces smooth graphs and tables of the relevant results. Details of the methods can be found in Quatto P, Margaritella N, et al. (2019) .

Algorithm for Searching the Space of Gaussian Directed Acyclic Graph Models Through Moment Fractional Bayes Factors

We propose an objective Bayesian algorithm for searching the space of Gaussian directed acyclic graph (DAG) models. The algorithm uses moment fractional Bayes factors (MFBF) and is suitable for learning sparse graphs. The algorithm is implemented using Armadillo, an open-source C++ linear algebra library.

Differential Exon Usage Test for RNA-Seq Data via Empirical Bayes Shrinkage of the Dispersion Parameter

Differential exon usage test for RNA-Seq data via an empirical Bayes shrinkage method for the dispersion parameter the utilizes inclusion-exclusion data to analyze the propensity to skip an exon across groups. The input data consists of two matrices where each row represents an exon and the columns represent the biological samples. The first matrix is the count of the number of reads expressing the exon for each sample. The second matrix is the count of the number of reads that either express the exon or explicitly skip the exon across the samples, a.k.a. the total count matrix. Dividing the two matrices yields proportions representing the propensity to express the exon versus skipping the exon for each sample.

Spatial Dependence: Weighting Schemes, Statistics

A collection of functions to create spatial weights matrix objects from polygon 'contiguities', from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial 'autocorrelation', including global 'Morans I' and 'Gearys C' proposed by 'Cliff' and 'Ord' (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), 'Hubert/Mantel' general cross product statistic, Empirical Bayes estimates and 'Assunção/Reis' (1999) Index, 'Getis/Ord' G ('Getis' and 'Ord' 1992) and multicoloured join count statistics, 'APLE' ('Li et al.' ) , local 'Moran's I', 'Gearys C' ('Anselin' 1995) and 'Getis/Ord' G ('Ord' and 'Getis' 1995) , 'saddlepoint' approximations ('Tiefelsdorf' 2002) and exact tests for global and local 'Moran's I' ('Bivand et al.' 2009) and 'LOSH' local indicators of spatial heteroscedasticity ('Ord' and 'Getis') . The implementation of most of these measures is described in 'Bivand' and 'Wong' (2018) , with further extensions in 'Bivand' (2022) . 'Lagrange' multiplier tests for spatial dependence in linear models are provided ('Anselin et al'. 1996) , as are 'Rao' score tests for hypothesised spatial 'Durbin' models based on linear models ('Koley' and 'Bera' 2023) . Additions in 2024 include Local Indicators for Categorical Data based on 'Carrer et al.' (2021) and 'Bivand et al.' (2017) ; also Weighted Multivariate Spatial Autocorrelation Measures ('Bavaud' 2024) . . A local indicators for categorical data (LICD) implementation based on 'Carrer et al.' (2021) and 'Bivand et al.' (2017) was added in 1.3-7. Multivariate 'spatialdelta' ('Bavaud' 2024) was added in 1.3-13 ('Bivand' 2025 ). From 'spdep' and 'spatialreg' versions >= 1.2-1, the model fitting functions previously present in this package are defunct in 'spdep' and may be found in 'spatialreg'.