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) .

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, 2024). 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 (2024) .

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.

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" .

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.

Classification and Visualization

Miscellaneous functions for classification and visualization, e.g. regularized discriminant analysis, sknn() kernel-density naive Bayes, an interface to 'svmlight' and stepclass() wrapper variable selection for supervised classification, partimat() visualization of classification rules and shardsplot() of cluster results as well as kmodes() clustering for categorical data, corclust() variable clustering, variable extraction from different variable clustering models and weight of evidence preprocessing.

Bayesian Inference for Marketing/Micro-Econometrics

Covers many important models used in marketing and micro-econometrics applications. The package includes: Bayes Regression (univariate or multivariate dep var), Bayes Seemingly Unrelated Regression (SUR), Binary and Ordinal Probit, Multinomial Logit (MNL) and Multinomial Probit (MNP), Multivariate Probit, Negative Binomial (Poisson) Regression, Multivariate Mixtures of Normals (including clustering), Dirichlet Process Prior Density Estimation with normal base, Hierarchical Linear Models with normal prior and covariates, Hierarchical Linear Models with a mixture of normals prior and covariates, Hierarchical Multinomial Logits with a mixture of normals prior and covariates, Hierarchical Multinomial Logits with a Dirichlet Process prior and covariates, Hierarchical Negative Binomial Regression Models, Bayesian analysis of choice-based conjoint data, Bayesian treatment of linear instrumental variables models, Analysis of Multivariate Ordinal survey data with scale usage heterogeneity (as in Rossi et al, JASA (01)), Bayesian Analysis of Aggregate Random Coefficient Logit Models as in BLP (see Jiang, Manchanda, Rossi 2009) For further reference, consult our book, Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch (Wiley second edition 2024) and Bayesian Non- and Semi-Parametric Methods and Applications (Princeton U Press 2014).