23,440 research outputs found
Improved multivariate prediction regions for Markov process models
This paper concerns the specification of multivariate prediction regions which may be useful in time series applications whenever we aim at considering not just one single forecast but a group of consecutive forecasts. We review a general result on improved multivariate prediction and we use it in order to calculate conditional prediction intervals for Markov process models so that the associated coverage probability turns out to be close to the target value. This improved solution is asymptotically superior to the estimative one, which is simpler but it may lead to unreliable predictive conclusions. An application to general autoregressive models is presented, focusing in particular on AR and ARCH models
A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters
Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM-UA algorithm is a modified version of the original SCE-UA global optimization algorithm developed by Duan et al. [1992]. The SCEM-UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM-UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis-Hastings samplers
Conjugate Bayes for probit regression via unified skew-normal distributions
Regression models for dichotomous data are ubiquitous in statistics. Besides
being useful for inference on binary responses, these methods serve also as
building blocks in more complex formulations, such as density regression,
nonparametric classification and graphical models. Within the Bayesian
framework, inference proceeds by updating the priors for the coefficients,
typically set to be Gaussians, with the likelihood induced by probit or logit
regressions for the responses. In this updating, the apparent absence of a
tractable posterior has motivated a variety of computational methods, including
Markov Chain Monte Carlo routines and algorithms which approximate the
posterior. Despite being routinely implemented, Markov Chain Monte Carlo
strategies face mixing or time-inefficiency issues in large p and small n
studies, whereas approximate routines fail to capture the skewness typically
observed in the posterior. This article proves that the posterior distribution
for the probit coefficients has a unified skew-normal kernel, under Gaussian
priors. Such a novel result allows efficient Bayesian inference for a wide
class of applications, especially in large p and small-to-moderate n studies
where state-of-the-art computational methods face notable issues. These
advances are outlined in a genetic study, and further motivate the development
of a wider class of conjugate priors for probit models along with methods to
obtain independent and identically distributed samples from the unified
skew-normal posterior
Bayesian Nonstationary Spatial Modeling for Very Large Datasets
With the proliferation of modern high-resolution measuring instruments
mounted on satellites, planes, ground-based vehicles and monitoring stations, a
need has arisen for statistical methods suitable for the analysis of large
spatial datasets observed on large spatial domains. Statistical analyses of
such datasets provide two main challenges: First, traditional
spatial-statistical techniques are often unable to handle large numbers of
observations in a computationally feasible way. Second, for large and
heterogeneous spatial domains, it is often not appropriate to assume that a
process of interest is stationary over the entire domain.
We address the first challenge by using a model combining a low-rank
component, which allows for flexible modeling of medium-to-long-range
dependence via a set of spatial basis functions, with a tapered remainder
component, which allows for modeling of local dependence using a compactly
supported covariance function. Addressing the second challenge, we propose two
extensions to this model that result in increased flexibility: First, the model
is parameterized based on a nonstationary Matern covariance, where the
parameters vary smoothly across space. Second, in our fully Bayesian model, all
components and parameters are considered random, including the number,
locations, and shapes of the basis functions used in the low-rank component.
Using simulated data and a real-world dataset of high-resolution soil
measurements, we show that both extensions can result in substantial
improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure
- …