Please cite this article as: Frühwirth-Schnatter, S., Wagner, H., Stochastic model specification search for Gaussian and partial non-Gaussian state space models. Journal of Econometrics (2009Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A C C E P T E D M A N U S C R I P T
We consider parameter-driven models of time series of counts, where the observations are assumed to arise from a Poisson distribution with a mean changing over time according to a latent process. Estimation of these models is carried out within a Bayesian framework using data augmentation and Markov chain Monte Carlo methods. We suggest a new auxiliary mixture sampler, which possesses a Gibbsian transition kernel, where we draw from full conditional distributions belonging to standard distribution families only. Emphasis lies on application to state space modelling of time series of counts, but we show that auxiliary mixture sampling may be applied to a wider range of parameterdriven models, including random-effects models and panel data models based on the Poisson distribution.
An important task in building regression models is to decide which regressors should be included in the final model. In a Bayesian approach, variable selection can be performed using mixture priors with a spike and a slab component for the effects subject to selection. As the spike is concentrated at zero, variable selection is based on the probability of assigning the corresponding regression effect to the slab component. These posterior inclusion probabilities can be determined by MCMC sampling. In this paper we compare the MCMC implementations for several spike and slab priors with regard to posterior inclusion probabilities and their sampling efficiency for simulated data. Further, we investigate posterior inclusion probabilities analytically for different slabs in two simple settings. Application of variable selection with spike and slab priors is illustrated on a data set of psychiatric patients where the goal is to identify covariates affecting metabolism.Zusammenfassung: Ein wesentliches Problem der Regressionsmodellierung ist die Auswahl der Regressoren, die ins Modell aufgenommen werden. In einem Bayes-Ansatz kann Variablenselektion durchgeführt werden, indem als a-priori-Verteilung für die Regressionseffekte der in Frage kommenden Variablen eine Mischverteilung mit zwei Komponenten gewählt wird: die erste Komponente mit einer Spitze bei Null wird als "spike", die zweite flache Komponente als "slab" bezeichnet. Die Selektion der Variablen erfolgt dann auf Basis der posteriori Wahrscheinlichkeit, mit der ein Effekt der slabKomponente zugeordnet wird. Diese sogenannten Inklusionswahrscheinlichkeiten können mit Hilfe der MCMC-Ziehungen geschätzt werden. Im vorliegenden Beitrag werden MCMC-Implementierungen für verschiedene spikeand-slab-Verteilungen hinsichtlich der Inklusionswahrscheinlichkeiten und der Effizienz ihrer Schätzung anhand von simulierten Daten verglichen. Außer-dem untersuchen wir die Inklusionswahrscheinlichkeiten für verschiedene Slab-Komponenten in zwei einfachen Fällen auch analytisch. Schließlich wird Variablenselektion mit Spike-and-Slab-Priori-Verteilungen auf einen medizinischen Datensatz angewendet, um Regressoren, die den Stoffwechsel von psychiatrischen Patienten beeinflussen, zu indetnifizieren.
Mortality in hydrocephalic pediatric patients is high especially in the first postoperative years but is even significant in adult patients with pediatric hydrocephalus. As deaths occur even after 20 years, routine follow-up of long-term survivors remains necessary.
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