Bayesian Statistics

Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. Bayesian methods update prior beliefs on distributions or model parameters upon observation of data. Specifically, I have used Bayesian nonparametric methods in obtaining inferences for lifetime modeling and Bayesian latent variable methods for missing data imputation. Here Bayesian nonparametric methods refer to classes of flexible priors on the space of distributions, for example, Polya trees, Dirichlet processes, and splines.

Complicate lifetime modeling

Broadly, lifetime modeling is a category of research dealing with time-to-event data, which typically records the lengths of times among events of interest, such as mechanical failures, heart attacks, and cancer relapses. Often subjects are monitored over multiple time points as well as their locations; hence, longitudinal and spatial dimensions are added to the data correlation structure. A significant number of scientific questions arise in understanding the effects of risk factors on time distributions of events. Besides inferential results on the risk factors' effects, statistical studies also typically extend to diagnostics on model assumptions and to predictions for unknown responses of interest. I have five publications on lifetime modeling or hypothesis tests.

A Bayesian nonparametric test for minimal repair

A Bayesian semiparametric regression model for reliability data using effective age

Spatial extended hazard model with application to Prostate Cancer Survival

Latent promotion time cure rate model using dependent tailfree mixtures

Marginal Bayesian semiparametric modeling of mis-measured multivariate interval-censored data

Causal inference and mediation analysis

Causal inference is the process of concluding a causal connection based on the conditions of the occurrence of an effect and mediation analysis searches for mechanisms behind causes and effects. Several application studies in which I am participating, aim to investigate the effects of heavy metal exposures on Navajo native Indian children's neuro-developmental assessments. Causal inference plays a key role in disentangling the effects of metals.

Missing data problems

Missing data often occur in data collection due to nonresponse- no information provided for one or more items or a whole unit, mistakes made in data entry, and even sample corruption. Most methods and theories were developed for full data, and they could be much more complicated if they are needed to handle missing data properly. I have one publication on extending methods for missing data.

A Bayesian transition model for missing longitudinal binary outcomes and an application to a smoking cessation study

Biostatistics

My biostatistical/environmental collaborations have focused on investigating the effects of heavy metal exposures on Navajo native Indian children's neuro-developmental assessments (work with UNM METALS Superfund Research Program Center). I have coauthored a paper on neuro-developmental assessments and several manuscripts are under development.

Use of Age and Stages Questionnaire (ASQ) in a Navajo Population: comparison with the U.S. normative dataset.

Behavioral science

I am interested in developing and applying statistical methods for psychology experiments. I have one manuscript under review on analysis of covariance with heterogeneity of regression and a random Covariate.