on the equivalence of time and frequency domain maximum likelihood estimation maximum likelihood estimation has a rich history it has been successfully applied to many problems including dynamical system identification different approaches have been proposed in the time and frequency domains in this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data a key point in this context is how initial and final conditions are considered and how they are introduced in the likelihood function

algebraic approach to system identification a variety of identification procedures exists for estimating the parameters of an autoregressive moving average arma process from noise free excitation and noise contaminated response data in this paper an identification procedure is proposed for the more realistic situation in which both the excitation and response are contaminated by white noises the method is based upon the null space characterization of an associated data matrix some of the more important algebraic properties possessed by this data matrix are first established in the ideal noise free data case in particular it is found that an overordering of the arma model will not impair the identification of the underlying system in the more realistic noise contaminated data case an approximation of the data matrix s null space is affected by using an eigenvalue eigenvector decomposition by incorporating this null space approximation the deleterious effects of the noise are significantly reduced thereby giving rise to improved modeling performance this improvement is demonstrated by means of a standard example in which the proposed identification method is shown to produce a better modeling behavior than does the classical least squares method the corresponding iterative generalized least squares method and a commonly employed instrumental variable method

persistence of a continuous stochastic process with discrete time sampling non markov processes we consider the problem of discrete time persistence which deals with the zero crossings of a continuous stochastic process x t measured at discrete times t ndeltat for a gaussian stationary process the persistence no crossing probability decays as exp theta d t rho a n for large n where a exp deltat 2 and the discrete persistence exponent theta d is given by theta d ln rho 2 ln a using the independent interval approximation we show how theta d varies with deltat for small deltat and conclude that experimental measurements of persistence for smooth processes such as diffusion are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker we extend the matrix method developed by us previously phys rev e 64 015101 r 2001 to determine rho a for a two dimensional random walk and the one dimensional random acceleration problem we also consider alternating persistence which corresponds to a 0 and calculate rho a for this case

errors in variables identification using maximum likelihood estimation in the frequency domain this paper deals with the identification of errors in variables eiv models corrupted by additive and uncorrelated white gaussian noises when the noise free input is an arbitrary signal not required to be periodic in particular a frequency domain maximum likelihood ml estimator is proposed and analyzed in some detail as some other eiv estimators this method assumes that the ratio of the noise variances is known the estimation problem is formulated in the frequency domain it is shown that the parameter estimates are consistent an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived the possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed analyzed and illustrated

statistics of zero crossings in rough interfaces with fractional elasticity we study numerically the distribution of zero crossings in one dimensional elastic interfaces described by an overdamped langevin dynamics with periodic boundary conditions we model the elastic forces with a riesz feller fractional laplacian of order z 1 2 such that the interfaces spontaneously relax with a dynamical exponent z to a self affine geometry with roughness exponent by continuously increasing from 1 2 macroscopically flat interface described by independent ornstein uhlenbeck processes phys rev 36 823 1930 phrvao0031 899x10 1103 physrev 36 823 to 3 2 super rough mullins herring interface three different regimes are identified i 1 2 1 the effect on p l of short scale smoothening is also analyzed numerically and analytically a tight relation between the mean interval the mean width of the interface and the density of zeros is also reported the results drawn from our analysis of rough interfaces subject to particular boundary conditions or constraints along with discretization effects are relevant for the practical analysis of zeros in interface imaging experiments or in numerical analysis

brief paper frequency domain maximum likelihood estimation of linear dynamic errors in variables models this paper studies the linear dynamic errors in variables problem for filtered white noise excitations first a frequency domain gaussian maximum likelihood ml estimator is constructed that can handle discrete time as well as continuous time models on a part s of the unit circle or imaginary axis next the ml estimates are calculated via a computationally simple and numerically stable gauss newton minimization scheme finally the cramer rao lower bound is derived

fractional laplacian in bounded domains the fractional laplacian operator ensuremath ensuremath ensuremath delta ensuremath alpha 2 appears in a wide class of physical systems including l evy flights and stochastic interfaces in this paper we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval the implementation of boundary conditions is justified by appealing to two physical models namely hopping particles and elastic springs the eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions some analytical results concerning the structure of the eigenvalue spectrum are also obtained

frequency domain system identification using arbitrary signals it is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors this paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain by estimating simultaneously some initial conditions and the system model parameters

width distribution of contact lines on a disordered substrate we have studied the roughness of a contact line on a disordered substrate by measuring its width distribution which characterizes the roughness completely the measured distribution is in excellent agreement with the distribution calculated in previous works extended here to the case of open boundary conditions this type of analysis which is performed here on experimental data provides a strong confirmation that the joanny de gennes model is not sufficient to describe the dynamics of the contact line at the depinning threshold

multi step length gradient iterative algorithm for equation error type models abstract this letter develops a multi step length gradient iterative algorithm for equation error type eet models the algorithm analysis is based upon the gradient search principle by applying the gram schmidt procedure the eet model can be turned into an orthogonal model in which each parameter in the parameter vector is independent of the other parameters then a multi step length gradient iterative algorithm is proposed for the orthogonal model and can estimate the parameters in one iteration finally based on the estimated parameters the parameter estimates of the eet model can be computed different from the traditional gradient iterative algorithm which has slower convergence rates and is sensitive to the initial values of the unknown variables the method in this letter has quicker convergence rates and is robust to the initial values of the unknown variables the simulation studies demonstrate the feasibility and effectiveness of the proposed algorithm

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

generalized arcsine laws for fractional brownian motion the three arcsine laws for brownian motion are a cornerstone of extreme value statistics for a brownian b t starting from the origin and evolving during time t one considers the following three observables i the duration t the process is positive ii the time t mathrm last the process last visits the origin and iii the time t mathrm max when it achieves its maximum or minimum all three observables have the same cumulative probability distribution expressed as an arcsine function thus the name arcsine laws we show how these laws change for fractional brownian motion x t a non markovian gaussian process indexed by the hurst exponent h it generalizes standard brownian motion i e h frac 1 2 we obtain the three probabilities using a perturbative expansion in h ensuremath frac 1 2 while all three probabilities are different this distinction can only be made at second order in our results are confirmed to high precision by extensive numerical simulations

a generalized instrumental variable estimation method for errors in variables identification problems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper it is shown how a number of common methods for errors in variables methods can be put into a general framework resulting into a generalized instrumental variable estimator give various computational aspects of give are presented and the asymptotic distribution of the parameter estimates is derived

spatial persistence and survival probabilities for fluctuating interfaces we report the results of numerical investigations of the steady state ss and finite initial conditions fic spatial persistence and survival probabilities for 1 1 dimensional interfaces with dynamics governed by the nonlinear kardar parisi zhang equation and the linear edwards wilkinson ew equation with both white uncorrelated and colored spatially correlated noise we study the effects of a finite sampling distance on the measured spatial persistence probability and show that both ss and fic persistence probabilities exhibit simple scaling behavior as a function of the system size and the sampling distance analytical expressions for the exponents associated with the power law decay of ss and fic spatial persistence probabilities of the ew equation with power law correlated noise are established and numerically verified

persistence of a continuous stochastic process with discrete time sampling we introduce the concept of discrete time persistence which deals with zero crossings of a continuous stochastic process x t measured at discrete times t n delta t for a gaussian markov process with relaxation rate mu we show that the persistence no crossing probability decays as rho a n for large n where a exp mu delta t and we compute rho a to high precision we also define the concept of alternating persistence which corresponds to a 1 corresponding to motion in an unstable potential mu 0 there is a nonzero probability of having no zero crossings in infinite time and we show how to calculate it

extended accuracy analysis of a covariance matching approach for identifying errors in variables systems a system identification method for errors in variables problems based on covariance matching was recently proposed in the first step a small amount of covariances of noisy input output data are computed and then a parametric model is fitted to these covariances in this paper the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances as an important byproduct an efficient algorithm is presented for computing the covariance matrix of the computed input output covariances

spatial survival probability for one dimensional fluctuating interfaces in the steady state we report numerical and analytic results for the spatial survival probability for fluctuating one dimensional interfaces with edwards wilkinson or kardar parisi zhang dynamics in the steady state our numerical results are obtained from analysis of steady state profiles generated by integrating a spatially discretized form of the edwards wilkinson equation to long times we show that the survival probability exhibits scaling behavior in its dependence on the system size and the sampling interval used in the measurement for both steady state and finite initial conditions analytic results for the scaling functions are obtained from a path integral treatment of a formulation of the problem in terms of one dimensional brownian motion a deterministic approximation is used to obtain closed form expressions for survival probabilities from the formally exact analytic treatment the resulting approximate analytic results provide a fairly good description of the numerical data

a covariance matching approach for identifying errors in variables systems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper a covariance matching approach is proposed to solve the identification problem it applies for general types of input signals the method utilizes a small set of covariances of the measured input output data this property applies also for some other methods such as the frisch scheme and the bias eliminating least squares method algorithmic details for the proposed method are provided user choices for example specification of which input output covariances to utilize are discussed in some detail the method is evaluated by using numerical examples and is shown to have competitive properties as compared to alternative methods

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

brief paper maximum likelihood identification of noisy input output models this work deals with the identification of errors in variables models corrupted by white and uncorrelated gaussian noises by introducing an auxiliary process it is possible to obtain a maximum likelihood solution of this identification problem by means of a two step iterative algorithm this approach allows also to estimate as a byproduct the noise free input and output sequences moreover an analytic expression of the finite cramer rao lower bound is derived the method does not require any particular assumption on the input process however the ratio of the noise variances is assumed as known the effectiveness of the proposed algorithm has been verified by means of monte carlo simulations

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

comments on two tailed significance tests for 2 2 contingency tables what is the alternative by robin j prescott statistics in medicine 2019 38 4264 4269

frequency domain system identification using non parametric noise models estimated from a small number of data sets abstract this paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise a typical example of such a problem is the identification of a system in a feedback loop it is known that this problem can be solved using errors in varaibles methods if the covariance matrices of the disturbing noise on input and output measurements are a priori known it is shown that the exact covariance matrices can be replaced by the sample covariance matrices the system can be identified from the sample means and sample covariance matrices calculated from a small number m of independently repeated experiments it is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points n in each experiment n if m 4 the loss in efficiency is quantified m 6 and the expected value of the cost function m 4 and its variance m 6 are calculated

sensitivity of fisher s exact test to minor perturbations in 2 2 contingency tables the two tailed fisher s exact p value is extremely sensitive to small perturbations in 2 x 2 contingency tables an example indicates that a 1 per cent increase in the denominator of one treatment group results in a 32 per cent drop in the exact p value but a mere 0 1 per cent decrease in the treatment success rate this is equivalent to the increase in significance obtained by a 20 per cent increase in the sample size of both treatments without changing the observed success rates this drop results from small changes in the probabilities of unobserved events a systematic evaluation of 920 pairs of similar contingency tables shows that these fluctuations occur frequently over a wide range of sample sizes and significance levels doubling the one tailed exact p value provides a more consistent measure of inferential strength we discuss various chi squared continuity corrections

brief paper box jenkins identification revisited part iii part i of this series of three papers handles the identification of single input single output box jenkins models on arbitrary frequency grids in an open and closed loop setting part ii discusses the computational aspects and illustrates the theory on simulations and a real life problem this paper extends the results of parts i and ii to multiple input multiple output systems contrary to the classical time domain approach the presented technique does not require symbolic calculus for multiple output polynomial box jenkins models

longest excursion of fractional brownian motion numerical evidence of non markovian effects we study using exact numerical simulations the statistics of the longest excursion l text max t up to time t for the fractional brownian motion with hurst exponent 0lhl1 we show that in the large t limit l text max t ensuremath propto q ensuremath infty t where q ensuremath infty ensuremath equiv q ensuremath infty h depends continuously on h these results are compared with exact analytical results for a renewal process with an associated persistence exponent ensuremath theta 1 ensuremath h this comparison shows that q ensuremath infty h carries the clear signature of non markovian effects for h ensuremath ne 1 2 the preasymptotic behavior of l text max t is also discussed

errors in variables identification of dynamic systems excited by arbitrary non white input abstract this work deals with the identification of dynamic systems from noisy input output observations where the noise free input is not parameterized the basic assumptions made are 1 the dynamic system can be modeled by a discrete or continuous time rational transfer function model 2 the temporal input output disturbances are mutually independent identically distributed noises and 3 the input power spectrum is non white not necessarily rational and is modeled nonparametrically the system identifiability is guaranteed by exploiting the non white spectrum property of the noise free input a frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input output noise variances the uncertainty bound of the estimates is calculated and compared to the cramer rao lower bound the efficiency of the proposed algorithm is illustrated on numerical examples

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

extreme value statistics of fractional brownian motion bridges fractional brownian motion is a self affine non markovian and translationally invariant generalization of brownian motion depending on the hurst exponent h here we investigate fractional brownian motion where both the starting and the end point are zero commonly referred to as bridge processes observables are the time t the process is positive the maximum m it achieves and the time t max when this maximum is taken using a perturbative expansion around brownian motion h 1 2 we give the first order result for the probability distribution of these three variables and the joint distribution of m and t max our analytical results are tested and found to be in excellent agreement with extensive numerical simulations for both h 1 2 and h 1 2 this precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process in generalization to what is usually done for brownian motion

frequency domain identification of fir models in the presence of additive input output noise this paper describes a new approach for identifying fir models from a finite number of measurements in the presence of additive and uncorrelated white noise in particular two different frequency