A marginalised Markov Chain Monte Carlo approach for model based analysis of EEG data

The work presented in this paper focuses on fitting of a neural mass model to EEG data. Neurophysiology inspired mathematical models were developed for simulating brain's electrical activity imaged through Electroencephalography (EEG) more than three decades ago. At the present well informative models which even describe the functional integration of cortical regions also exists. However, a very limited amount of work is reported in literature on the subject of model fitting to actual EEG data. Here, we present a Bayesian approach for parameter estimation of the EEG model via a marginalized Markov Chain Monte Carlo (MCMC) approach.

Comparison of Two Methods for Caluculating the Partition Functions of Various Spatial Statistical Models

Likelihood computation in spatial statistics requires accurate and efficient calculation of the normalizing constant (i.e. partition function) of the Gibbs distribution of the model. Two available methods to calculate the normalizing constant by Markov chain Monte Carlo methods are compared by simulation experiments for an Ising model, a Gaussian Markov field model and a pairwise interaction point field model.

Credit risk of interest rate swaps : a comparative study of CIR and Monte Carlo simulation approach

This paper compares the credit risk profile for two types of model, the Monte Carlo model used in the existing literature, and the Cox, Ingersoll and Ross (CIR) model. Each of the profiles has a concave or hump-backed shape, reflecting the amortisation and diffusion effects. However, the CIR model generates significantly different results. In addition, we consider the sensitivity of these models of credit risk to initial interest rates, volatility, maturity, kappa and delta. The results show that the sensitivities vary across the models, and we explore the meaning of that variation.

Monte Carlo calculations of the free energy of binary SII hydrogen clathrate hydrates for identifying efficient promoter molecules

The thermodynamics of binary sII hydrogen clathrates with secondary guest molecules is studied with Monte Carlo simulations. The small cages of the sII unit cell are occupied by one H2 guest molecule. Different promoter molecules entrapped in the large cages are considered. Simulations are conducted at a pressure of 1000 atm in a temperature range of 233?293 K. To determine the stabilizing effect of different promoter molecules on the clathrate, the Gibbs free energy of fully and partially occupied sII hydrogen clathrates are calculated. Our aim is to predict what would be an efficient promoter molecule using properties such as size, dipole moment, and hydrogen bonding capability. The gas clathrate configurational and free energies are compared. The entropy makes a considerable contribution to the free energy and should be taken into account in determining stability conditions of binary sII hydrogen clathrates.

Monte Carlo simulations and capital structure research

The evolution of the debt ratio under alternative types of managerialbehavior can generate non-standard leverage processes. This createsproblems for statistical inference in empirical capital structure research. We argue in this paper that when the data generating process is not standard, a useful way to evaluate the appropriateness of inferences and the empirical methodology is via Monte Carlo simulations that mimic the data generating process under alternative assumptions about managerial behavior. We illustrate with several examples.

The cost of granting executive stock options with strike prices adjusted by the cost of capital

Purpose – The purpose of this paper is to estimate the cost of granting executive stocks with strike prices adjusted by the cost of capital.

Design/methodology/approach – In the paper a Monte Carlo simulation approach developed in Longstaff and Schwartz is used in conjunction with the subjective valuation model developed in Ingersoll to value these executive stock options that are subject to performance hurdles.

Findings – The paper finds that standard European Black-Scholes-Merton option values overstate the true cost to the firm of granting these executive stock options. The option values also decrease with a higher dividend yield, a higher performance hurdle, a longer vesting period, and a shorter maturity.

Research limitations/implications – While the study in the paper is limited to the valuation of executive options, the methodology can be used to study incentive effects of executive stock options that have a performance hurdle.

Practical implications – The approach used in this paper to estimate the cost of granting executive stock options is a clear improvement over standard European option pricing approaches that often result in biased estimates.

Originality/value – This paper presents a first attempt to integrate the Ingersoll utility-theoretic model and the Longstaff and Schwartz least squares Monte Carlo algorithm to estimate the subjective value and the objective cost of executive stock options with a performance hurdle. This valuation approach will be useful in the study of other types of executive compensation.

Hurdle rate : executive stock options

Executive stock options with a rising strike price are a recent innovation in executive compensation in Australia and New Zealand. These options combine a dividend protection feature and a strike price that increases at a hurdle rate set with reference to a cost of capital estimate. With a constant dividend yield, the strike price becomes a path-dependent function of the stock price and exact analytic valuation becomes intractable. However, path-dependent American options can be valued using a Monte Carlo approach proposed in Longstaff and Schwartz (2001). We examine procedures for valuing these options and compare them with Black and Scholes (1973) and Merton (1973) formula valuations.

Egg colour matching in an African cuckoo, as revealed by ultraviolet-visible reflectance spectrophotometry

Despite major differences between human and avian colour vision, previous studies of cuckoo egg mimicry have used human colour vision (or standards based thereon) to assess colour matching. Using ultraviolet-visible reflectance spectrophotometry (300-700 nm), we measured museum collections of eggs of the red-chested cuckoo and its hosts. The first three principal components explained more than 99% of the variance in spectra, and measures of cuckoo-host egg similarity derived from these transformations were compared with measures of cuckoo-host egg similarity estimated by human observers unaware of the hypotheses we were testing. Monte Carlo methods were used to simulate laying of cuckoo eggs at random in nests. Results showed that host and cuckoo eggs were very highly matched for an ultraviolet versus greenness component, which was not detected by humans. Furthermore, whereas cuckoo and host were dissimilar in achromatic brightness, humans did not detect this difference. Our study thus reveals aspects of cuckoo-host egg colour matching which have hitherto not been described. These results suggest subtleties and complexities in the evolution of host-cuckoo egg mimicry that were not previously suspected. Our results also have the potential to explain the longstanding paradox that some host species accept cuckoo eggs that are non-mimetic to the human eye.

Inferring activity budgets in wild animals to estimate the consequences of disturbances

Activity budgets can provide a direct link to an animal's bioenergetic budget and is thus a valuable unit of measure when assessing human-induced nonlethal effects on wildlife conservation status. However, activity budget inference can be challenging for species that are difficult to observe and require multiple observational variables. Here, we assessed whether whalewatching boat interactions could affect the activity budgets of minke whales (Balaenoptera acutorostrata). We used a stepwise modeling approach to quantitatively record, identify, and assign activity states to continuous behavioral time series data, to estimate activity budgets. First, we used multiple behavioral variables, recorded from continuous visual observations of individual animals, to quantitatively identify and define behavioral types. Activity states were then assigned to each sampling unit, using a combination of hidden and observed states. Three activity states were identified: nonfeeding, foraging, and surface feeding (SF). From the resulting time series of activity states, transition probability matrices were estimated using first-order Markov chains. We then simulated time series of activity states, using Monte Carlo methods based on the transition probability matrices, to obtain activity budgets, accounting for heterogeneity in state duration. Whalewatching interactions reduced the time whales spend foraging and SF, potentially resulting in an overall decrease in energy intake of 42%. This modeling approach thus provides a means to link short-term behavioral changes resulting from human disturbance to potential long-term bioenergetic consequences in animals. It also provides an analytical framework applicable to other species when direct observations of activity states are not possible.

Quantification of the finger functional range via explicit descriptions of reachable subspaces

In recent times, the finger flexibility assessment by means of reachable space is considered as an effective tool to describe the range of motion of the hand. Existing approaches numerically compute the reachable space using forward kinematics such as exhaustive scanning or Monte Carlo methods. In this paper, we provide explicit formulas mathematically determining the reachable space boundary. Green's theorem is used to deduce the corresponding capacity formula for the size of the reachable space as opposed to an implicit numerical solution. Using this new mechanism, we accurately quantify and compare the reachable space of different subjects in order to effectively compare the functionality of the fingers. We evaluate the performance of our proposed method against the kinematic feed-forward (KFF) approach in calculating the reachable space. The execution time to capture the reachable space is significantly less than that for the standard KFF method. The computational cost for quantifying the reachable space capacity is significantly improved due to explicit capacity formulas resulting from the abstract form of boundary descriptions of the reachable space, unique to the proposed approach.

Describing human finger flexibility via reachable subspaces

In recent years, the reachable space concept has attracted the attention of many researchers as a mean of describing finger flexibility. Existing approaches such as exhaustive scanning or Monte Carlo methods to obtain the reachable space are resource-hungry techniques. In this paper, we introduce a novel approach to determine and quantify the reachable space of the finger. The approach was developed around a set of formulae determining the boundary of the reachable space. The Monte Carlo simulation is proposed to estimate the capacity of the reachable space. Using the new technique, reachable spaces can be visualised and quantified in order to effectively compare the functionality of different subjects and their therapeutic status. The performance of the proposed method was evaluated against the kinematic feed-forward approach. The computational cost to obtain the reachable space is significantly less than the standard kinematic feed-forward approach due to exclusive description of the reachable space boundary, unique to the proposed approach.