Inferences from prior-based loss functions

Inferences that arise from loss functions determined by the prior are considered and it is shown that these lead to limiting Bayes rules that are closely connected with likelihood. The procedures obtained via these loss functions are invariant under reparameterizations and are Bayesian unbiased or limits of Bayesian unbiased inferences. These inferences serve as well-supported alternatives to MAP-based inferences

Invariant PP-values for model checking

$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution, it is not clear that there is a better choice for a measure of surprise. This paper is concerned with the definition of appropriate model-based $P$-values for model checking.Comment: Published in at http://dx.doi.org/10.1214/09-AOS727 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effect of epitaxial strain on ferroelectric polarization in multiferroic BiFeO3 films

Multiferroic BiFeO3 epitaxial films with thickness ranging from 40 nm to 960 nm were grown by pulsed laser deposition on SrTiO3 (001) substrates with SrRuO3 bottom electrodes. X-ray characterization shows that the structure evolves from angularly-distorted tetragonal with c/a ~ 1.04 to more bulk-like distorted rhombohedral (c/a ~ 1.01) as the strain relaxes with increasing thickness. Despite this significant structural evolution, the ferroelectric polarization along the body diagonal of the distorted pseudo-cubic unit cells, as calculated from measurements along the normal direction, barely changes.Comment: Legend in Fig.3 corrected and et

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the R\"ossler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -- thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set