efficient high dimensional importance sampling the paper describes a simple generic and yet highly accurate efficient importance sampling eis monte carlo mc procedure for the evaluation of high dimensional numerical integrals eis is based upon a sequence of auxiliary weighted regressions which actually are linear under appropriate conditions it can be used to evaluate likelihood functions and byproducts thereof such as ml estimators for models which depend upon unobservable variables a dynamic stochastic volatility model and a logit panel data model with unobserved heterogeneity random effects in both dimensions are used to provide illustrations of eis high numerical accuracy even under small number of mc draws mc simulations are used to characterize the finite sample numerical and statistical properties of eis based ml estimators

heights of heegner cycles and derivatives of l series 0 introduction 99 1 intersections and heights 103 2 kuga sato varieties and cm cycles 117 3 heights of cm cycles 124 4 heights of heegner cycles 137 5 proof of the main identity and the consequences 147 references 151

big line bundles over arithmetic varieties 5 equidistribution theory 26 5 1 a generic equidistribution theorem 27 5 2 equidistribution at infinite places 30 5 3 equidistribution at finite places 32 5 4 equidistribution of small subvarieties 35 5 5 equidistribution over algebraic dynamical systems 37 5 6 equidistribution over multiplicative groups 39 5 7 equidistribution theory 41

numerical properties of a gaussian translation operator for the 2d fmm a diagonal gaussian translation operator for the time harmonic fast multipole method fmm in two dimensions is examined numerically the gaussian translation operator depends on a beam parameter that determines its sharpness when the beam parameter is set to zero the gaussian translation operator reduces to the standard fmm translation operator the sampling rate can be determined straightforwardly to achieve any desired accuracy the directionality of the gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy the required number of plane waves depends strongly on the actual source receiver locations not just on the diameter of the source and receiver regions

estimation of stochastic volatility models via monte carlo maximum likelihood this paper discusses the monte carlo maximum likelihood method of estimating stochastic volatility sv models the basic sv model can be expressed as a linear state space model with log chi square disturbances the likelihood function can be approximated arbitrarily accurately by decomposing it into a gaussian part constructed by the kalman filter and a remainder function whose expectation is evaluated by simulation no modifications of this estimation procedure are required when the basic sv model is extended in a number of directions likely to arise in applied empirical research this compares favorably with alternative approaches the finite sample performance of the new estimator is shown to be comparable to the monte carlo markov chain mcmc method

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

particle efficient importance sampling abstract the efficient importance sampling eis method is a general principle for the numerical evaluation of high dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers despite a number of successful applications in high dimensions it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases we solve this problem by recognising that the eis framework has an offline sequential monte carlo interpretation the particle eis method is based on non standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density we apply the method for a range of univariate and bivariate stochastic volatility specifications we also develop a new application of the eis approach to state space models with student s t state innovations our results show that the particle eis method strongly outperforms both the standard eis method and particle filters for likelihood evaluation in high dimensions we illustrate the efficiency of the method for bayesian inference using the particle marginal metropolis hastings and importance sampling squared algorithms

monte carlo methods for estimating smoothing and filtering one and two factor stochastic volatility models one and two factor stochastic volatility models are assessed over three sets of stock returns data sp the problem is to get the shape of the conditional returns distribution right none of the models come close to matching the tails of this distribution including a second factor provides only a relatively small improvement over the single factor models fitting this aspect of the data is important for option pricing and risk management

a phase space beam summation formulation for ultrawide band radiation a new discrete phase space gaussian beam gb summation representation for ultrawide band uwb radiation from an aperture source distribution is presented the formulation is based on the theory of the windowed fourier transform wft frames wherein we introduce a novel relation between the frequency and the frame overcompleteness with this procedure the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent so that only a single set of beams needs to be traced through the medium for all the frequencies in the band it is also shown that a properly tuned class of iso diffracting id gaussian windows provides the snuggest frame representation for all frequencies thus generating stable and localized expansion coefficients furthermore due to the id property the resulting gbs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies consequently the theory may also be expressed directly in the time domain as will be presented elsewhere the localization implied by the new formulation is demonstrated numerically for an uwb focused aperture it is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties i e those residing near the phase space lagrange manifold further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point it is thus shown that the total number of beams is much smaller than the landau pollak bound on the aperture s degrees of freedom

concernant la relation de distribution satisfaite par la fonction φ associee a un reseau complexe for any pair of latticesl andl satisfying i l l and ii the indexn ofl intol is prime to 6 we construct from the usual function ofl cf no 1 some elliptic function psi psi z l underset raise0 3em hbox smash scriptscriptstyle l of the variablez with period latticel and divisor n 0 l sum limits i 1 n t i l over the torus l where the complex numberst i 1 i n describe a complete set of representatives of the quotientl l

un lemme matriciel effectif we show an almost optimal effective version of masser s matrix lemma lecture notes math 1290 109 148 1987 giving a lower bound of the height of an abelian variety in terms of its period lattices

multiloop calculations in p adic string theory and bruhat tits trees we treat the openp adic string world sheet as a coset spacef t wheret is the bruhat tits tree for thep adic linear groupgl 2 p and pgl 2 p is some schottky group the boundary of this world sheet corresponds to ap adic mumford curve of finite genus the string dynamics is governed by the local gaussian action on the coset spacef the tachyon amplitudes expressed in terms ofp adic functions are proposed for the mumford curve of arbitrary genus we compare them with the corresponding usual archimedean amplitudes the sum over moduli space of the algebraic curves is conjectured to be expressed in the arithmetic surface terms we also give the necessary mathematical background including the mumford approach top adic algebraic curves the connection of the problem of closedp adic strings with the considered topics is discussed

second variation of zhang s λ invariant on the moduli space of curves we compute the second variation of the invariant recently introduced by s zhang on the complex moduli space mg of curves of genus g 2 using work of n kawazumi as a result we prove that 8g 4 is equal up to a constant to the invariant introduced some time ago by r hain and d reed we deduce some consequences for example we calculate the invariant for each hyperelliptic curve expressing it in terms of the petersson norm of the discriminant modular form 1 introduction recently independently s zhang 27 and n kawazumi 16 introduced a new interesting real valued function on the moduli space mg of complex curves of genus g 2 its value at a curve x m g is given as follows let h 0 x x be the space of holomorphic differentials on x equipped with the

symmetric roots and admissible pairing using the discriminant modular form and the noether formula it is possible to write the admissible self intersection of the relative dualising sheaf of a semistable hyperelliptic curve over a number field or function field as a sum over all places of a certain adelic invariant we provide a simple geometric interpretation for this invariant based on the arithmetic of symmetric roots we propose the conjecture that the invariant coincides with the invariant introduced in a recent paper by s w zhang this conjecture is true in the genus 2 case and we obtain a new proof of the bogomolov conjecture for curves of genus 2 over number fields

partiallyu 1 compactified scalar massless field on the compact riemann surface and the bosonic string amplitudes the theory of the partiallyu 1 compactified scalar massless field on the compact riemann surface with nambu goto action is defined the partition function is determined completely by a choice of the finite dimensional approximations the correlation functions are the only correctly defined objects of the theory the averages of the correlation function asymptotic values provide the amplitudes for the compact riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes

arakelov self intersection numbers of minimal regular models of modular curves x_0 p 2 x0 p2 we compute an asymptotic expression for the arakelov self intersection number of the relative dualizing sheaf of edixhoven s minimal regular model for the modular curve x 0 p 2 over mathbb q the computation of the self intersection numbers are used to prove an effective version of the bogolomov conjecture for the semi stable models of modular curves x 0 p 2 and obtain a bound on the stable faltings height for those curves in a companion article banerjee and chaudhuri in isr j math 2020

complex point dipole formulation of probe corrected cylindrical and spherical near field scanning of electromagnetic fields a probe corrected electromagnetic theory based on complex point dipoles is presented for computing the field of an arbitrary source of finite extent for example a test antenna from measurements of its near field on a cylindrical or spherical scanning surface by representing the probe with complex point dipoles probe correction is achieved by simple factors that involve hankel functions evaluated at complex points only four complex point dipoles are needed to represent a typical precision probe used in near field measurements the theory uses neither translation and rotation theorems nor differential operators one disadvantage of the theory is that it employs nonlinear optimization to determine the parameters of the probe model the complex point dipole representation of the probe makes realistic simulations of near field scanning systems straightforward the cylindrical theory is validated through a numerical example the spherical theory is validated by experimental data

testing the assumptions behind importance sampling importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals its reliable use requires the sampler to possess a variance for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral however this assumption is seldom checked in this paper we use extreme value theory to empirically assess the appropriateness of this assumption our main application is the stochastic volatility model where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

explicit arithmetic intersection theory and computation of neron tate heights we describe a general algorithm for computing intersection pairings on arithmetic surfaces we have implemented our algorithm for curves over q and we show how to use it to compute regulators for a number of jacobians of smooth plane quartics and to numerically verify the conjecture of birch and swinnerton dyer for the jacobian of the split cartan curve of level 13 up to squares

hauteur de faltings de quotients de j 0 n discriminants d algebres de hecke et congruences entre formes modulaires in this paper we compute the faltings height of the jacobian of the modular curve j 0 n we explain how it is related to the discriminant of the hecke algebra this discriminant measures congruences between modular forms as a corollary we obtain a lower bound for this discriminant the faltings height of a quotient a of j 0 n is also computed

summations over equilaterally triangulated surfaces and the critical string measure we propose a new approach to the summation over dynamically triangulated riemann surfaces which does not rely on properties of the potential in a matrix model instead we formulate a purely algebraic discretization of critical string path integral this is combined with a technique which assigns to each equilateral triangulation of a two dimensional surface a riemann surface defined over a certain finite extension of the field of rational numbers i e an arthmetic surface thus we establish a new formulation in which the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces it is shown that because of this it is far from obvious that this measure for large genera approximates the measure defined by the continuum theory i e liouville theory or critical string theory in low genus this subtlety does not exist in the case of critical string theory we explicity compute the volume of the moduli space of arithmetic surfaces in terms of the modular height function and show that for low genus it approximates correctly the continuum measure we also discuss a continuum limit which bears some resemblance with a double scaling limit in matrix models

lower bounds on the arithmetic self intersection number of the relative dualizing sheaf on arithmetic surfaces we give an explicitly computable lower bound for the arithmetic self intersection number of the dualizing sheaf on a large class of arithmetic surfaces if some technical conditions are satisfied then this lower bound is positive in particular these technical conditions are always satisfied for minimal arithmetic surfaces with simple multiplicities and at least one reducible fiber but we have also used our techniques to obtain lower bounds for some arithmetic surfaces with non reduced fibers

maximum likelihood estimation of partially observed diffusion models this paper develops a maximum likelihood ml method to estimate partially observed diffusion models based on data sampled at discrete times the method combines two techniques recently proposed in the literature in two separate steps in the first step the closed form approach of ait sahalia 2008 is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states in the second step the efficient importance sampling technique of richard and zhang 2007 is used to integrate out the latent states thereby yielding the likelihood function using both simulated and real data we show that the proposed ml method works better than alternative methods the new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations therefore the method has a wide range of applicability and its computational cost is moderate

the asymptotics of the arakelov geen s function and faltings delta invariant we study the behavior of the arakelov green s function and faltings delta invariant on degenerating riemann surfaces

higher picard varieties and the height pairing let x be a smooth projective variety which is defined over a number field beilinson and bloch have defined under suitable asssumptions height pairings between chow groups of homologically trivial cycles on x beilinson has also formulated a hard lefschetz and a hodge index conjecture for these chow groups we show that the restriction of the height pairing to cycles algebraically equivalent to zero can be computed via abel jacobi maps in terms of the neron tate height pairing on the higher picard varieties of x this description is used in the case where x is an abelian variety to prove a consequence of beilinson conjectures namely we prove a hard lefschetz and a hodge index theorem for the groups of cycles algebraically equivalent to zero modulo incidence equivalence

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

variational multinomial logit gaussian process gaussian process prior with an appropriate likelihood function is a flexible non parametric model for a variety of learning tasks one important and standard task is multi class classification which is the categorization of an item into one of several fixed classes a usual likelihood function for this is the multinomial logistic likelihood function however exact inference with this model has proved to be difficult because high dimensional integrations are required in this paper we propose a variational approximation to this model and we describe the optimization of the variational parameters experiments have shown our approximation to be tight in addition we provide data independent bounds on the marginal likelihood of the model one of which is shown to be much tighter than the existing variational mean field bound in the experiments we also derive a proper lower bound on the predictive likelihood that involves the kullback leibler divergence between the approximating and the true posterior we combine our approach with a recently proposed sparse approximation to give a variational sparse approximation to the gaussian process multi class model we also derive criteria which can be used to select the inducing set and we show the effectiveness of these criteria over random selection in an experiment

complex source beam moment method procedure for accelerating numerical integral equation solutions of radiation and scattering problems a new hybrid complex source beam moment method csb mom procedure is presented to accelerate the matrix vector product mvp computation in the iterative solution of moment method integral equation problems the scattering object in this csb mom algorithm is partitioned into groups in a manner similar to the fast multipole method fmm however unlike fmm the interactions between well separated groups are computed by using the complex source beams csbs which represent the radiation from the basis elements in the group the directional properties of csbs allow a fast evaluation for these interactions such that the overall mvp is computed very efficiently the direct solution time and the storage requirement of the csb mom method is numerically shown to be o n3 2 by optimally selecting the number of groups a low memory version of a new hybrid complex source beam moment method csb mom procedure is presented to accelerate the matrix vector product mvp computation in the iterative solution of moment method integral equation problems the scattering object in this csb mom algorithm is partitioned into groups in a manner similar to the fast multipole method fmm however unlike fmm the interactions between well separated groups are computed by using the complex source beams csbs which represent the radiation from the basis elements in the group the directional properties of csbs allow a fast evaluation for these interactions such that the overall mvp is computed very efficiently the direct solution time and the storage requirement of the csb mom method is numerically shown to be o n3 2 by optimally selecting the number of groups a low memory version of the csb mom method is also presented wherein separated group interactions are computed on the fly the csb mom method is also presented wherein separated group interactions are computed on the fly

stochastic volatility in asset prices estimation with simulated maximum likelihood abstract the stochastic volatility model is used to estimate daily asset price dynamics the model is estimated by integrating latent volatility out of the joint density of prices and volatility to obtain the marginal density of prices due to high number of dimensions of the integral no conventional integration technique is applicable a monte carlo method called simulated maximum likelihood is used to obtain the marginal density where the latent variable is simulated conditional on available information the model is estimated by 2022 observations from the s p 500 index for comparison arch type models are estimated with the same data

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

exact complex source point beam expansions for electromagnetic fields complex source point csp beams or cspbs are known to be exact solutions of maxwell s equations hence they can be used as basis functions to represent the electromagnetic fields generated by arbitrary sources in this work it is shown that any fully vector electromagnetic field can be represented exactly as an expansion of cspbs originating from a relatively arbitrary surface enclosing the sources three different variants of the cspb representation are first considered for a spherical expansion surface and their properties are discussed it is shown that the cspb expansion set can be conveniently truncated by selecting only the significantly contributing beams for efficient field calculations the cspb representations are next extended to the case of relatively arbitrary expansion surfaces numerical results are presented to demonstrate and compare the convergence and efficiency of the three approaches

heights and arakelov s intersection theory introduction this paper relates the neron tate height on jacobian varieties to an intersection theory on arithmetic surfaces constructed by s arakelov a1 here i extend and prove a statement of arakelov to the effect that his intersection pairing is a neron pairing a2i i use this to prove an analogue of the hodge index theorem for arithmetic surfaces a result due independently to g faltings the results of this paper have been extracted from my thesis written under the direction of michael artin it differs from the thesis in three ways firstly it employs the language of local height functions as defined by a neron and j tate and expounded by s lang li in the thesis i used neron s language of local intersection pairings n1 the second major difference is in the proof of theorem 1 3 in my thesis i proved this result by using work of raynaud and picard functors r 1 this method was suggested by m artin in this paper i provide a simpler proof observed by s lang and independently by b gross finally the development of arakalov s theory in the context of neron functions in section 2 is due to s lang who has kindly given me leave to publish it this exposition of my results is due in considerable part to s lang it is essentially an edited transcript of a series of conversations between us which he provided it is my great pleasure to thank both him and michael artin for their help and encouragement 1 the neron pairing neron ne has given a pairing between divisors and points on abelian varieties and also on arbitrary varieties under suitable conditions we shall give a complement to the neron theory on curves let c be a curve by which we mean a complete regular curve geometrically irreducible over a field k with an absolute value v let

transformation of antenna generalized scattering matrix during rotation and linear displacement the problem of generalized scattering matrix gsm transformation during an angular or linear displacement of the antenna is considered to work out the problem it is suggested that the entries of the antenna gsm are presented as two different sets of matrices one set is used for gsm transformation in case of antenna rotation whereas the other in case of antenna linear displacement expressions have been derived that allow gsm calculation for the antenna s new position in space from its initial i e predisplacement or prerotation gsm the derived computation formulas comprise universal and independent of a particular moving antenna transformation matrices the sizes of which are smaller than the dimension of the overall transformation matrix usually required to perform gsm calculations results of a practical computation verifying the derived equations are presented

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

a dynamical pairing between two rational maps this is the publisher s final pdf the published article is copyrighted by american mathematical society and can be found at http www ams org home page

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

discriminants and artin conductors we study questions of multiplicities of discriminants for degenerations coming from projective duality over discrete valuation rings the main observation is a type of discriminant different formula in the sense of classical algebraic number theory and we relate it to artin conductors via bloch s conjecture in the case of discriminants of planar curves we can calculate the different precisely in general these multiplicities encode topological invariants of the singular fibers and in the case of characteristic p also wild ramification data in the form of swan conductors this builds upon results of t saito

spherical near field scanning with higher order probes a general method for higher order probe correction in spherical scanning is obtained from a renormalized least squares approach the renormalization causes the normal matrix of the least squares problem to closely resemble the identity matrix when most of the energy of the probe pattern resides in the first order modes the normal equation can be solved either with a linear iterative solver leading to an iterative scheme or with a neumann series leading to a direct scheme the computation scheme can handle non symmetric probes requires only the output of two independent ports of a dual polarized probe and works for both and scans the probe can be characterized either by a complex dipole model or by a standard spherical wave representation the theory is validated with experimental data

computing canonical heights using arithmetic intersection theory the canonical height on an abelian variety a defined over a global field k is an object of fundamental importance in the study of the arithmetic of a for many applications it is required to compute p for a given point p a k for instance given generators of a subgroup of the mordell weil group a k of finite index this is necessary for most known approaches to the computation of generators of the mordell weil group a k furthermore the regulator of a k which appears in the statement of the conjecture of birch and swinnerton dyer is defined in terms of the canonical height and thus we need the ability to compute canonical heights in order to gather numerical evidence for the conjecture in the case of positive rank

bayesian leave one out cross validation approximations for gaussian latent variable models the future predictive performance of a bayesian model can be estimated using bayesian cross validation in this article we consider gaussian latent variable models where the integration over the latent values is approximated using the laplace method or expectation propagation ep we study the properties of several bayesian leave one out loo cross validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data our main objective is to assess the accuracy of the approximative loo cross validation estimators that is for each method laplace and ep we compare the approximate fast computation with the exact brute force loo computation secondarily we evaluate the accuracy of the laplace and ep approximations themselves against a ground truth established through extensive markov chain monte carlo simulation our empirical results show that the approach based upon a gaussian approximation to the loo marginal distribution the so called cavity distribution gives the most accurate and reliable results among the fast methods

asymptotics of determinants from functional integration the expression for the determinant of the laplace operator is used in terms of functional integration to compute the asymptotic behavior on degenerating riemann surfaces in the case of the arakelov metric the information is sufficiently precise to give a value for the absolute constants appearing in bosonization formulas

monte carlo estimation for nonlinear non gaussian state space models we develop a proposal or importance density for state space models with a nonlinear non gaussian observation vector y p y and an unobserved linear gaussian signal vector p the proposal density is obtained from the laplace approximation of the smoothing density p y we present efficient algorithms to calculate the mode of p y and to sample from the proposal density the samples can be used for importance sampling and markov chain monte carlo methods the new results allow the application of these methods to state space models where the observation density p y is not log concave additional results are presented that lead to computationally efficient implementations we illustrate the methods for the stochastic volatility model with leverage

exact gaussian beam theory for outgoing and standing spherical waves application to transmitting and receiving antennas outgoing spherical vector wave functions are expressed in terms of gaussian beams also called complex source point beams radiating in all directions by use of a vector wave expansion the electromagnetic field of an arbitrary source of finite extent is thus expressed in terms of gaussian beams with weights determined directly from the spherical expansion coefficients of the source these outgoing wave formulas allow the field of any transmitting antenna to be expressed in terms of gaussian beams elementary gaussian beam receivers are introduced as the electromagnetic field at complex points in space the outputs of elementary gaussian beam receivers pointing in all directions determine the spherical expansion coefficients in a standing wave expansion these standing wave formulas allow the output of any receiving antenna to be expressed in terms of the outputs of elementary gaussian beam receivers combining the formulas for outgoing and standing waves produces a new antenna antenna transmission formula based solely on gaussian beams the theory is exact and validated through numerical examples

generalized dynamic panel data models with random effects for cross section and time abstract an exact maximum likelihood method is developed for the estimation of parameters in a nonlinear non gaussian dynamic panel data model with unobserved random individual specific and time varying effects we propose an estimation procedure based on the importance sampling technique in particular a sequence of conditional importance densities is derived which integrates out all random effects from the joint distribution of endogenous variables we disentangle the integration over both the cross section and the time series dimensions the estimation method facilitates the modeling of large panels in both dimensions we evaluate the method in an extended monte carlo study for dynamic panel data models with observations from different non gaussian distributions we finally present three empirical illustrations for i union choice of young males using a binary panel ii crime rates of families using a binomial panel and iii economic growth modeling using a student s t panel