Qingyang Liu

Implements the Mixed Treatment-State Causal Model (MTSCM), a Bayesian framework for estimating causal effects of clinical interventions on bounded continuous outcomes in longitudinal observational studies with irregular visits. The methodology is specifically designed for periodontal disease research, where discrete treatments and continuous disease states (e.g., proportion of periodontal pockets exceeding 3 mm) reciprocally influence one another under dynamic feedback. The package integrates a double-censored Tobit likelihood to handle boundary mass at zero and one, subject-specific random effects to capture within-subject correlation, and flexible tree-based ensemble priors (standard BART and Soft BART) to model complex nonlinear interactions without parametric restrictions. Causal identification is established under the potential outcomes framework via the G-computation formula, with key estimands including the Mixed Average Potential Outcome (MAPO) and the Mixed Probability of Disease Resolution (MPDR). The package provides functions for model fitting, posterior inference, and causal estimand estimation.

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are explored, including model identifiability and flexibility in capturing heavy-tailed data that exhibit different directions of skewness over a wide range. Both frequentist and Bayesian methods are developed to infer parameters in the new distribution. Simulation studies are conducted to demonstrate satisfactory performance of both methods. By fitting the proposed model to simulated data and data from an application in hydrology, it is shown that the proposed flexible distribution is especially suitable for data containing extreme values in either direction, with the mode being a location parameter of interest. A regression model concerning the mode of a response given covariates based on the proposed unimodal distribution can be easily formulated, which we apply to data from an application in criminology to reveal interesting data features that are obscured by outliers.

A new unimodal distribution family indexed via the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are explored, including model identifiability and flexibility in capturing heavy-tailed data that exhibit different directions of skewness over a wide range. Both frequentist and Bayesian methods are developed to infer parameters in the new distribution. Simulation studies are conducted to demonstrate satisfactory performance of both methods. By fitting the proposed model to simulated data and data from an application in hydrology, it is shown that the proposed flexible distribution is especially suitable for data containing extreme values in either direction, with the mode being a location parameter of interest. Using the proposed unimodal distribution, one can easily formulate a regression model concerning the mode of a response given covariates. We apply this model to data from an application in criminology to reveal interesting data features that are obscured by outliers.

An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score‐based diagnostic tool exploiting parametric bootstrap is developed to assess adequacy of parametric assumptions imposed on the regression model. The proposed estimation method and diagnostic tool are applied to synthetic data generated from simulation experiments and data from real‐world applications to demonstrate their implementation and performance. These empirical examples illustrate the importance of adequately accounting for measurement error in the error‐prone covariate when inferring the association between a response and covariates based on a modal regression model that is especially suitable for skewed and heavy‐tailed response data.

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. We propose a unified framework for Bayesian modal regression based on a family of unimodal distributions indexed by the mode along with other parameters that allow for flexible shapes and tail behaviors. Following prior elicitation, we carry out regression analysis of simulated data and datasets from several real-life applications. Besides drawing inference for covariate effects that are easy to interpret, we consider prediction and model selection under the proposed Bayesian modal regression framework. Evidence from these analyses suggest that the proposed inference procedures are very robust to outliers, enabling one to discover interesting covariate effects missed by mean or median regression, and to construct much tighter prediction intervals than those from mean or median regression. Computer programs for implementing the proposed Bayesian modal regression are available at https://github.com/rh8liuqy/Bayesian_modal_regression.