a practical guide to heavy tails statistical techniques and applications part 1 applications heavy tailed probability distributions in the world wide web m e crovella et al self similarity and heavy tails structural modelling of network traffic w willinger et al heavy tails in high frequency financial data u a muller et al stable paretian modelling in finance some empirical and theoretical aspects s mittnik et al risk management and quantile estimation f bassi et al part 2 time series analyzing stable time series r j adler et al inference for linear processes with stable noise m calder r a davis on estimating the intensity of long range dependence in finite and infinite variance time series m s taqqu v teverovsky why non linearities can ruin the heavy tailed modeller s day s i resnick periodogram estimates from heavy tailed data t mikosch bayesian inference for time series with infinite variance stable innovations n ravishanker z qiou part 3 heavy tail estimation hill bootstrap and jackknife estimators for heavy tails o v pictet et al characteristic function based estimation of stable distribution parameters s m kogan d b williams part 4 regression bootstrapping signs and permutations for regression with heavy tailed errors a robust resampling r lepage et al linear regression with stable disturbances j h mcculloch part 5 signal processing deviation from normality in statistical signal processing parameter estimation with alpha stable distributions p tsakalides c l nikias statistical modelling and receiver design for multi user communication networks g a tsihrintzis part 6 model structures subexponential distributions c m goldie c kluppelberg structure of stationary stable processes j rosinski tail behaviour of some shot noise processes g samorodnitsky part 7 numerical procedures numerical approximation of the symmetric stable distribution and density j h mcculloch table of the maximally skewed stable distributions j h mcculloch d b panton multivariate stable distributions approximation estimation simulation and identification j p nolan univariate stable distributions parametrizations and software j p nolan

the matrix stick breaking process flexible bayes meta analysis in analyzing data from multiple related studies it often is of interest to borrow information across studies and to cluster similar studies although parametric hierarchical models are commonly used of concern is sensitivity to the form chosen for the random effects distribution a dirichlet process dp prior can allow the distribution to be unknown while clustering studies however the dp does not allow local clustering of studies with respect to a subset of the coefficients without making independence assumptions motivated by this problem we propose a matrix stick breaking process msbp as a prior for a matrix of random probability measures properties of the msbp are considered and methods are developed for posterior computation using markov chain monte carlo using the msbp as a prior for a matrix of study specific regression coefficients we demonstrate advantages over parametric modeling in simulated examples the methods are further illustrated using a multinational uterotrophic bioassay s

modeling for dynamic ordinal regression relationships an application to estimating maturity of rockfish in california abstractwe develop a bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time the motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age length and maturity the latter recorded on an ordinal scale the methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses this approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut off points relating the latent continuous and ordinal responses a novel dependent dirichlet process prior for time dependent mixing distributions extends the model to the dynamic setting the methodology is used for a detailed study of relationships between maturity age and length for chilipepper rockfish using data collected over 15 years along th

a modified kolmogorov smirnov test sensitive to tail alternatives it is well known that the kolmogorov smirnov k s test exhibits poor sensitivity to deviations from the hypothesized distribution that occur in the tails a modified version of the k s test is introduced that is more sensitive than the k s test to deviations in the tails the finite and infinite sample distribution along with the consistency properties of the proposed test are studied tables of critical values are provided for two versions of the test one sensitive to heavy tail alternatives and one sensitive to light tail alternatives and the finite sample properties of these two versions of the test are investigated

moments of random matrices and hypergeometric orthogonal polynomials we establish a new connection between moments of n times n random matrices xn and hypergeometric orthogonal polynomials specifically we consider moments mathbb e rm tr x n s as a function of the complex variable s in mathbb c whose analytic structure we describe completely we discover several remarkable features including a reflection symmetry or functional equation zeros on a critical line in the complex plane and orthogonality relations an application of the theory resolves part of an integrality conjecture of cunden et al j math phys 57 111901 2016 on the time delay matrix of chaotic cavities in each of the classical ensembles of random matrix theory gaussian laguerre jacobi we characterise the moments in terms of the askey scheme of hypergeometric orthogonal polynomials we also calculate the leading order n rightarrow infty asymptotics of the moments and discuss their symmetries and zeroes we discuss aspects of these phenomena beyond the random matrix setting including the mellin transform of products and wronskians of pairs of classical orthogonal polynomials when the random matrix model has orthogonal or symplectic symmetry we obtain a new duality formula relating their moments to hypergeometric orthogonal polynomials

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

output tracking for nonlinear systems with singular points some of the well known linear results on output tracking have been generalized to include nonlinear control systems by removing from the state space a codimension one submanifold of singular points these points do not exist in the linear case but in nonlinear tracking applications the system trajectory can begin at or pass through singular points the purpose of this paper is to study nonlinear output tracking with singular points

power law statistics and universal scaling in the absence of criticality critical states are sometimes identified experimentally through power law statistics or universal scaling functions we show here that such features naturally emerge from networks in self sustained irregular regimes away from criticality in these regimes statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics we thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power law statistics indicating that these are not sufficient to establish criticality we rather suggest that these are universal features of large scale networks when considered macroscopically these results put caution on the interpretation of scaling laws found in nature

radial structure of the internet the structure of the internet at the autonomous system as level has been studied by the physics mathematics and computer science communities we extend this work to include features of the core and the periphery taking a radial perspective on as network structure new methods for plotting as data are described and they are used to analyse datasets that have been extended to contain edges missing from earlier collections the average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure common vertex specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices two datasets are analysed

bayesian poisson process partition calculus with an application to bayesian levy moving averages this article develops and describes how to use results concerning disintegrations of poisson random measures these results are fashioned as simple tools that can be tailor made to address inferential questions arising in a wide range of bayesian nonparametric and spatial statistical models the poisson disintegration method is based on the formal statement of two results concerning a laplace functional change of measure and a poisson palm fubini calculus in terms of random partitions of the integers 1 n the techniques are analogous to but much more general than techniques for the dirichlet process and weighted gamma process developed in ann statist 12 1984 351 3571 and ann inst statist math 41 1989 227 245 in order to illustrate the flexibility of the approach large classes of random probability measures and random hazards or intensities which can be expressed as functionals of poisson random measures are described we describe a unified posterior analysis of classes of discrete random probability which identifies and exploits features common to all these models the analysis circumvents many of the difficult issues involved in bayesian nonparametric calculus including a combinatorial component this allows one to focus on the unique features of each process which are characterized via real valued functions h the applicability of the technique is further illustrated by obtaining explicit posterior expressions for levy cox moving average processes within the general setting of multiplicative intensity models in addition novel computational procedures similar to efficient procedures developed for the dirichlet process are briefly discussed for these models

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

recursion for the smallest eigenvalue density of β wishart laguerre ensemble the statistics of the smallest eigenvalue of wishart laguerre ensemble is important from several perspectives the smallest eigenvalue density is typically expressible in terms of determinants or pfaffians these results are of utmost significance in understanding the spectral behavior of wishart laguerre ensembles and among other things unveil the underlying universality aspects in the asymptotic limits however obtaining exact and explicit expressions by expanding determinants or pfaffians becomes impractical if large dimension matrices are involved for the real matrices beta 1 edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices very recently an analogous recurrence scheme has been obtained for the complex matrices beta 2 in the present work we extend this to beta wishart laguerre ensembles for the case when exponent alpha in the associated laguerre weight function lambda alpha e beta lambda 2 is a non negative integer while beta is positive real this also gives access to the smallest eigenvalue density of fixed trace beta wishart laguerre ensemble as well as moments for both cases moreover comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly exact evaluations for large values of n the matrix dimension and alpha also enable us to compare with tracy widom density and large deviation results of katzav and castillo we also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the wigner smith matrix and are relevant to the problem of quantum chaotic scattering

theory of random matrices with strong level confinement orthogonal polynomial approach strongly non gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in the presence and the absence of a hard edge in their energy spectra employing a theory of polynomials orthogonal with respect to exponential weights we calculate with an asymptotic accuracy the two point kernel over all distance scale and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the end points of the spectrum we also obtain the exact expressions for density of levels one and two point green s functions and prove that a universal local relationship exists for the suitably normalized and rescaled connected two point green s function the connection between the structure of the szeg o function entering strong polynomial asymptotics and mean field equation is traced textcopyright 1996 the american physical society

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

controlling the reinforcement in bayesian non parametric mixture models summary the paper deals with the problem of determining the number of components in a mixture model we take a bayesian non parametric approach and adopt a hierarchical model with a suitable non parametric prior for the latent structure a commonly used model for such a problem is the mixture of dirichlet process model here we replace the dirichlet process with a more general non parametric prior obtained from a generalized gamma process the basic feature of this model is that it yields a partition structure for the latent variables which is of gibbs type this relates to the well known exchangeable product partition models if compared with the usual mixture of dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter belonging to the interval 0 1 it is shown that such a parameter greatly influences the clustering behaviour of the model a value of that is close to 1 generates a large number of clusters most of which are of small size then a reinforcement mechanism which is driven by acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements these features turn out to be very useful in the context of mixture modelling since it is difficult to specify a priori the reinforcement rate it is reasonable to specify a prior for hence the strength of the reinforcement mechanism is controlled by the data

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

hierarchical mixture modeling with normalized inverse gaussian priors in recent years the dirichlet process prior has experienced a great success in the context of bayesian mixture modeling the idea of overcoming discreteness of its realizations by exploiting it in hierarchical models combined with the development of suitable sampling techniques represent one of the reasons of its popularity in this article we propose the normalized inverse gaussian n ig process as an alternative to the dirichlet process to be used in bayesian hierarchical models the n ig prior is constructed via its finite dimensional distributions this prior although sharing the discreteness property of the dirichlet prior is characterized by a more elaborate and sensible clustering which makes use of all the information contained in the data whereas in the dirichlet case the mass assigned to each observation depends solely on the number of times that it occurred for the n ig prior the weight of a single observation depends heavily on the whole number of ties in the sample moreover expressio

estimation and prediction for stochastic blockstructures a statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed the probability model assumes that the vertices of the digraph are partitioned into several unobserved latent classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong a bayesian estimator based on gibbs sampling is proposed the basic model is not identified because class labels are arbitrary the resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership in addition models are considered where class labels are identified by prior distributions for the class membership of some of the vertices the model is illustrated by an example from the social networks literature kapferer s tailor shop

semiparametric bayesian inference for stochastic frontier models in this paper we propose a semiparametric bayesian framework for the analysis of stochastic frontiers and efficiency measurement the distribution of inefficiencies is modelled nonparametrically through a dirichlet process prior we suggest prior distributions and implement a bayesian analysis through an efficient markov chain monte carlo sampler which allows us to deal with practically relevant sample sizes we also consider the case where the efficiency distribution varies with firm characteristics the methodology is applied to a cost frontier estimated from a panel data set on 382 u s hospitals

a method for combining inference across related nonparametric bayesian models summary we consider the problem of combining inference in related nonparametric bayes models analogous to parametric hierarchical models the hierarchical extension formalizes borrowing strength across the related submodels in the nonparametric context modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional we discuss a formal definition of such a hierarchical model the approach includes a regression at the level of the nonparametric model for the special case of dirichlet process mixtures we develop a markov chain monte carlo scheme to allow efficient implementation of full posterior inference in the given model

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

exact output tracking theory for systems with parameter jumps in this paper we consider the exact output tracking problem for systems with parameter jumps necessary and sufficient conditions are derived for the elimination of switching introduced output transient previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps switches such techniques are however only applicable to minimum phase systems in contrast our approach is applicable to nonminimum phase systems and obtains bounded but possibly non causal solutions if the reference trajectories are generated by an exo system then we develop an exact tracking controller in a feedback form as in standard regulator theory we obtain a linear map from the states of the exo system to the desired system state which is defined via a matrix differential equation the constant solution of this differential equation provides asymptotic tracking and coincides with the feedback law used in standard regulator theory the obtained results are applied to a simple flexible manipulator with jumps in the pay load mass

switching through singularities asymptotic tracking is studied for systems which are not regular that is the relative degree is not well defined for these systems the input output linearizing control law has singularities we propose a tracking control law which switches between an approximate tracking law hauser et al ieee trans automat control 37 3 1992 392 398 close to the singularities and an exact tracking law away from the singularities and we study the applicability of this law based on the behavior of the system s zero dynamics at the switching boundary as in hauser et al ieee trans automat control 37 3 1992 392 398 the ball and beam example is used to motivate the study

incremental sliding mode control of the ball and beam we show that using a switched periodic controller we can incrementally track integral curves of certain lie brackets of the drift and controlled vector fields for the ball and beam this allows us to design a sliding mode controller which overcomes the problems associated with singular states and results in effective global tracking of large motions of the ball

consistency of community detection in networks under degree corrected stochastic block models community detection is a fundamental problem in network analysis with applications in many diverse areas the stochastic block model is a common tool for model based community detection and asymptotic tools for checking consistency of community detection under the block model have been recently developed however the block model is limited by its assumption that all nodes within a community are stochastically equivalent and provides a poor fit to networks with hubs or highly varying node degrees within communities which are common in practice the degree corrected stochastic block model was proposed to address this shortcoming and allows variation in node degrees within a community while preserving the overall block community structure in this paper we establish general theory for checking consistency of community detection under the degree corrected stochastic block model and compare several community detection criteria under both the standard and the degree corrected models we show which criteria are consistent under which models and constraints as well as compare their relative performance in practice we find that methods based on the degree corrected block model which includes the standard block model as a special case are consistent under a wider class of models and that modularity type methods require parameter constraints for consistency whereas likelihood based methods do not on the other hand in practice the degree correction involves estimating many more parameters and empirically we find it is only worth doing if the node degrees within communities are indeed highly variable we illustrate the methods on simulated networks and on a network of political blogs

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

on some simple estimates of an exponent of regular variation summary we present a class of simple estimates of an exponent of regular variation unlike those proposed recently by de haan and resnick 1980 ours converge at an algebraic rather than a logarithmic rate and unlike those considered by teugels 1980 their form does not depend on the unknown exponent

statistical distribution of the wigner smith time delay matrix moments for chaotic cavities we derive the joint distribution of the moments trq 1 of the wigner smith matrix for a chaotic cavity supporting a large number of scattering channels n this distribution turns out to be asymptotically gaussian and we compute explicitly averages and covariances the results are in a compact form and have been verified numerically the general methodology of proof and computations has a wide range of applications

matrix models for beta ensembles this paper constructs tridiagonal random matrix models for general 0 hermite gaussian and laguerre wishart ensembles these generalize the well known gaussian and wishart models for 1 2 4 furthermore in the cases of the laguerre ensembles we eliminate the exponent quantization present in the previously known models we further discuss applications for the new matrix models and present some open problems

exchangeable random measures for sparse and modular graphs with overlapping communities we propose a novel statistical model for sparse networks with overlapping community structure the model is based on representing the graph as an exchangeable point process and naturally generalizes existing probabilistic models with overlapping block structure to the sparse regime our construction builds on vectors of completely random measures and has interpretable parameters each node being assigned a vector representing its level of affiliation to some latent communities we develop methods for simulating this class of random graphs as well as to perform posterior inference we show that the proposed approach can recover interpretable structure from two real world networks and can handle graphs with thousands of nodes and tens of thousands of edges

on the fractal characterization of paretian poisson processes abstract paretian poisson processes are poisson processes which are defined on the positive half line have maximal points and are quantified by power law intensities paretian poisson processes are elemental in statistical physics and are the bedrock of a host of power law statistics ranging from pareto s law to anomalous diffusion in this paper we establish evenness based fractal characterizations of paretian poisson processes considering an array of socioeconomic evenness based measures of statistical heterogeneity we show that amongst the realm of poisson processes which are defined on the positive half line and have maximal points paretian poisson processes are the unique class of fractal processes exhibiting scale invariance the results established in this paper are diametric to previous results asserting that the scale invariance of poisson processes with respect to physical randomness based measures of statistical heterogeneity is characterized by exponential poissonian intensities

coordinated path following for unicycles we formulate a coordinated path following problem for n unicycle mobile robots as an instance of a nested set stabilization problem stabilization of the first set corresponds to driving the unicycles to their assigned paths stabilization of the second set a subset of the first corresponds to meeting the coordination specification the first set is stabilized for initial conditions sufficiently close to the set in a decentralized manner using feedback linearization for general coordination tasks we utilize feedback linearization to stabilize the nested set in a centralized manner again for initial conditions sufficiently close to the second set in the special case in which coordination entails making the unicycles maintain a formation along their paths we employ a semi distributed control law under less restrictive communication assumptions experimental results are provided

stability in a system subject to noise with regulated periodicity the stability of a simple dynamical system subject to multiplicative one side pulse noise with hidden periodicity is investigated both analytically and numerically the stability analysis is based on the exact result for the characteristic functional of the renewal pulse process the influence of the memory effects on the stability condition is analyzed for two cases i the dead time distorted poissonian process and ii the renewal process with pareto distribution we show that for fixed noise intensity the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

a robust hybrid stabilization strategy for equilibria for an equilibrium of a general dynamical system the domain of stability of a linear feedback controller is enlarged by the use of a general hybrid or switching strategy the strategy is illustrated for numerical simulations of an inverted double pendulum on a cart

understanding the determinants of volatility clustering in terms of stationary markovian processes abstract volatility is a key variable in the modeling of financial markets the most striking feature of volatility is that it is a long range correlated stochastic variable i e its autocorrelation function decays like a power law for large time lags in the present work we investigate the determinants of such feature starting from the empirical observation that the exponent of a certain stock s volatility is a linear function of the average correlation of such stock s volatility with all other volatilities we propose a simple approach consisting in diagonalizing the cross correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts as a result the diagonalized volatilities result to share with the original volatilities either the power law decay of the probability density function and the power law decay of the autocorrelation function this would indicate that volatility clustering is already present in the diagonalized un correlated volatilities we therefore present a parsimonious univariate model based on a non linear langevin equation that well reproduces these two stylized facts of volatility the model helps us in understanding that the main source of volatility clustering once volatilities have been diagonalized is that the economic forces driving volatility can be modeled in terms of a smoluchowski potential with logarithmic tails

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation abstract the generalized logistic equation is proposed to model kinetics and statistics of natural processes such as earthquakes forest fires floods landslides and many others this equation has the form d n a d a s 1 n a n a q a q 0 and a 0 is the size of an element of a structure and 0 the equation contains two exponents and q taking into account two important properties of elements of a system their fractal geometry and their ability to interact either to enhance or to damp the process of aggregation the function n a can be understood as an approximation to the number of elements the size of which is less than a the function d n a d a where n a is the general solution of this equation for q 1 is a product of an increasing bounded function and power law function with stretched exponential cut off the relation with tsallis non extensive statistics is demonstrated by solving the generalized logistic equation for q 0 in the case 0 q 1 the equation models super additive and the case q 1 it models sub additive structures the gutenberg richter g r formula results from interpretation of empirical data as a straight line in the area of stretched exponent with small the solution is applied for modeling distribution of foreshocks and aftershocks in the regions of napa valley 2014 and sumatra 2004 earthquakes fitting the observed data well both qualitatively and quantitatively

a class of hazard rate mixtures for combining survival data from different experiments mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism the present article introduced a new class of vectors of random hazard rate functions that are expressed as kernel mixtures of dependent completely random measures this leads to define dependent nonparametric prior processes that are suitably tailored to draw inferences in the presence of heterogenous observations besides its flexibility an important appealing feature of our proposal is analytical tractability we are indeed able to determine some relevant distributional properties and a posterior characterization that is also the key for devising an efficient markov chain monte carlo sampler for illustrative purposes we specialize our general results to a class of dependent extended gamma processes we finally display a few numerical examples including both simulated and real two sample datasets these allow us to identify the effect of a borrow

a unified fluctuation formula for one cut β ensembles of random matrices using a coulomb gas approach we compute the generating function of the covariances of power traces for one cut ensembles of random matrices in the limit of large matrix size this formula depends only on the support of the spectral density and is therefore universal for a large class of models this allows us to derive a closed form expression for the limiting covariances of an arbitrary one cut ensemble as particular cases of the main result we consider the classical gaussian wishart and jacobi ensembles for which we derive previously available results as well as new ones within a unified simple framework we also discuss the connections between the problem of trace fluctuations for the gaussian unitary ensemble and the enumeration of planar maps

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

compound random measures and their use in bayesian non parametrics summary a new class of dependent random measures which we call compound random measures is proposed and the use of normalized versions of these random measures as priors in bayesian non parametric mixture models is considered their tractability allows the properties of both compound random measures and normalized compound random measures to be derived in particular we show how compound random measures can be constructed with gamma stable and generalized gamma process marginals we also derive several forms of the laplace exponent and characterize dependence through both the levy copula and the correlation function an augmented polya urn scheme sampler and a slice sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a non parametric mixture model and a data example is discussed

reducing nonideal to ideal coupling in random matrix description of chaotic scattering application to the time delay problem we write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with m statistically equivalent channels at nonideal coupling to that for ideal coupling unfolding the phases by their local density leads to universality of their local fluctuations for large m a relation between the partial time delays and diagonal matrix elements of the wigner smith matrix is revealed for ideal coupling this helped us in deriving the joint probability distribution of partial time delays and the distribution of the wigner time delay

bounded tracking for non minimum phase nonlinear systems with fast zero dynamics in this paper we derive tracking control laws for non minimum phase nonlinear systems with both fast and slow possibly unstable zero dynamics the fast zero dynamics arise from a perturbation of a nominal system these fast zeros can be problematic in that they may be in the right half plane and may cause large magnitude tracking control inputs in this paper we combine the ideas from some recent work of hunt meyer and su with that of devasia chen and paden on an asymptotic tracking procedure for non minimum phase nonlinear systems we give somewhat subtle conditions under which the tracking control input is bounded as the magnitude of the perturbation of the nominal system becomes zero explicit bounds on the control inputs are calculated for both siso and mimo systems using some interesting non standard singular perturbation techniques the method is applied to a suite of examples including the simplified planar dynamics of vtol and ctol aircraft

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

comparing distributions by using dependent normalized random measure mixtures a methodology for the simultaneous bayesian nonparametric modelling of several distributions is developed our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes the properties of the prior are described and the modelling possibilities of this framework are explored in some detail efficient slice sampling methods are developed for inference various posterior summaries are introduced which allow better understanding of the differences between distributions the methods are illustrated on simulated data and examples from survival analysis and stochastic frontier analysis

mimo design models and internal regulators for cyclicly switched parameter adaptive control systems in pait and morse 1994 the concept of cyclic switching was proposed as a means of dealing with the well known stabilizability problem which arises in adaptive controller synthesis because of the existence of points in parameter space where the design model upon which certainty equivalence control is based loses stabilizability while the procedure outlined in the above paper is specific enough to enable one to construct cyclicly switched adaptive controllers for siso process models for the mimo case two key issues are left unresolved the objective of this paper is to address both of these issues thereby extending excitation free identifier based adaptive control methods to minimum and nonminimum phase mimo linear systems

a bayesian hierarchical model for related densities by using polya trees bayesian hierarchical models are used to share information between related samples and to obtain more accurate estimates of sample level parameters common structure and variation between samples when the parameter of interest is the distribution or density of a continuous variable a hierarchical model for continuous distributions is required various such models have been described in the literature using extensions of the dirichlet process and related processes typically as a distribution on the parameters of a mixing kernel we propose a new hierarchical model based on the polya tree which enables direct modelling of densities and enjoys some computational advantages over the dirichlet process the polya tree also enables more flexible modelling of the variation between samples providing more informed shrinkage and permitting posterior inference on the dispersion function which quantifies the variation between sample densities we also show how the model can be extended to cluster samples in situations where the observed samples are believed to have been drawn from several latent populations

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

growing networks of overlapping communities with internal structure we introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks the model comprises two complementary mechanisms one mechanism accounts for the evolution of the internal link structure of a single community and the second mechanism coordinates the growth of multiple overlapping communities the first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates we demonstrate that this simple mechanism gives rise to an effective maximal degree within communities this observation is related to the anthropological theory known as dunbar s number i e the empirical observation of a maximal number of ties which an average individual can sustain within its social groups the second mechanism is based on a recently proposed generalization of preferential attachment to community structure appropriately called structural preferential attachment spa the combination of these two mechanisms into a single model spa allows us to reproduce a number of the global statistics of real networks the distribution of community sizes of node memberships and of degrees the spa model also predicts a three qualitative regimes for the degree distribution within overlapping communities and b strong correlations between the number of communities to which a node belongs and its number of connections within each community we present empirical evidence that support our findings in real complex networks

on the bias of traceroute sampling or power law degree distributions in regular graphs understanding the graph structure of the internet is a crucial step for building accurate network models and designing efficient algorithms for internet applications yet obtaining this graph structure can be a surprisingly difficult task as edges cannot be explicitly queried for instance empirical studies of the network of internet protocol ip addresses typically rely on indirect methods like traceroute to build what are approximately single source all destinations shortest path trees these trees only sample a fraction of the network s edges and a paper by lakhina et al 2003 found empirically that the resulting sample is intrinsically biased further in simulations they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is poisson in this article we study the bias of traceroute sampling mathematically and for a very general class of underlying degree distributions explicitly calculate the distribution that will be observed as example applications of our machinery we prove that traceroute sampling finds power law degree distributions in both regular and poisson distributed random graphs thus our work puts the observations of lakhina et al on a rigorous footing and extends them to nearly arbitrary degree distributions

moments of the wigner delay times the wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system for chaotic systems the statistics of the individual delay times whose average is the wigner time delay are thought to be well described by random matrix theory here we present a semiclassical derivation showing the validity of random matrix results in order to simplify the semiclassical treatment we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies in the semiclassical approximation the elements of the scattering matrix are given in terms of the classical scattering trajectories requiring one to study correlations between sets of such trajectories we describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number this allows us to derive a polynomial equation satisfied by the generating function of the moments along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory we infer that the scattering matrix is unitary to all orders in the semiclassical approximation

power law distribution of degree degree distance a better representation of the scale free property of complex networks whether real world complex networks are scale free or not has long been controversial recently in broido and clauset a d broido a clauset nat commun 10 1017 2019 it was claimed that the degree distributions of real world networks are rarely power law under statistical tests here we attempt to address this issue by defining a fundamental property possessed by each link the degree degree distance the distribution of which also shows signs of being power law by our empirical study surprisingly although full range statistical tests show that degree distributions are not often power law in real world networks we find that in more than half of the cases the degree degree distance distributions can still be described by power laws to explain these findings we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted two way selection process the model does not always produce solid power law distributions but predicts that the degree degree distance distribution exhibits stronger power law behavior than the degree distribution of a finite size network especially when the network is dense we test the strength of our model and its predictive power by examining how real world networks evolve into an overly dense stage and how the corresponding distributions change we propose that being scale free is a property of a complex network that should be determined by its underlying mechanism e g preferential attachment rather than by apparent distribution statistics of finite size we thus conclude that the degree degree distance distribution better represents the scale free property of a complex network

on a switching control scheme for nonlinear systems with ill defined relative degree this paper discusses the applicability of a switching control scheme for a nonlinear system with ill defined relative degree the control scheme switches between exact and approximate input output linearisation control laws unlike a linear system under a switching control scheme the equilibria of a nonlinear system may change with the switching it is pointed out that this is not sufficient to cause instability when the region of the approximate linearisation control law is attractive to the exact zero dynamics it is possible that the closed loop system under the switching control scheme is still stable the results in this paper shows that the switching control scheme proposed in tomlin and sastry systems control lett 35 3 1998 145 is applicable for a wider class of nonlinear systems

bayesian nonparametric ordination for the analysis of microbial communities abstracthuman microbiome studies use sequencing technologies to measure the abundance of bacterial species or operational taxonomic units otus in samples of biological material typically the data are organized in contingency tables with otu counts across heterogeneous biological samples in the microbial ecology community ordination methods are frequently used to investigate latent factors or clusters that capture and describe variations of otu counts across biological samples it remains important to evaluate how uncertainty in estimates of each biological sample s microbial distribution propagates to ordination analyses including visualization of clusters and projections of biological samples on low dimensional spaces we propose a bayesian analysis for dependent distributions to endow frequently used ordinations with estimates of uncertainty a bayesian nonparametric prior for dependent normalized random measures is constructed which is marginally equivalent to the normalized generalized gamma pr

dynamical generalized hurst exponent as a tool to monitor unstable periods in financial time series we investigate the use of the hurst exponent dynamically computed over a weighted moving time window to evaluate the level of stability instability of financial firms financial firms bailed out as a consequence of the 2007 2008 credit crisis show a neat increase with time of the generalized hurst exponent in the period preceding the unfolding of the crisis conversely firms belonging to other market sectors which suffered the least throughout the crisis show opposite behaviors we find that the multifractality of the bailed out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing these findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm in this paper we introduce a method to compute the generalized hurst exponent which assigns larger weights to more recent events with respect to older ones in this way large fluctuations in the remote past are less likely to influence the recent past we also investigate the scaling associated with the tails of the log returns distributions and compare this scaling with the scaling associated with the hurst exponent observing that the processes underlying the price dynamics of these firms are truly multi scaling

estimating heavy tail exponents through max self similarity in this paper a novel approach to the problem of estimating the heavy tail exponent 0 of a distribution is proposed it is based on the fact that block maxima of size m scale at a rate m1 for independent as well as for a number of dependent data this scaling rate can be captured well by the max spectrum plot of the data that leads to regression based estimators for consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution the proposed estimators have an important computational advantage over existing methods namely they can be calculated and updated sequentially in an on line fashion without having to store the entire data set practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes robust to contaminants and continues to work under the presence of substantial amount of dependence the proposed estimators are used to illustrate the close connection between long range dependence and heavy tails over an internet traffic trace