correlation factors describing primary and spatial sensations of sound fields abstract the theory of subjective preference of the sound field in a concert hall is established based on the model of human auditory brain system the model consists of the autocorrelation function acf mechanism and the interaural crosscorrelation function iacf mechanism for signals arriving at two ear entrances and the specialization of human cerebral hemispheres this theory can be developed to describe primary sensations such as pitch or missing fundamental loudness timbre and in addition duration sensation which is introduced here as a fourth these four primary sensations may be formulated by the temporal factors extracted from the acf associated with the left hemisphere and spatial sensations such as localization in the horizontal plane apparent source width and subjective diffuseness are described by the spatial factors extracted from the iacf associated with the right hemisphere any important subjective responses of sound fields may be described by both temporal and spatial factors

a semi parametric bayesian approach to the instrumental variable problem we develop a bayesian semi parametric approach to the instrumental variable problem we assume linear structural and reduced form equations but model the error distributions non parametrically a dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors our implementation of the dirichlet process prior uses a normal distribution as a base model it can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components we demonstrate that this procedure is both feasible and sensible using actual and simulated data sampling experiments compare inferences from the non parametric bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics when errors are non normal our procedure is more efficient than standard bayesian or classical methods

jeffreys prior analysis of the simultaneous equations model in the case with n 1 endogenous variables this paper analyzes the behavior of posterior distributions under the jereys prior in a simul taneous equations model the case under study is that of a general limited information setup with n 1 endogenous variables the jereys prior is shown to give rise to a marginal pos terior density which has cauchy like tails similar to that exhibited by the exactnite sample distribution of the corresponding liml estimator a stronger correspondence is established in the special case of a just identied orthonormal canonical model where the posterior density under the jereys prior is shown to have the same functional form as the density of thenite sample distribution of the liml estimator the work here generalizes that of chao and phillips j econ 87 1998 49 which gave analogous results for the special case of an equation with two endogenous variables c 2002 elsevier science b v all rights reserved jel classication c11 c31

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

using secondary outcomes to sharpen inference in randomized experiments with noncompliance we develop new methods for analyzing randomized experiments with noncompliance and by extension instrumental variable settings when the often controversial but key exclusion restriction assumption is violated we show how existing large sample bounds on intention to treat effects for the subpopulations of compliers never takers and always takers can be tightened by exploiting the joint distribution of the outcome of interest and a secondary outcome for which the exclusion restriction is satisfied the derived bounds can be used to detect violations of the exclusion restriction and the magnitude of these violations in instrumental variables settings it is shown that the reduced width of the bounds depends on the strength of the association of the auxiliary variable with the primary outcome and the compliance status we also show how the setup we consider offers new identifying assumptions of intention to treat effects the role of the auxiliary information is shown in two examples of a real social

structure ranks of matrices abstract the structure rank of a matrix i e the maximum order of a nonsingular submatrix all of whose entries are located in a given structure a subset of m n where m n are the row and column index sets respectively were previously studied for the off diagonal part here results on more general ranks e g off block diagonal strictly upper triangular and strictly upper block triangular are presented in particular it is shown that for a nonsingular matrix a in each of the last mentioned three cases the ranks of a and a 1 coincide

subjective preference of cellists for the delay time of a single reflection in a performance abstract to provide knowledge useful in designing the stage enclosure in a concert hall nakayama reported the subjective preference of alto recorder players for sound fields with a single reflection acustica54 217 221 1984 the present study evaluates the subjective preferences with regard to ease of performance of five cello soloists for the delay time of a single reflection the scale values of preference for the delay time of a single reflection were obtained using a paired comparison method and the results were compared with those for the alto recorder players and listeners the scale values of preference for both individuals and for global cellists with regard to the delay time of reflection can be expressed by a single approximate formula normalizing the delay time by the most preferred delay time observed for different music motifs a notable finding is that the most preferred delay time of a single reflection for each cellist can be calculated from the amplitude of the reflection and the minimum value of the effective duration e minof the running autocorrelation function of the music motifs played by each cellist

sound quality characteristics of refrigerator noise in real living environments with relation to psychoacoustical and autocorrelation function parameters psychoacoustical and autocorrelation function acf parameters were employed to describe the temporal fluctuations of refrigerator noise during starting transition into from the stationary phase and termination of operation the temporal fluctuations of refrigerator noise include a click at start up followed by a rapid increase in volume a change of pitch and termination of the operation subjective evaluations of the noise of 24 different refrigerators were conducted in a real living environment the relationship between objective measures and perceived noisiness was examined by multiple regression analysis sound quality indices were developed based on psychoacoustical and acf parameters the psychoacoustical parameters found to be important for evaluating noisiness in the stationary phase were loudness and roughness the relationship between noisiness and acf parameters shows that sound energy and its fluctuations are important for evaluating noisiness also refrigerator sounds that had a fluctuat

dissimilarity judgments in relation to temporal and spatial factors for the sound field in an existing hall in relation to the temporal and spatial factors of sound fields dissimilarity judgments for different source locations on a stage were performed this study is based on the model of the auditory brain system which consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemispheres there are three temporal factors 1 1 and e extracted from the autocorrelation function and four spatial factors ll iacc iacc and w iacc from the interaural crosscorrelation function of binaural signals in addition to these temporal and spatial factors the orthogonal factors of the subjective preference for sound field t 1 and t sub were taken into account the psychological distance between sound fields of different source locations on the stage were calculated by using these temporal spatial and orthogonal factors of sound fields using these distances and their linear combination dissimilarity can be calculated results of multivariable analysis show that the calculated scale values of dissimilarity agree well with the measured scale values

nonlinear response in evaluating the subjective diffuseness of sound fields tests were conducted to determine which horizontal reflection angles are most effective in stimulating subjective diffuseness for a listener in a room paired comparison tests were carried out where subjects were asked to judge in which of two sound fields they perceived more diffuseness results show that the most effective horizontal angle depends on the frequency of the one third octave band noise as is indicated by the interaural cross correlation the remarkable finding in this investigation is that the scale value of subjective diffuseness may be formulated in terms of the 3 2 power of the magnitude of interaural cross correlation iacc and that the scale value does not vary with the frequency of the bandpass noise source

subjective diffuseness of music signals convolved with binaural impulse responses abstract the spatial impression of sound in a hall can be quantified using sound field factors such as the interaural cross correlation coefficient iacc calculated from binaural impulse response bir henceforth denoted by iaccir the subjective diffuseness for the listener is a spatial attribute which depends on factors associated both with the source signal and with the actual sound field and is quantified using the iacc of the signal received by the listener henceforth denoted by iaccsr therefore the subjective diffuseness in a given hall may change with the music the aims of this study are to estimate the iaccsr from the iaccir and the factors which is obtained from autocorrelation function acf of music signal and to evaluate the subjective diffuseness by these factors first the relationship between the iaccir and iaccsr was investigated second subjective diffuseness was measured by a psycho acoustical experiment as a result the iaccsr could be estimated from the iaccir of the bir and the effective duration e from the acf of music signal it was found that the effects of birs on subjective diffuseness could be evaluated by iaccir for almost all subjects while the effects of music signals could be evaluated by the e and the width of the peak at 0 w 0 of the acf

a divide and conquer method for unitary and orthogonal eigenproblems leth n xn be a unitary upper hessenberg matrix whose eigenvalues and possibly also eigenvectors are to be determined we describe how this eigenproblem can be solved by a divide and conquer method in which the matrixh is split into two smaller unitary upper hessenberg matricesh 1 andh 2 by a rank one modification ofh the eigenproblems forh 1 andh 2 can be solved independently and the solutions of these smaller eigenproblems define a rational function whose zeros on the unit circle are the eigenvalues ofh the eigenvector ofh can be determined from the eigenvalues ofh and the eigenvectors ofh 1 andh 2 the outlined splitting of unitary upper hessenberg matrices into smaller such matrices is carried out recursively this gives rise to a divide and conquer method that is suitable for implementation on a parallel computer whenh n xn is orthogonal the divide and conquer scheme simplifies and is described separately our interest in the orthogonal eigenproblem stems from applications in signal processing numerical examples for the orthogonal eigenproblem conclude the paper

more on structure ranks of matrices abstract the structure rank of a matrix is the largest rank of a submatrix which lies within a specified structure we characterize those structures avoiding the main diagonal for which a matrix and its inverse have the same structure rank thereby generalizing some results of m fiedler

natural conjugate priors for the instrumental variables regression model applied to the angrist krueger data we propose a natural conjugate prior for the instrumental variables regression model the prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior the jeffreys prior results from a specific setting of the prior parameters and results in a marginal posterior of the structural parameter that has an identical functional form as the sampling density of the limited information maximum likelihood estimator we construct informative priors for the angrist krueger 1991 does compulsory school attendance affect schooling and earnings quarterly journal of economics 106 979 1014 data and show that the marginal posterior of the return on education in the us coincides with the marginal posterior from the southern region when we use the jeffreys prior this result occurs since the instruments are the strongest in the southern region and the posterior using the jeffreys prior identical to maximum likelihood focusses on the strongest available instruments we construct informative priors for the other regions that make their posteriors of the return on education similar to that of the us and the southern region these priors show the amount of prior information needed to obtain comparable results for all regions

the frequency range applicable to pitch identification based upon the auto correlation function model abstract pitch identification experiments were conducted to determine the upper boundary of the frequency range within which the autocorrelation function acf model described by ando see reference 16 is applicable to the phenomenon of the missing fundamental of a complex tone pitch matching tests were conducted using 1 complex tones consisting of 2 f 3 f and 4 f where f denotes the fundamental frequencies of 0 5 1 0 1 2 1 6 2 0 or 3 0 khz and 2 complex tones consisting of 2 f and 3 f these tests showed that for both kinds of complex tones the acf model can account for the perception of pitch when the fundamental frequency is below 1200 hz

measurement of regional environmental noise by use of a pc based system an application to the noise near airport g marconi in bologna abstract measurements of aircraft noise were made at the airport g marconi in bologna by using a measurement system for regional environmental noise the system is based on the model of the human auditory brain system which is based on the interplay of autocorrelators and an interaural cross correlator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres see reference 8 measurements were taken through dual microphones at ear entrances of a dummy head the aircraft noise was characterized with the following physical factors calculated from the autocorrelation function acf and interaural cross correlation function iacf for binaural signals from the acf analysis 1 energy represented at the origin of delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude 1were extracted from the iacf analysis 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc wiaccwere extracted the factor 0 can be represented as the geometrical mean of the energies at both ears a noise source may be identified by these factors as timbre

acoustical properties of aircraft noise measured by temporal and spatial factors abstract acoustical properties of aircraft noise were investigated by means of temporal and spatial factors in sound fields based on the model of auditory brain system see reference 10 the model consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemisphere there are four temporal factors extracted from the autocorrelation function acf 1 sound energy 0 2 effective duration of acf e 3 delay time of the first peak 1 and 4 its amplitude 1 from the interaural crosscorrelation function iacf three spatial factors are extracted as 1 magnitude of the interaural crosscorrelation iacc 2 interaural delay time at iacc iacc and 3 width of the maximum peak of the iacf wiacc it is found that the acoustical properties are well represented by the factors extracted from the acf and the iacf

duration sensation when listening to bandpass noises abstract the duration sensation of bandpass noise was examined while changing the factors 1 1and e extracted from the autocorrelation function the white noise and bandpass noises with six center frequencies 125 250 500 1000 2000 and 4000 hz with different bandwidths were used as stimuli a paired comparison test comparing the white noise duration with bandpass noise duration was conducted under the conditions of constant sound pressure level spl 80 db a and rise and fall times 1 ms results indicate that the duration of bandpass noise is judged to be longer than that of the white noise the duration sensation of the bandpass stimuli with longer 1is significantly longer than that of the stimuli with shorter 1 p

bayesian reduced rank regression in econometrics abstract the reduced rank regression model arises repeatedly in theoretical and applied econometrics to date the only general treatment of this model have been frequentist this paper develops general methods for bayesian inference with noninformative reference priors in this model based on a markov chain sampling algorithm and procedures for obtaining predictive odds ratios for regression models with different ranks these methods are used to obtain evidence on the number of factors in a capital asset pricing model

duration sensation of the simulated environmental noise in relation to its auto correlation function this is the report of an investigation into the sensation of the duration of environmental noise simulated by mixing a pure tone 1 khz with white noise in paired comparison tests five subjects judged whether simulated environmental noise stimuli were longer or shorter than a standard pure tone stimulus with the same sound pressure level and rise fall time in experiment i the attenuation level o m of the envelope of the normalized autocorrelation function acf i e the repetition of similar features in the stimulus was varied by changing the relative amplitude of the pure tone and white noise components results show that the sensation of duration of the white noise stimulus with a small value of o m is significantly p 0 05 longer than a pure tone stimulus with a higher value of o m results of experiment 2 showed that the duration of pure tone stimuli with lower frequencies as presented by the 1 extracted from the acf are perceived as being longer p 0 01 than those of pure tone stimuli with higher frequencies

problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak abstract we draw attention to two problems associated with the use of instrumental variables iv the importance of which for empirical work has not been fully appreciated first the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the iv estimates even if only a weak relationship exists between the instruments and the error in the structural equation second in finite samples iv estimates are biased in the same direction as ordinary least squares ols estimates the magnitude of the bias of iv estimates approaches that of ols estimates as the r 2 between the instruments and the endogenous explanatory variable approaches 0 to illustrate these problems we reexamine the results of a recent paper by angrist and krueger who used large samples from the u s census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment we find evidence that despite huge sample sizes th

generalized oscillatory matrices we define a new class of generalized oscillatory matrices shortly go matrices over a noncommutative ring with identity and a positive part similarly to the classical case this class consists of square generalized totally nonnegative matrices gtn matrices of which some power is generalized totally positive using the previously defined ordering of invertible gtn matrices we study in particular so called basic go matrices which form in a sense atoms of this ordering

hybrid ikebe newton s iteration for inverting general nonsingular hessenberg matrices after a concise survey the expanded ikebe algorithm for inverting the lower half plus the superdiagonal of an n n unreduced upper hessenberg matrix h is extended to general nonsingular upper hessenberg matrices by computing in the reduced case a block diagonal form of the factor matrix hl in the inverse factorization h 1 h l u 1 this factorization enables us to propose hybrid and accurate nongaussian procedures for computing h 1 thus hl is computed directly in the aim to be used as a fine initial guess for newton s iteration which converges to h 1 in a suitable number of iterations

preliminary study on recommended time duration of source signals to be analyzed in relation to its effective duration of the auto correlation function abstract a workable model of human auditory brain system including the auto correlation function acf and the interaural cross correlation function iacf has been reported 1 subjective evaluations can be described by physical factors extracted from both the acf of sound source and the iacf the purpose of this study is to find a recommended integration time 2 t r by using several noise and sound sources existing in an office results show the most suitable integration interval from the viewpoints of the loudness and the pitch can be determined in relation to the effective duration e of the sound source

generalized hessenberg matrices we define and study generalized hessenberg matrices i e square matrices which have subdiagonal rank one here subdiagonal rank means the maximum order of a nonsingular submatrix all of whose entries are in the subdiagonal part we prove that the property of being generalized hessenberg matrix is preserved by post and premultiplication by a nonsingular upper triangular matrix by inversion for invertible matrices etc we also study a special kind of generalized hessenberg matrices

schur parameter pencils for the solution of the unitary eigenproblem abstract let u v be an n n pencil with unitary matrices u and v an algorithm is presented which reduces u and v simultaneously to unitary block diagonal matrices g o q h up and g e q h vp with block size at most two it is an o n 3 process using householder eliminations and it is backward stable in the special case v i the block diagonal matrices g o g h e can be normalized so that their entries are just the schur parameters of the hessenberg condensed form of u we call g o g e a schur parameter pencil it can also be derived from u v by a lanczos like process for the solution of the eigenvalue problem for g o g e a qr type algorithm can be developed based on this unitary reduction of a pencil u v to a schur parameter pencil the condensed form is preserved throughout the process each iteration step needs only o n operations this method of solving the unitary eigenvalue problem seems to be the closest possible analogy to the qr method for the hermitian eigenvalue problem

bayesian and classical approaches to instrumental variable regression we establish relationships between certain bayesian and classical approaches to instrumental variable regression we determine the form of priors that lead to posteriors for structural parameters that have similar properties as classical 2sls and liml and in doing so provide some new insight especially in the context of weak instruments to the small sample behavior of bayesian and classical procedures using a reduced rank restriction on a multivariate linear model we determine the priors that give rise to posteriors that are identical in functional form to the sampling densities of the classical 2sls and liml estimators

bayesian inference in a correlated random coefficients model modeling causal effect heterogeneity with an application to heterogeneous returns to schooling abstract we consider the problem of causal effect heterogeneity from a bayesian point of view this is accomplished by introducing a three equation system similar in spirit to the work of heckman and vytlacil 1998 describing the joint determination of a scalar outcome an endogenous treatment variable and an individual specific causal return to that treatment we describe a bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population the object which has been the focus of most previous work parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed combining data sets from high school and beyond hsb and the 1980 census we illustrate our methods in practice and investigate heterogeneity in returns to education our analysis decomposes the impact of key hsb covariates on log wages into three parts a direct effect and two separate indirect effects through educational attainment and returns to education our results strongly suggest that the quantity of schooling attained is determined at least in part by the individual s own return to education specifically a one percentage point increase in the return to schooling parameter is associated with the receipt of approximately 0 14 more years of schooling furthermore when we control for variation in returns to education across individuals we find no difference in predicted schooling levels for men and women however women are predicted to attain approximately 1 4 of a year more schooling than men on average as a result of higher rates of return to investments in education

posterior distributions in limited information analysis of the simultaneous equations model using the jeffreys prior abstract this paper studies the use of the jeffreys prior in bayesian analysis of the simultaneous equations model sem exact representations are obtained for the posterior density of the structural coefficient in canonical sems with two endogenous variables for the general case with m endogenous variables and an unknown covariance matrix the laplace approximation is used to derive an analytic formula for the same posterior density both the exact and the approximate formulas we derive are found to exhibit cauchy like tails analogous to comparable results in the classical literature on liml estimation moreover in the special case of a two equation just identified sem in canonical form the posterior density of is shown to have the same infinite series representation as the density of the finite sample distribution of the corresponding liml estimator this paper also examines the occurrence first documented in kleibergen and van dijk 1994a of a nonintegrable asymptotic cusp in the posterior distribution of the coefficient matrix of the reduced form equations for the included endogenous regressors an explanation for this phenomenon is provided in terms of the jacobian of the mapping from the structural model to the reduced form this interpretation assists in understanding the success of the jeffreys prior in resolving this problem

bayesian specification analysis and estimation of simultaneous equation models using monte carlo methods bayesian procedures for specification analysis or diagnostic checking of modeling assumptions for structural equations of econometric models are developed and applied using monte carlo numerical methods checks on the validity of identifying restrictions exogeneity assumptions and other specifying assumptions are performed using posterior distributions for discrepancy vectors and functions representing departures from specifying assumptions several mappings or functions of reduced form coefficients are defined and their posterior distributions are computed a restricted reduced form approach is used to compute posterior distributions for structural parameters these procedures are applied in analyses of two econometric models

the loudness of complex noise in relation to the factors extracted from the auto correlation function abstract the loudness of complex signals which include bandpass noises with different center frequencies complex noise is examined while changing the effective duration of the autocorrelation function e based on a model of the human auditory brain system for subjective response to a sound field the center frequencies of each component of the complex noises were 2000 and 3000 hz so that the perceived pitch was centered on 1000 hz the bandwidth of each component was changed by using a 2068 db octave sharp filter to control the e of the source signal the scale values for the loudness of the complex noises were obtained using a paired comparison method the results showed that the loudness increases with the eof the source signal similar to that of the single noise component centered on 1000 hz the loudness of complex noises having equal sound pressure levels is not constant within the critical band 160 hz

generalized reduced rank tests using the singular value decomposition we propose a novel statistic to test the rank of a matrix the rank statistic overcomes deficiencies of existing rank statistics like a kronecker covariance matrix for the canonical correlation rank statistic of anderson annals of mathematical statistics 1951 22 327 351 sensitivity to the ordering of the variables for the ldu rank statistic of cragg and donald journal of the american statistical association 1996 91 1301 1309 and gill and lewbel journal of the american statistical association 1992 87 766 776 a limiting distribution that is not a standard chi squared distribution for the rank statistic of robin and smith econometric theory 2000 16 151 175 usage of numerical optimization for the objective function statistic of cragg and donald journal of econometrics 1997 76 223 250 and ignoring the non negativity restriction on the singular values in ratsimalahelo 2002 rank test based on matrix perturbation theory unpublished working paper u f r science economique university de franche comte in the non stationary cointegration case the limiting distribution of the new rank statistic is identical to that of the johansen trace statistic

annoyance of noise stimuli in relation to the spatial factors extracted from the interaural cross correlation function abstract while considering auditory brain model for subjective responses effects of spatial factors extracted from the interaural cross correlation function iacf on annoyance of noise stimuli are examined the previously developed indices to measure sound pressure levels spl and frequency characteristics cannot fully explain the psychological effects of noise in the first experiment subjects judged their annoyance by changing fluctuations in the magnitude of interaural cross correlation function iacc and the spl in the second they judged their annoyance by changing fluctuations in the interaural time delay iacc and the spl results show that 1 annoyance increased by increasing the fluctuations of iacc as well as the spl 2 annoyance increased by increasing the fluctuations of iacc as well as the spl

generalized totally nonnegative matrices we define a new class of generalized totally nonnegative matrices shortly gtn matrices over a noncommutative ring with identity and a positive part the class of gtn matrices is closed under multiplication every submatrix of a gtn matrix is a gtn matrix as well we also define a standard form of a gtn matrix we then study the invertible gtn matrices of a fixed order and classify them the classes form a partially ordered set can be noncommutatively multiplied and multiplication preserves ordering

on band matrices and their inverses abstract structural properties of the inverses of band matrices are discussed the definition of semiseparable matrices is given and the theorem is proved that the inverse of a strict band matrix is a semiseparable matrix and vice versa finally a recurrence algorithm is recommended for computing the blocks of the inverses of strict band matrices

a cholesky lr algorithm for the positive definite symmetric diagonal plus semiseparable eigenproblem abstract we present a cholesky lr algorithm with laguerre s shift for computing the eigenvalues of a positive definite symmetric diagonal plus semiseparable matrix by exploiting the semiseparable structure each step of the method can be performed in linear time

cues for localization in the median plane as extracted from the auto correlation function abstract this study evaluates using factors extracted from the autocorrelation function acf as cues for sound localization of the median plane the amplitude of the transfer function for sound incident from the median plane to the ear entrances measured see reference 6 is translated into the acf it is shown that the sound localization in the median plane can be characterized by factors extracted from the acf these cues are the effective duration of the normalized acf e the delay time of the first peak 1 and its amplitude 1

a bayesian analysis of simultaneous equation models by combining recursive analytical and numerical approaches abstract inference on simultaneous equation models using a bayesian approach is still far from a routine procedure serious numerical problems may occur in most practical situations in this paper a unifying framework is proposed using recent analytical see steel 1988 and well documented poly t based methods in order to reduce the dimension of the final monte carlo integration different integration sequences are examined and the implications for various model and prior assumptions are tabulated an application to klein s model i clearly illustrates the computational feasibility and numerical stability of the hybrid method proposed

the cochlear frequency map for the cat labeling auditory nerve fibers of known characteristic frequency iontophoresis of horseradish peroxidase was used to label single auditory nerve fibers after determination of threshold tuning curves and rates of spontaneous discharge the relation between characteristic frequency cf and cochlear longitudinal location is reconstructed from 52 labeled neurons in 16 cochleas the length of the organ of corti alotted to an octave of stimulus frequency increases steadily from low to high frequencies thus there is not a simple linear distance to log frequency conversion when comparing cochleas of different total length the best predictor of cf at a given location is the distance from base or apex expressed as a percentage of the total length the cochlear frequency map derived from these single neuron labeling experiments is compared to maps derived by a number of different physiological and psychophysical techniques and the significance of the similarities and differences is discussed

pitch of iterated rippled noise iterated rippled noise irn stimuli are generated by a cascade of delay d gain g and add networks the matched pitch of irn stimuli was determined as a function of the type of network used to generate irn stimuli the delay d 2 4 and 8 ms the number of iterations n 1 2 3 4 6 8 of the delay and add networks and whether the delayed noise was added g 1 to or subtracted g 1 from the undelayed noise the matched pitch of irn stimuli did not depend on the type of network when g 1 addition the matched pitch did not depend on the number of stages of iterations n and was always equal to the reciprocal of the delay 1 d when g 1 subtraction the match pitch depended on n when n 1 the matched pitch of irn stimuli was ambiguous having two pitches in the region of 1 d 10 when n 8 the match pitch was equal to 1 2d this change in the pitch occurred between n 2 and 6 the results are discussed in terms of spectral and temporal models of complex pitch processing a temporal model based on autocorrelation was able to provide quantitative predictions for the pitch of these irn stimuli however a spectral type of model can also account for the pitch of these irn stimuli

loudness in relation to iterated rippled noise abstract this study examined the loudness of iterated rippled noises irns with different number of iterations under conditions of equal sound pressure the scale values of loudness were obtained using a paired comparison method the results showed that the loudness of irns was not constant even though the sound pressure level was equivalent the loudness of irns increased with increasing iteration number this indicated that repetitive components of sounds might affect their loudness

loudness of sharply 2068 db octave filtered noises in relation to the factors extracted from the autocorrelation function this study examines the loudness of bandpass noises with center frequencies of 250 500 and 1000hz while changing the autocorrelation function acf the bandwidth of the source signal was altered with a 2068 db octave sharp filter to control the acf of the source signal the scale values of loudness were obtained using a paired comparison method it is shown that the loudness of the bandpass noises inside the critical band is not constant the loudness of the pure tone is greater than that of sharply filtered noises the loudness of the bandpass noises increases with increasing effective duration of the acf e of the source signal

some further results on the exact small sample properties of the instrumental variable estimator we present new results on the exact small sample distribution of the instrumental variable estimator in particular we compare the small sample distribution to the asymptotic distribution

invariant bayesian inference in regression models that is robust against the jeffreys lindley s paradox we obtain the prior and posterior probability of a nested regression model as the hausdorff integral of the prior and posterior on the parameters of an encompassing linear regression model over a lower dimensional set that represents the nested model the hausdorff integral is invariant and therefore avoids the borel kolmogorov paradox basing priors and prior probabilities of nested regression models on the prior on the parameters of an encompassing linear regression model reduces the discrepancies between classical and bayesian inference like the jeffreys lindley s paradox we illustrate the analysis with examples of linear restrictions i e a linear regression model and non linear restrictions i e a cointegration and an autoregressive moving average model on the parameters of an encompassing linear regression model

a note on generalized hessenberg matrices two different generalizations of the concept of hessenberg matrices have appeared recently in the literature in this note we study their connections in more detail and give a general structure theorem for these classes of matrices

duration sensation in relation to the autocorrelation function of sound stimuli relationships were investigated between subjective judgment of physical duration and the factors extracted from the autocorrelation function acf of sound stimuli factors of acf were changed by using different properties of pure tone complex tone white noise and bandpass noise stimuli experiments by paired comparison method were conducted in the sound proof chamber except for one in a concert hall sound stimuli were selected on the basis of the measured factors of acf as parameters subjects were asked to compare the durations of two stimuli in the pair subjective durations were obtained in the psychometric function and were interpreted as duration sensation ds on the basis of the auditory brain model and the theory of primary sensation results p 0 05 are shown as below 1 dss are longer with larger 1 being time delay of first peak of acf corresponding to pitch 2 dss are longer with higher 0 being energy at the beginning of acf 3 dss are longer with smaller m being constant am

diagnostic system based on the human auditory brain model for measuring environmental noise an application to railway noise abstract measurements of railway noise were conducted by use of a diagnostic system of regional environmental noise the system is based on the model of the human auditory brain system the model consists of the interplay of autocorrelators and an interaural crosscorrelator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres different kinds of railway noise were measured through binaural microphones of a dummy head to characterize the railway noise physical factors extracted from the autocorrelation functions acf and interaural crosscorrelation function iacf of binaural signals were used the factors extracted from acf were 1 energy represented at the origin of the delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude o 1 the factors extracted from iacf were 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc w iacc the factor 0 can be represented as a geometrical mean of energies at both ears as listening level ll

a note on the nullity theorem in this paper we take a closer look at the nullity theorem as formulated by markham and fiedler in 1986 the theorem is a valuable tool in the computations with structured rank matrices it connects ranks of subblocks of an invertible matrix a with ranks of other subblocks in his inverse a 1 a little earlier barrett and feinsilver 1981 proved a theorem very close to the nullity theorem but restricted to semiseparable and tridiagonal matrices which are each others inverses we will adapt the ideas of barrett and feinsilver to come to a new alternative proof of the nullity theorem based on determinantal formulas in the second part of the paper we extend the nullity theorem to make it suitable for two types of decompositions namely the lu and the qr decomposition these theorems relate the ranks of subblocks of the factors l u and q to the ranks of subblocks of the factored matrix it is shown that a combination of the nullity theorem and his extended versions is suitable to predict in an easy manner the structure of decompositions and or of inverses of structured rank matrices e g higher order band higher order semiseparable hessenberg and many other types of matrices as examples to show the power of the nullity theorem and the related theorems we apply them to semiseparable and related matrices

completing a matrix when certain entries of its inverse are specified abstract suppose a a 11 a 12 a 21 a 22 is an n n matrix where a 11 has order p q if a is nonsingular let a 1 have the transposed partitioning b 11 b 12 b 21 b 22 first we show that the nullities of a 11 and b 22 are equal the remainder of our paper deals with the following completion problem suppose m 1 m 2 n 1 n 2 are nonnegative integers such that m 1 m 2 n 1 n 2 n 0

on the relationship between the autocorrelation function of continuous brain waves and the subjective preference of the sound field in change of the iacc this study analyzed the range of waves 8 13 hz of continuous brain waves cbw and compared them with the scale value of the subjective preference of the sound field in a change of the interaural cross correlation function iacc ando concert hall acoustics springer verlag heidelberg 1985 the source signal was sinfonietta opus 48 third movement composed by arnold the scale value of the subjective preference and the cbws to a paired stimuli i e reference stimuli iacc 1 0 and test stimuli iacc 0 3 or 0 65 which were presented alternatively were compared it is found that the value of the effective duration e of the autocorrelation function acf of the waves from only the right hemisphere corresponds well to the subjective preference it is considered therefore that e is an objective measure reflecting the subjective preference chen and ando unpublished

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli