24,012 research outputs found
A Bayesian framework for verification and recalibration of ensemble forecasts: How uncertain is NAO predictability?
Predictability estimates of ensemble prediction systems are uncertain due to
limited numbers of past forecasts and observations. To account for such
uncertainty, this paper proposes a Bayesian inferential framework that provides
a simple 6-parameter representation of ensemble forecasting systems and the
corresponding observations. The framework is probabilistic, and thus allows for
quantifying uncertainty in predictability measures such as correlation skill
and signal-to-noise ratios. It also provides a natural way to produce
recalibrated probabilistic predictions from uncalibrated ensembles forecasts.
The framework is used to address important questions concerning the skill of
winter hindcasts of the North Atlantic Oscillation for 1992-2011 issued by the
Met Office GloSea5 climate prediction system. Although there is much
uncertainty in the correlation between ensemble mean and observations, there is
strong evidence of skill: the 95% credible interval of the correlation
coefficient of [0.19,0.68] does not overlap zero. There is also strong evidence
that the forecasts are not exchangeable with the observations: With over 99%
certainty, the signal-to-noise ratio of the forecasts is smaller than the
signal-to-noise ratio of the observations, which suggests that raw forecasts
should not be taken as representative scenarios of the observations. Forecast
recalibration is thus required, which can be coherently addressed within the
proposed framework.Comment: 36 pages, 10 figure
Bayesian Nonparametric Calibration and Combination of Predictive Distributions
We introduce a Bayesian approach to predictive density calibration and
combination that accounts for parameter uncertainty and model set
incompleteness through the use of random calibration functionals and random
combination weights. Building on the work of Ranjan, R. and Gneiting, T. (2010)
and Gneiting, T. and Ranjan, R. (2013), we use infinite beta mixtures for the
calibration. The proposed Bayesian nonparametric approach takes advantage of
the flexibility of Dirichlet process mixtures to achieve any continuous
deformation of linearly combined predictive distributions. The inference
procedure is based on Gibbs sampling and allows accounting for uncertainty in
the number of mixture components, mixture weights, and calibration parameters.
The weak posterior consistency of the Bayesian nonparametric calibration is
provided under suitable conditions for unknown true density. We study the
methodology in simulation examples with fat tails and multimodal densities and
apply it to density forecasts of daily S&P returns and daily maximum wind speed
at the Frankfurt airport.Comment: arXiv admin note: text overlap with arXiv:1305.2026 by other author
Bayesian nonparametric sparse VAR models
High dimensional vector autoregressive (VAR) models require a large number of
parameters to be estimated and may suffer of inferential problems. We propose a
new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional
VAR models that can improve estimation efficiency and prediction accuracy. Our
hierarchical prior overcomes overparametrization and overfitting issues by
clustering the VAR coefficients into groups and by shrinking the coefficients
of each group toward a common location. Clustering and shrinking effects
induced by the BNP-Lasso prior are well suited for the extraction of causal
networks from time series, since they account for some stylized facts in
real-world networks, which are sparsity, communities structures and
heterogeneity in the edges intensity. In order to fully capture the richness of
the data and to achieve a better understanding of financial and macroeconomic
risk, it is therefore crucial that the model used to extract network accounts
for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the
paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ----
Supplementary Material available on reques
A Comment on âA Review of Student Test Properties in Condition of Multifactorial Linear Regressionâ
A recent article (Pavelescu, 2009) proposes a correction to the conventional student-t test of significance in linear regression models, but offers no formal description of its properties. This comment formally characterizes the sampling properties of the corrected student-t statistic. In application to multifactorial regressions, it turns out that the corrected student-t statistic is not ancillary â its sampling distribution depends on unknown nuisance parameters.Therefore, it is impossible to reasonably compute critical values and operatively designate a rejection criterion using such a test statistic, which makes the proposed testing procedure impractical. Some suggestions regarding the search for similar testing procedures are proposed and a Bayesian alternative is further discussed.multifactorial classical normal regression, collinearity, multicollinearity, significance test, sampling distributions, power functions, Bayesian linear regression, prior information, posterior distributions
NEW APPROACHES FOR VERY SHORT-TERM STEADY-STATE ANALYSIS OF AN ELECTRICAL DISTRIBUTION SYSTEM WITH WIND FARMS
Distribution networks are undergoing radical changes due to the high level of penetration of dispersed generation. Dispersed generation systems require particular attention due to their incorporation of uncertain energy sources, such as wind farms, and due to the impacts that such sources have on the planning and operation of distribution networks. In particular, the foreseeable, extensive use of wind turbine generator units in the future requires that distribution system engineers properly account for their impacts on the system. Many new technical considerations must be addressed, including protection coordination, steady-state analysis, and power quality issues. This paper deals with the very short-term, steady-state analysis of a distribution system with wind farms, for which the time horizon of interest ranges from one hour to a few hours ahead. Several wind-forecasting methods are presented in order to obtain reliable input data for the steady-state analysis. Both deterministic and probabilistic methods were considered and used in performing deterministic and probabilistic load-flow analyses. Numerical applications on a 17-bus, medium-voltage, electrical distribution system with various wind farms connected at different busbars are presented and discusse
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