Discrete chain graph models

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen--Wermuth--Frydenberg) or block concentration type, yields discrete models for categorical data that are smooth. This paper considers the structural properties of the discrete models based on the three alternative Markov properties. It is shown by example that two of the alternative Markov properties can lead to non-smooth models. The remaining model class, which can be viewed as a discrete version of multivariate regressions, is proven to comprise only smooth models. The proof employs a simple change of coordinates that also reveals that the model's likelihood function is unimodal if the chain components of the graph are complete sets.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ172 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Deterministic Brownian motion generated from differential delay equations

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.Comment: 15 pages, 13 figure

Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure -- network modularity (the propensity for edges to be cluster into dense groups that are sparsely connected between each other). To reach this goal, we design a model of reaction-systems where network modularity can be controlled and measure how well the reduction to simple graphs capture the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate-product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction-systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreate correlations between degree and mass of the molecules.Comment: to appear in J. Roy. Soc. Intefac

Target differentiation with simple infrared sensors using statistical pattern recognition techniques

Cataloged from PDF version of article.This study compares the performances of various statistical pattern recognition techniques for the differentiation of commonly encountered features in indoor environments, possibly with different surface properties, using simple infrared (IR) sensors. The intensity measurements obtained from such sensors are highly dependent on the location, geometry, and surface properties of the reflecting feature in a way that cannot be represented by a simple analytical relationship, therefore complicating the differentiation process. We construct feature vectors based on the parameters of angular IR intensity scans from different targets to determine their geometry and/or surface type. Mixture of normals classifier with three components correctly differentiates three types of geometries with different surface properties, resulting in the best performance (100%) in geometry differentiation. Parametric differentiation correctly identifies six different surface types of the same planar geometry, resulting in the best surface differentiation rate (100%). However, this rate is not maintained with the inclusion of more surfaces. The results indicate that the geometrical properties of the targets are more distinctive than their surface properties, and surface recognition is the limiting factor in differentiation. The results demonstrate that simple IR sensors, when coupled with appropriate processing and recognition techniques, can be used to extract substantially more information than such devices are commonly employed for. (C) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserve

Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world

We study behavioral action sequences of players in a massive multiplayer online game. In their virtual life players use eight basic actions which allow them to interact with each other. These actions are communication, trade, establishing or breaking friendships and enmities, attack, and punishment. We measure the probabilities for these actions conditional on previous taken and received actions and find a dramatic increase of negative behavior immediately after receiving negative actions. Similarly, positive behavior is intensified by receiving positive actions. We observe a tendency towards anti-persistence in communication sequences. Classifying actions as positive (good) and negative (bad) allows us to define binary 'world lines' of lives of individuals. Positive and negative actions are persistent and occur in clusters, indicated by large scaling exponents alpha~0.87 of the mean square displacement of the world lines. For all eight action types we find strong signs for high levels of repetitiveness, especially for negative actions. We partition behavioral sequences into segments of length n (behavioral `words' and 'motifs') and study their statistical properties. We find two approximate power laws in the word ranking distribution, one with an exponent of kappa-1 for the ranks up to 100, and another with a lower exponent for higher ranks. The Shannon n-tuple redundancy yields large values and increases in terms of word length, further underscoring the non-trivial statistical properties of behavioral sequences. On the collective, societal level the timeseries of particular actions per day can be understood by a simple mean-reverting log-normal model.Comment: 6 pages, 5 figure

Heterogeneity, Profitability and Autocorrelations

This paper contributes to the development of recent literature on the explanation power and calibration issue of heterogeneous asset pricing models by presenting a simple stochastic market fraction asset pricing model of two types of traders (fundamentalists and trend followers) under a market maker scenario. It seeks to explain aspects of financial market behaviour (such as market dominance, under and over-reaction, profitability and survivability) and to characterize various statistical properties (including autocorrelation structure) of the stochastic model by using the the dynamics of the underlying deterministic system, traders? behaviour and market fractions. Statistical analysis based on Monte Carlo simulations shows that the long-run behaviour and convergence of the market prices, long (short)-run profitability of the fundamental (trend following) trading strategy, survivability of chartists, and various under and over-reaction autocorrelation patterns of returns can be characterized by the stability and bifurcations of the underlying deterministic system. Our analysis underpins mechanism on various market behaviour (such as under/over-reactions), market dominance and stylized facts in high frequency financial markets.asset pricing; heterogeneous beliefs; market fraction; stability; bifurcation; market behaviour; profitability; survivability; autocorrelation

Evidence for self-interaction of charge distribution in charge-coupled devices

Charge-coupled devices (CCDs) are widely used in astronomy to carry out a variety of measurements, such as for flux or shape of astrophysical objects. The data reduction procedures almost always assume that ther esponse of a given pixel to illumination is independent of the content of the neighboring pixels. We show evidence that this simple picture is not exact for several CCD sensors. Namely, we provide evidence that localized distributions of charges (resulting from star illumination or laboratory luminous spots) tend to broaden linearly with increasing brightness by up to a few percent over the whole dynamic range. We propose a physical explanation for this "brighter-fatter" effect, which implies that flatfields do not exactly follow Poisson statistics: the variance of flatfields grows less rapidly than their average, and neighboring pixels show covariances, which increase similarly to the square of the flatfield average. These covariances decay rapidly with pixel separation. We observe the expected departure from Poisson statistics of flatfields on CCD devices and show that the observed effects are compatible with Coulomb forces induced by stored charges that deflect forthcoming charges. We extract the strength of the deflections from the correlations of flatfield images and derive the evolution of star shapes with increasing flux. We show for three types of sensors that within statistical uncertainties,our proposed method properly bridges statistical properties of flatfields and the brighter-fatter effect