A Bayesian Framework for Estimating Seismic Wave Arrival Time

Because earthquakes have a large impact on human society, statistical methods for better studying earthquakes are required. One characteristic of earthquakes is the arrival time of seismic waves at a seismic signal sensor. Once we can estimate the earthquake arrival time accurately, the earthquake location can be triangulated, and assistance can be sent to that area correctly. This study presents a Bayesian framework to predict the arrival time of seismic waves with associated uncertainty. We use a change point framework to model the different conditions before and after the seismic wave arrives. To evaluate the performance of the model, we conducted a simulation study where we could evaluate the predictive performance of the model framework. The results show that our method has acceptable performance of arrival time prediction with accounting for the uncertainty

"Bayesian Estimation and Particle Filter for Max-Stable Processes"

Extreme values are often correlated over time, for example, in a financial time series, and these values carry various risks. Max-stable processes such as maxima of moving maxima (M3) processes have been recently considered in the literature to describe timedependent dynamics, which have been difficult to estimate. This paper first proposes a feasible and efficient Bayesian estimation method for nonlinear and non-Gaussian state space models based on these processes and describes a Markov chain Monte Carlo algorithm where the sampling efficiency is improved by the normal mixture sampler. Furthermore, a unique particle filter that adapts to extreme observations is proposed and shown to be highly accurate in comparison with other well-known filters. Our proposed algorithms were applied to daily minima of high-frequency stock return data, and a model comparison was conducted using marginal likelihoods to investigate the time-dependent dynamics in extreme stock returns for financial risk management.

New Estimation Approaches for the Hierarchical Linear Ballistic Accumulator Model

The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters. Modern approaches use hierarchical Bayesian models and Markov chain Monte-Carlo (MCMC) methods to estimate the posterior distribution of the parameters. Although there are several approaches available for model selection, they are all based on the posterior samples produced via MCMC, which means that the model selection inference inherits the properties of the MCMC sampler. To improve on current approaches to LBA inference we propose two methods that are based on recent advances in particle MCMC methodology; they are qualitatively different from existing approaches as well as from each other. The first approach is particle Metropolis-within-Gibbs; the second approach is density tempered sequential Monte Carlo. Both new approaches provide very efficient sampling and can be applied to estimate the marginal likelihood, which provides Bayes factors for model selection. The first approach is usually faster. The second approach provides a direct estimate of the marginal likelihood, uses the first approach in its Markov move step and is very efficient to parallelize on high performance computers. The new methods are illustrated by applying them to simulated and real data, and through pseudo code. The code implementing the methods is freely available.Comment: 35 pages, 6 figures, 7 table

Toward improved identifiability of hydrologic model parameters: The information content of experimental data

We have developed a sequential optimization methodology, entitled the parameter identification method based on the localization of information (PIMLI) that increases information retrieval from the data by inferring the location and type of measurements that are most informative for the model parameters. The PIMLI approach merges the strengths of the generalized sensitivity analysis (GSA) method [Spear and Hornberger, 1980], the Bayesian recursive estimation (BARE) algorithm [Thiemann et al., 2001], and the Metropolis algorithm [Metropolis et al., 1953]. Three case studies with increasing complexity are used to illustrate the usefulness and applicability of the PIMLI methodology. The first two case studies consider the identification of soil hydraulic parameters using soil water retention data and a transient multistep outflow experiment (MSO), whereas the third study involves the calibration of a conceptual rainfall-runoff model