Related papers: A general class of zero-or-one inflated beta regre…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…
Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from…
We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great…
The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…
We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means of the random variables belonging to a non-empty, bounded interval; (ii) the means of the random variables belonging to an…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
Pattern-mixture models provide a transparent approach for handling missing data, where the full-data distribution is factorized in a way that explicitly shows the parts that can be estimated from observed data alone, and the parts that…
The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the…
Beta regression is often used to model the relationship between a dependent variable that assumes values on the open interval (0,1) and a set of predictor variables. An important challenge in beta regression is to find residuals whose…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
Meta-analysis, because of both logistical convenience and statistical efficiency, is widely popular for synthesizing information on common parameters of interest across multiple studies. We propose developing a generalized meta-analysis…
Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors $X_1,\ldots, X_p$ (for example: $Y = 1$ if the outcome occurred and $Y = 0$…