7 research outputs found
Bayesian spectral modeling for multiple time series
We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single spectral density, we develop a hierarchical extension for multiple time series. Specifically, we set the mean functions to be common to all spectral densities and make the weights specific to the time series through the parameters of the logit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation is that it allows for ready posterior simulation through a Gibbs sampler with closed form full conditional distributions for all model parameters. The modeling approach is illustrated with simulated datasets, and used for spectral analysis of multichannel electroencephalographic recordings (EEGs), which provides a key motivating application for the proposed methodology
Triple the gamma -- A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models
Time-varying parameter (TVP) models are very flexible in capturing gradual
changes in the effect of a predictor on the outcome variable. However, in
particular when the number of predictors is large, there is a known risk of
overfitting and poor predictive performance, since the effect of some
predictors is constant over time. We propose a prior for variance shrinkage in
TVP models, called triple gamma. The triple gamma prior encompasses a number of
priors that have been suggested previously, such as the Bayesian lasso, the
double gamma prior and the Horseshoe prior. We present the desirable properties
of such a prior and its relationship to Bayesian Model Averaging for variance
selection. The features of the triple gamma prior are then illustrated in the
context of time varying parameter vector autoregressive models, both for
simulated datasets and for a series of macroeconomics variables in the Euro
Area
Shrinkage in the Time-Varying Parameter Model Framework Using the R Package shrinkTVP
Time-varying parameter (TVP) models are widely used in time series analysis
to flexibly deal with processes which gradually change over time. However, the
risk of overfitting in TVP models is well known. This issue can be dealt with
using appropriate global-local shrinkage priors, which pull time-varying
parameters towards static ones. In this paper, we introduce the R package
shrinkTVP (Knaus, Bitto-Nemling, Cadonna, and Fr\"uhwirth-Schnatter 2019),
which provides a fully Bayesian implementation of shrinkage priors for TVP
models, taking advantage of recent developments in the literature, in
particular that of Bitto and Fr\"uhwirth-Schnatter (2019). The package
shrinkTVP allows for posterior simulation of the parameters through an
efficient Markov Chain Monte Carlo (MCMC) scheme. Moreover, summary and
visualization methods, as well as the possibility of assessing predictive
performance through log predictive density scores (LPDSs), are provided. The
computationally intensive tasks have been implemented in C++ and interfaced
with R. The paper includes a brief overview of the models and shrinkage priors
implemented in the package. Furthermore, core functionalities are illustrated,
both with simulated and real data
Bayesian modeling and clustering for spatio-temporal areal data: An application to Italian unemployment
Spatio-temporal areal data can be seen as a collection of time series which
are spatially correlated according to a specific neighboring structure.
Incorporating the temporal and spatial dimension into a statistical model poses
challenges regarding the underlying theoretical framework as well as the
implementation of efficient computational methods. We propose to include
spatio-temporal random effects using a conditional autoregressive prior, where
the temporal correlation is modeled through an autoregressive mean
decomposition and the spatial correlation by the precision matrix inheriting
the neighboring structure. Their joint distribution constitutes a Gaussian
Markov random field, whose sparse precision matrix enables the usage of
efficient sampling algorithms. We cluster the areal units using a nonparametric
prior, thereby learning latent partitions of the areal units. The performance
of the model is assessed via an application to study regional unemployment
patterns in Italy. When compared to other spatial and spatio-temporal
competitors, the proposed model shows more precise estimates and the additional
information obtained from the clustering allows for an extended economic
interpretation of the unemployment rates of the Italian provinces
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Bayesian mixture models for spectral density estimation
We introduce a novel Bayesian modeling approach to spectral density estimation for multiple time series. Considering first the case of non-stationary timeseries, the log-periodogram of each series is modeled as a mixture of Gaussiandistributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functionswith frequency-dependent weights. The mixture weights are built throughsuccessive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single log-spectraldensity, we develop a hierarchical extension for multiple stationary time series.Specifically, we set the mean functions to be common to all log-spectral densities and model time series specific mixtures through the parameters of thelogit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation isthat it allows for ready posterior simulation through a Gibbs sampler withclosed form full conditional distributions for all model parameters. We thenextend the model to multiple locally stationary time series, a particular class of non-stationary time series, making it suitable for the analysis of time series with spectral characteristics that vary slowly with time. The modelingapproach is illustrated with different types of simulated datasets, and used forspectral analysis of multichannel electroencephalographic recordings (EEGs),which provides a key motivating application for the proposed methodology
Posterior predictive model checking using formal methods in a spatio-temporal model
We propose an interdisciplinary framework, Bayesian formal predictive model
checking (Bayes FPMC), which combines Bayesian predictive inference, a well
established tool in statistics, with formal verification methods rooting in the
computer science community.
Bayesian predictive inference allows for coherently incorporating uncertainty
about unknown quantities by making use of methods or models that produce
predictive distributions which in turn inform decision problems. By formalizing
these problems and the corresponding properties, we can use spatio-temporal
reach and escape logic to probabilistically assess their satisfaction. This
way, competing models can directly be ranked according to how well they solve
the actual problem at hand.
The approach is illustrated on an urban mobility application, where the
crowdedness in the center of Milan is proxied by aggregated mobile phone
traffic data. We specify several desirable spatio-temporal properties related
to city crowdedness such as a fault tolerant network or the reachability of
hospitals. After verifying these properties on draws from the posterior
predictive distributions, we compare several spatio-temporal Bayesian models
based on their overall and property-based predictive performance