TY  - JOUR
T1  - A Bayesian nonparametric Markovian model for nonstationary time series
JF  - Statistics and Computing
Y1  - 2016
A1  - De Yoreo, M.
A1  - Kottas, A.
KW  - Autoregressive Models
KW  - Bayesian Nonparametrics
KW  - Dirichlet Process Mixtures
KW  - Markov chain Monte Carlo
KW  - Nonstationarity
KW  - Time Series
AB  - Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture nonstandard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This implies a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, nonstationary, Markovian model for real-valued data indexed in discrete-time. To obtain a more computationally tractable algorithm for posterior inference, we utilize a square-root-free Cholesky decomposition of the mixture kernel covariance matrix. Results from simulated data suggest the model is able to recover challenging transition and predictive densities. We also illustrate the model on time intervals between eruptions of the Old Faithful geyser. Extensions to accommodate higher order structure and to develop a state-space model are also discussed.
ER  - 

TY  - RPRT
T1  - Modeling for Dynamic Ordinal Regression Relationships: An Application to Estimating Maturity of Rockfish in California
Y1  - 2015
A1  - DeYoreo, M.
A1  - Kottas, A.
KW  - Statistics - Applications
AB  - We develop a Bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models. A novel dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California.
PB  - ArXiv
UR  - http://arxiv.org/abs/1507.01242
ER  - 

TY  - RPRT
T1  - Bayesian Nonparametric Modeling for Multivariate Ordinal Regression
Y1  - 2014
A1  - DeYoreo, M.
A1  - Kottas, A.
KW  - Statistics - Methodology
AB  - Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate and multivariate ordinal regression, which is based on mixture modeling for the joint distribution of latent responses and covariates. The modeling framework enables highly flexible inference for ordinal regression relationships, avoiding assumptions of linearity or additivity in the covariate effects. In standard parametric ordinal regression models, computational challenges arise from identifiability constraints and estimation of parameters requiring nonstandard inferential techniques. A key feature of the nonparametric model is that it achieves inferential flexibility, while avoiding these difficulties. In particular, we establish full support of the nonparametric mixture model under fixed cut-off points that relate through discretization the latent continuous responses with the ordinal responses. The practical utility of the modeling approach is illustrated through application to two data sets from econometrics, an example involving regression relationships for ozone concentration, and a multirater agreement problem.
PB  - ArXiv
UR  - http://arxiv.org/abs/1408.1027
ER  -