Bulge Globular Clusters in Spiral Galaxies

There is now strong evidence that the metal-rich globular clusters (GC) near the center of our Galaxy are associated with the Galactic bulge rather than the disk as previously thought. Here we extend the concept of bulge GCs to the GC systems of nearby spiral galaxies. In particular, the kinematic and metallicity properties of the GC systems favor a bulge rather than a disk origin. The number of metal-rich GCs normalized by the bulge luminosity is roughly constant (i.e. bulge S_N ~ 1) in nearby spirals, and this value is similar to that for field ellipticals when only the red (metal--rich) GCs are considered. We argue that the metallicity distributions of GCs in spiral and elliptical galaxies are remarkably similar, and that they obey the same correlation of mean GC metallicity with host galaxy mass. We further suggest that the metal-rich GCs in spirals are the direct analogs of the red GCs seen in ellipticals. The formation of a bulge/spheroidal stellar system is accompanied by the formation of metal-rich GCs. The similarities between GC systems in spiral and elliptical galaxies appear to be greater than the differences.Comment: 5 pages, Latex, 2 figures, 1 table, Accepted for publication in ApJ Letter

Bayesian Analysis of the Stochastic Conditional Duration Model

A Bayesian Markov Chain Monte Carlo methodology is developed for estimating the stochastic conditional duration model. The conditional mean of durations between trades is modelled as a latent stochastic process, with the conditional distribution of durations having positive support. The sampling scheme employed is a hybrid of the Gibbs and Metropolis Hastings algorithms, with the latent vector sampled in blocks. The suggested approach is shown to be preferable to the quasi-maximum likelihood approach, and its mixing speed faster than that of an alternative single-move algorithm. The methodology is illustrated with an application to Australian intraday stock market data.Transaction data, Latent factor model, Non-Gaussian state space model, Kalman filter and simulation smoother.

Decision Tree Analysis as a Supplementary Tool to Enhance Histomorphological Differentiation when Distinguishing Human from Non-human Cranial Bone in both Burnt and Unburnt States: A feasibility study

This feasibility study was undertaken to describe and record the histological characteristics of burnt and unburnt cranial bone fragments from human and non-human bones. Reference series of fully mineralised, transverse sections of cranial bone, from all variables and specimen states were prepared by manual cutting and semi-automated grinding and polishing methods. A photomicrograph catalogue reflecting differences in burnt and unburnt bone from human and non-humans was recorded and qualitative analysis was performed using an established classification system based on primary bone characteristics. The histomorphology associated with human and non-human samples was, for the main part, preserved following burning at high temperature. Clearly, fibro-lamellar complex tissue subtypes, such as plexiform or laminar primary bone, were only present in non-human bones. A decision tree analysis based on histological features provided a definitive identification key for distinguishing human from non-human bone, with an accuracy of 100%. The decision tree for samples where burning was unknown was 96% accurate, and multi-step classification to taxon was possible with 100% accuracy. The results of this feasibility study, strongly suggest that histology remains a viable alternative technique if fragments of cranial bone require forensic examination in both burnt and unburnt states. The decision tree analysis may provide an additional, but vital tool to enhance data interpretation. Further studies are needed to assess variation in histomorphology taking into account other cranial bones, ontogeny, species and burning conditions

Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices: Application of a Bivariate Kalman Filter

In this paper Bayesian methods are applied to a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Posterior densities for all model parameters, latent volatilities and the market price of volatility risk are produced via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws for the unobserved volatilities are obtained by applying the Kalman filter and smoother to a linearization of a state-space representation of the model. The method is illustrated using the Heston (1993) stochastic volatility model applied to Australian News Corporation spot and option price data. Alternative models nested in the Heston framework are ranked via Bayes Factors and via fit, predictive and hedging performance.Option Pricing; Volatility Risk; Markov Chain Monte Carlo; Nonlinear State Space Model; Kalman Filter and Smoother.

Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models

The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.Bayesian methodology, stochastic volatility, durations, non-centred in location, non-centred in scale, inefficiency factors.

Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two K\"ahler Forms

In this paper, we extend our geometrical derivation of expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples. We expect that our results can be easily generalized to arbitrary toric manifold.Comment: 45 pages, 2 figures, minor errors are corrected, English is refined. Section 1 and Section 2 are enlarged. Especially in Section 2, confusion between the notion of resolution and the notion of compactification is resolved. Computation under non-zero equivariant parameters are added in Section

Implicit Bayesian Inference Using Option Prices

A Bayesian approach to option pricing is presented, in which posterior inference about the underlying returns process is conducted implicitly via observed option prices. A range of models allowing for conditional leptokurtosis, skewness and time-varying volatility in returns are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Models are ranked according to several criteria, including out-of-sample fit, predictive and hedging performance. The methodology accommodates heteroscedasticity and autocorrelation in the option pricing errors, as well as regime shifts across contract groups. The method is applied to intraday option price data on the S&P500 stock index for 1995. Whilst the results provide support for models which accommodate leptokurtosis, no one model dominates according to all criteria considered.Bayesian Option Pricing; Leptokurtosis; Skewness; GARCH Option Pricing; Option Price Prediction; Hedging Errors.

Damp Mergers: Recent Gaseous Mergers without Significant Globular Cluster Formation?

Here we test the idea that new globular clusters (GCs) are formed in the same gaseous ("wet") mergers or interactions that give rise to the young stellar populations seen in the central regions of many early-type galaxies. We compare mean GC colors with the age of the central galaxy starburst. The red GC subpopulation reveals remarkably constant mean colors independent of galaxy age. A scenario in which the red GC subpopulation is a combination of old and new GCs (formed in the same event as the central galaxy starburst) can not be ruled out; although this would require an age-metallicity relation for the newly formed GCs that is steeper than the Galactic relation. However, the data are also well described by a scenario in which most red GCs are old, and few, if any, are formed in recent gaseous mergers. This is consistent with the old ages inferred from some spectroscopic studies of GCs in external systems. The event that induced the central galaxy starburst may have therefore involved insufficient gas mass for significant GC formation. We term such gas-poor events "damp" mergers.Comment: 17 pages, 5 figures, ApJ accepte