TY  - JOUR
T1  - Bayesian Lattice Filters for Time-Varying Autoregression and Time–Frequency Analysis
JF  - Project Euclid
Y1  - 2015
A1  - Yang, W. H.
A1  - Holan, Scott H.
A1  - Wikle, Christopher K.
KW  - locally stationary
KW  - model selection
KW  - nonstationary partial autocorrelation
KW  - piecewise stationary
KW  - sequential estimation
KW  - time-varying spectral density
AB  - Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time–frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).
UR  - http://projecteuclid.org/euclid.ba/1445263834
ER  - 

TY  - JOUR
T1  - Bayesian Marked Point Process Modeling for Generating Fully Synthetic Public Use Data with Point-Referenced Geography
JF  - Spatial Statistics
Y1  - 2015
A1  - Quick, Harrison
A1  - Holan, Scott H.
A1  - Wikle, Christopher K.
A1  - Reiter, Jerome P.
VL  - 14
UR  - http://www.sciencedirect.com/science/article/pii/S2211675315000718
ER  - 

TY  - JOUR
T1  - Bayesian Spatial Change of Support for Count-Valued Survey Data with Application to the American Community Survey
JF  - Journal of the American Statistical Association
Y1  - 2015
A1  - Bradley, Jonathan R.
A1  - Wikle, Christopher K.
A1  - Holan, Scott H.
KW  - Aggregation
KW  - American Community Survey
KW  - Bayesian hierarchical model
KW  - Givens angle prior
KW  - Markov chain Monte Carlo
KW  - Multiscale model
KW  - Non-Gaussian.
AB  - We introduce Bayesian spatial change of support methodology for count-valued survey data with known survey variances. Our proposed methodology is motivated by the American Community Survey (ACS), an ongoing survey administered by the U.S. Census Bureau that provides timely information on several key demographic variables. Specifically, the ACS produces 1-year, 3-year, and 5-year “period-estimates,” and corresponding margins of errors, for published demographic and socio-economic variables recorded over predefined geographies within the United States. Despite the availability of these predefined geographies it is often of interest to data-users to specify customized user-defined spatial supports. In particular, it is useful to estimate demographic variables defined on “new” spatial supports in “real-time.” This problem is known as spatial change of support (COS), which is typically performed under the assumption that the data follows a Gaussian distribution. However, count-valued survey data is naturally non-Gaussian and, hence, we consider modeling these data using a Poisson distribution. Additionally, survey-data are often accompanied by estimates of error, which we incorporate into our analysis. We interpret Poisson count-valued data in small areas as an aggregation of events from a spatial point process. This approach provides us with the flexibility necessary to allow ACS users to consider a variety of spatial supports in “real-time.” We show the effectiveness of our approach through a simulated example as well as through an analysis using public-use ACS data.
UR  - http://www.tandfonline.com/doi/abs/10.1080/01621459.2015.1117471
ER  -