derivations of the parabolic subalgebras of the general linear lie algebra over a commutative ring let r be an arbitrary commutative ring with identity gl n r the general linear lie algebra over r the aim of this paper is to give an explicit description of the derivation algebras of the parabolic subalgebras of gl n r

an exact likelihood analysis of the multinomial probit model abstract we develop new methods for conducting a finite sample likelihood based analysis of the multinomial probit model using a variant of the gibbs sampler an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors this approach avoids direct evaluation of the likelihood and thus avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches both simulated and actual consumer panel data are used to fit six dimensional choice models we also develop methods for analyzing random coefficient and multiperiod probit models

bayesian residual analysis for binary response regression models summary in a binary response regression model classical residuals are difficult to define and interpret due to the discrete nature of the response variable in contrast bayesian residuals have continuous valued posterior distributions which can be graphed to learn about outlying observations two definitions of bayesian residuals are proposed for binary regression data plots of the posterior distributions of the basic observed fitted residuals can be helpful in outlier detection alternatively the notion of a tolerance random variable can be used to define latent data residuals that are functions of the tolerance random variables and the parameters in the probit setting these residuals are attractive in that a priori they are a sample from a standard normal distribution and therefore the corresponding posterior distributions are easy to interpret these residual definitions are illustrated in examples and contrasted with classical outlier detection methods for binary data

graded morita theory for infinite groups abstract having shown that not all graded rings are graded equivalent via classical morita theory to a skew group ring we extend classical morita theory which is based on rings with identity to a generalized graded morita theory for rings with local units this enables us to give necessary and sufficient conditions for graded morita equivalence between two rings graded by a group we show that the strongly graded property is a graded morita invariant and we show that a graded ring is graded morita equivalent to a skew group ring namely r g g if and only if it is strongly graded these results extend the classical cohen montgomery duality theory to rings graded by infinite groups the fundamental tools include rings with local units and the results of boisen

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

adjustment and discrimination measurements of the precedence effect a simple model to summarize the precedence effect is proposed that uses a single metric to quantify the relative dominance of the initial interaural delay over the trailing interaural delay in lateralization this model is described and then used to relate new measurements of the precedence effect made with adjustment and discrimination paradigms in the adjustment task subjects matched the lateral position of an acoustic pointer to the position of a composite test stimulus made up of initial and trailing binaural noise bursts in the discrimination procedure subjects discriminated interaural time differences in a target noise burst in the presence of another burst either trailing or preceding the target experimental parameters were the delay between initial and trailing stimuli and the overall level of the stimulus the model parameters the metric c and the variability of lateral position judgments were estimated from the results of the matching experiment and used to predict results of the discrimination task with good success finally the observed values of the metric were compared to values derived from previous studies

psychometric functions for level discrimination in cochlearly impaired and normal listeners with equivalent threshold masking the purpose of this study was to determine whether the form of the psychometric functions for level discrimination also known as intensity discrimination measured in a two interval two alternative forced choice paradigm changes with hearing impairment measurements of sensitivity d as a function of delta l 20 log p delta p lp where p is pressure were obtained in six listeners with cochlear impairments five normal listeners tested in the quiet and two masked normal listeners stimuli were chosen to encompass a wide range of conditions and difference limens results show that the d is nearly proportional to delta l over the entire range of stimuli this simple relationship is not changed by cochlear impairments or masking noise these findings indicate that if the transformation from stimulus intensity to decision variable is affected by hearing impairment or masking the change affects both the mean and the standard deviation in the same manner i e the standard deviation may be proportional to the derivative of the transformation as was suggested by zwislocki and jordan j acoust soc am 79 772 780 1986 the results also lend support to the notion that delta l plotted on a logarithmic scale is an appropriate representation of level discrimination performance

a note on algebra automorphisms of strictly upper triangular matrices over commutative rings abstract in this note we explicitly describe the automorphism group of the r algebra of strictly upper triangular n n matrices over an arbitrary commutative ring

the influence of early reflections on the identification and lateralization of vowels sound coming directly from a source is often accompanied by reflections arriving from different directions however the precedence effect occurs when listeners judge such a source s direction information in the direct first arriving sound tends to govern the direction heard for the overall sound this paper asks whether the spectral envelope of the direct sound has a similar dominant influence on the spectral envelope perceived for the whole sound a continuum between two vowels was produced and then a two part filter distorted each step the beginning of this filter s unit sample response simulated a direct sound with no distortion of the spectral envelope the second part simulated a reflection pattern that distorted the spectral envelope the reflections frequency response was designed to give the spectral envelope of one of the continuum s end points to the other end point listeners identifications showed that the reflections in two part filters had a substantial influence because sounds tended to be identified as the positive vowel of the reflection pattern this effect was not reduced when the interaural delays of the reflections and the direct sound were substantially different also when the reflections were caused to precede the direct sound the effects were much the same by contrast in measurements of lateralization the precedence effect was obtained here the lateral position of the whole sound was largely governed by the interaural delay of the direct sound and was hardly affected by the interaural delay of the reflections

reduction techniques for strongly graded rings and finite representation type abstract we present reduction techniques for studying the category of lattices over strongly graded orders in particular we apply these techniques in order to reduce the problem of classifying those strongly graded orders with finite representation type to the case where the coefficient ring is a maximal order in a division ring

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

automorphisms and derivations of upper triangular matrix rings abstract kezlan proved that for a commutative ring c every c automorphism of the ring of upper triangular matrices over c is inner we generalize this result to rings in which all idempotents are central moreover we show that for a semiprime ring a and central subring c every c automorphism of the ring of upper triangular matrices over c is the composite of an inner automorphism and an automorphism induced from a c automorphism of a by the method of proof we re prove results of s p coelho and c p milies and of mathis stating that a derivation of a ring of upper triangular matrices of a c algebra n n matrices over a is a sum of an inner derivation and a derivation induced from a c derivation of a by an example we show that an extra assumption is needed for proving the above result of automorphisms of upper triangular matrices finally we consider automorphisms of subrings of n n matrices over a commutative ring c where entries over the diagonal are from c and below the diagonal are taken from a nil ideal we prove that all such automorphisms are inner

the automorphism group of a structural matrix algebra abstract we characterize the automorphism group of certain subalgebras of matrix algebras with entries from a field k known as structural matrix algebras these include the algebras of upper triangular matrices we also give necessary and sufficient conditions for every k automorphism of such a subalgebra to be inner

multiplicative semigroup automorphisms of upper triangular matrices over rings abstract suppose r is a ring with 1 and c a central subring of r let tn r be the c algebra of upper triangular n n matrices over r recently several authors have shown that if r is sufficiently well behaved then every c automorphism of tn r is the composites of an inner automorphism and an automorphism induced from a c automorphism of r see 1 5 to generalize these results in this paper we prove that if n 2 and r is a semiprime ring or a ring in which all idempotents are central then f tn r tn r tn r is only regarded as a multiplicative semigroup is a multiplicative semigroup automorphism if and only if there exist a nonsingular matrix p in tn r and a ring automorphism of r such that f a p 1 a p a a ij n n n r where a aij n n

automorphisms of tiled orders abstract let be a tiled r order we give a description of autr as the semidirect product of inn and a certain subgroup of aut q where q is the link graph of additionally we give criteria for determining when an element of aut q belongs to this subgroup in terms of the exponent matrix for

automorphisms of the standard borel subgroup of orthogonal group o 2m r over commutative rings abstract all automorphisms of the standard borel subgroup of orthogonal group o 2 m r are determined provided that r is a commutative ring with identity 2 3 are invertible in r and m 5

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

crossed product algebras defined by separable extensions abstract we generalize the classical construction of crossed product algebras defined by finite galois field extensions to finite separable field extensions by studying properties of rings graded by groupoids we are able to calculate the jacobson radical of these algebras we use this to determine when the analogous construction of crossed product orders yield azumaya maximal or hereditary orders in a local situation thereby we generalize results by haile larson and sweedler

sound localization precision under conditions of the precedence effect effects of azimuth and standard stimuli minimum audible angles maas were estimated for single noise bursts and for burst pairs that satisfied the conditions of the precedence effect that is produced fused images in one burst pair condition the bursts to be discriminated differed in lead location in the other they differed in lag location sounds were presented over loudspeakers maas were lowest for single bursts slightly higher for lead discrimination and much higher for lag discrimination presence of a standard reference burst had no reliable effect on performance the data are interpreted using a model of shinn cunningham et al j acoust soc am 93 2923 2932 1993 in which discrimination of precedence effect burst pairs is based on the lateral position of the auditory image which is a weighted average of the positions of the leading and lagging bursts

analysis of multivariate probit models summary this paper provides a practical simulation based bayesian and non bayesian analysis of correlated binary data using the multivariate probit model the posterior distribution is simulated by markov chain monte carlo methods and maximum likelihood estimates are obtained by a monte carlo version of the em algorithm a practical approach for the computation of bayes factors from the simulation output is also developed the methods are applied to a dataset with a bivariate binary response to a four year longitudinal dataset from the six cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the panel survey of income dynamics

automorphisms of the lie algebra of strictly upper triangular matrices over a commutative ring let r be an arbitrary commutative ring with identity denote by n r the lie algebra over r consisting of all strictly upper triangular n 1 n 1 matrices over r with n 3 in addition for n 3 assume that the annihilator of 2 in r is zero the aim of this paper is to describe the automorphism group of n r we show that any automorphism of n r can be expressed as where and are graph extremal central and inner automorphisms respectively of n r

intensity discrimination as the driving force for loudness application to pure tones in quiet loudness functions and their associated neural count functions are derived for steady state tones at 250 and 1000 hz from measurements of intensity discrimination obtained under gated and continuous conditions the calculations are based on a multichannel generalization of the mcgill goldberg counting model j acoust soc am 44 576 581 1968 using the data for just noticeable differences jnd in intensity as input the generalized version gives an integral relation between the neural count function n x and the intensity jnd function where x i i0 and i0 is the reference intensity loudness functions are generated through the prescription l x an x b to determine how the detailed shapes of the intensity jnd functions affect the form of the loudness function within the model integration was performed over the intensity jnd functions with and without a power function approximation over a range of intensity levels from 20 95 db the best agreement between the calculated and measured loudness func

intensity discrimination for precedence effect stimuli when two identical stimuli are presented from two loudspeakers with a brief delay between them a single image is heard near the source of the leading sound the delayed sound or echo appears to be suppressed whereas the preceding sound determines perceived location hence the name the precedence effect this study investigated normal hearing listeners sensitivity to changes in the intensity of the lagging sound pairs of 2 ms white noise bursts with a 2 ms delay between the onsets of lead and lag were presented from two loudspeakers 45 left and right of midline in an anechoic chamber a 2afc procedure was used to test discrimination of intensity changes in the lead lag and both sounds together the untreated results showed discrimination to be poorest for changes in the lag stimulus however when the intensity differences were transformed into predictions of equivalent monaural level based on kemar measurements and binaural loudness summation discrimination for the lag was equal to the other two

multiplicative semigroup automorphisms of the strictly upper triangular matrices over a commutative ring let r be an arbitrary commutative ring with identity and nn r b e the multiplicative semigroup consisting of all n n strictly upper triangular matrices over r t he aim of this paper is to give an explicit description of any automorphism of the semigroup nn r

bayesian analysis of autocorrelated ordered categorical data for industrial quality monitoring presently available methods to analyze the link between explanatory variables and an ordered categorical response implicitly assume independence this hypothesis is no longer valid when data are collected over time we assume temporal dependence and introduce autocorrelation using a latent variable formulation due to intractable distributions we resort to gibbs sampling for statistical inference within the bayesian paradigm variable selection is also addressed and appears as a straightforward byproduct of this framework we illustrate the method by analyzing on line quality data that possess such autocorrelation

the group of automorphisms of certain subalgebras of matrix algebras the purpose of this note is to find and characterize the full group of automorphisms of certain prime algebras which are subalgebras of matrix algebras over commutative rings here we extend the methods which we used in 6 to characterize automorphisms of certain upper triangular matrix rings for a central simple k algebra a the group of k automorphisms of a is extensively treated in the literature 5 theorem 6 21 other cases where the automorphism group of a ring is known are the automorphism group of a polynomial ring in two indeterminates over a field and the free algebra in two variables over a field 4 chap 61 finally if a is a prime p z algebra with center c then every c automorphism of a is x inner 7 example 3 91

three automorphism theorems for triangular matrix algebras abstract let t n a be the algebra of upper triangular n n matrices with entries from an associative k algebra a where k is a commutative ring recently several authors barker coelho jondrup kezlan have shown that if a is sufficiently well behaved then every k algebra automorphism of t n a decomposes into a product of an inner automorphism and an automorphism defined by an automorphism of a in this paper we find new sufficient conditions for a that guarantee such decompositions and we give comparisons with previous results as an intermediate step we show that a single automorphism admits such a decomposition if and only if it respects the subspace of strict upper triangular matrices we also consider the case of infinite matrices

epimorphisms of infinite triangular and unitriangular matrices we discuss the form of all epimorphisms of t f the group of all infinite upper triangular matrices over a field into itself we show that every such epimorphism is a composition of some standard maps moreover we present an analogous result for ut f we use the obtained results to describe the groups of automorphisms of these groups

bayesian analysis of ordered categorical data from industrial experiments data from industrial experiments often involve an ordered categorical response such as a qualitative rating analysis of variance based analyses may be inappropriate for such data suggesting the use of generalized linear models glm s when the data are observed from a fractionated experiment likelihood based glm estimates may be infinite especially when factors have large effects these difficulties are overcome with a bayesian glm which is implemented via the gibbs sampling algorithm techniques for modeling data and for subsequently using the identified model to optimize the process are outlined an important advantage in the optimization stage is that uncertainty in the parameter estimates is accounted for in the model for robust design experiments the bayesian approach easily incorporates the variability of the noise factors using the response modeling approach this approach and its techniques are used to analyze two data sets one of which arises from a robust design experiment

epsilon strongly graded rings separability and semisimplicity abstract we introduce the class of epsilon strongly graded rings and show that it properly contains both the class of strongly graded rings and the class of unital partial crossed products we determine precisely when an epsilon strongly graded ring is separable over its principal component thereby we simultaneously generalize a result for strongly group graded rings by n st sescu van den bergh and van oystaeyen and a result for unital partial crossed products by bagio lazzarin and paques we also show that the class of unital partial crossed products appears in the class of epsilon strongly graded rings in a fashion similar to how the classical crossed products present themselves in the class of strongly graded rings thereby we obtain in the special case of unital partial crossed products a short proof of a general result by dokuchaev exel and simon concerning when graded rings can be presented as partial crossed products we also provide some interesting classes of examples of separable epsilon strongly graded rings with finite as well as infinite grading groups in particular we obtain an answer to a question raised by le bruyn van den bergh and van oystaeyen in 1988

a bayesian sequential look at u control charts we extend the usual implementation of u control charts uccs in two ways first we overcome the restrictive and often inadequate assumptions of the poisson model next we eliminate the need for the questionable base period by using a sequential procedure we use empirical bayes eb and bayes methods and compare them with the traditional frequentist implementation eb methods are somewhat easy to implement and they deal nicely with extra poisson variability and at the same time informally check the adequacy of the poisson assumption however they still need the base period the sequential full bayes approach on the other hand also avoids this drawback of traditional u charts the implementation requires numerical simulation and also use of a prior distribution several possibilities for both objective and informative priors are explored we argue that the sequential full bayesian ucc is a powerful and versatile tool for process monitoring

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

likelihood analysis of multivariate probit models using a parameter expanded mcem algorithm multivariate binary data arise in a variety of settings in this article we propose a practical and efficient computational framework for maximum likelihood estimation of multivariate probit regression models this approach uses the monte carlo expectation maximization mcem algorithm with parameter expansion to complete the m step to avoid the direct evaluation of the intractable multivariate normal orthant probabilities the parameter expansion not only enables a closed form solution in the m step but also improves efficiency using the simulation studies we compare the performance of our approach with the mcem algorithms developed by chib and greenberg 1998 and song and lee 2005 as well as the iterative approach proposed by li and schafer 2008 our approach is further illustrated using a real world example

bayes regression with autoregressive errors a gibbs sampling approach abstract this paper develops a practical framework for the bayesian analysis of gaussian and student t regression models with autocorrelated errors as is customary in classical estimation procedures the posteriors are conditioned on the initial observations recourse is taken to the method of gibbs sampling an iterative markovian sampling method and it is shown that the proposed approach can readily deal with high order autoregressive processes without requiring an importance sampling function or other tuning constants several examples including one with ar 4 errors are used to illustrate the ideas

statistical inference in the multinomial multiperiod probit model abstract statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions posterior distributions or moment conditions in these models we describe three alternative estimators implemented using simulation based approaches to inference that circumvent the integration problem posterior means computed using gibbs sampling and data augmentation gibbs simulated maximum likelihood sml estimation using the ghk probability simulator and method of simulated moment msm estimation using ghk we perform a set of monte carlo experiments to compare the sampling distributions of these estimators although all three estimators perform reasonably well some important differences emerge our most important finding is that holding simulation size fixed the relative and absolute performance of the classical methods especially sml gets worse when serial correlation in disturbances is strong in data sets with an ar 1 parameter of 0 50 the rmses for sml and msm based on ghk with 20 draws exceed those of gibbs by 9 and 0 respectively but when the ar 1 parameter is 0 80 the rmses for sml and msm based on 20 draws exceed those of gibbs by 79 and 37 respectively and the number of draws needed to reduce the rmses to within 10 of gibbs are 160 and 80 respectively also the sml estimates of serial correlation parameters exhibit significant downward bias thus while conventional wisdom suggests that 20 draws of ghk is enough to render the bias and noise induced by simulation negligible our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strong

on the automorphisms of incidence algebras abstract given a locally finite partially ordered set x a ring with identity r and an automorphism of the incidence algebra of x over r it is determined when is the composite of an inner automorphism an automorphism of x and an induced automorphism of r

level discrimination of tones as a function of duration difference limens for level ls db 20 log p p p where p is the pressure were measured as a function of duration for tones at 250 500 and 8000 hz stimulus durations ranged from 2 ms to 2 s and the stimulus power was held constant rise and fall times were 1 ms the interstimulus interval was 250 ms at each frequency three levels were tested 85 65 and approximately 40 db spl an adaptive two alternative forced choice procedure with feedback was used for three normal listeners ls decreased as duration increased up to at least 2 s except at 250 hz at 250 hz l stopped decreasing at durations between 0 5 and 1 s in a double logarithmic plot of l versus duration the rate of decrease is generally well fitted by a sloping line the average slope is 0 28 it is steeper at high levels than at low levels because the average slope is shallower than the 0 5 slope predicted for an optimum detector it may be that fast adaptation of auditory nerve activity and or memory effects interfere w

dynamic processes in the precedence effect three experiments were conducted to investigate the dependence of echo suppression on the auditory stimulation just prior to a test stimulus subjects sat in an anechoic chamber between two loudspeakers one which presented the lead sound and the other the delayed lag sound in the first experiment subjects reported whether or not they heard an echo coming from the vicinity of the lag loudspeaker during a test click pair in seven of nine listeners perception of the lagging sound was strongly diminished by the presence of a train of conditioning clicks presented just before the test click echo threshold increased subjects were less sensitive to echoes as the number of clicks in the train increased from 3 to 17 for a fixed number of clicks the effect was essentially independent of click rate from 1 s through 50 s and duration of the train from 0 5 through 8 s a second experiment demonstrated a similar buildup of echo suppression with white noise bursts regardless of whether the bursts in the conditioning train were repeated samples of frozen noise or were independent samples of noise using an objective procedure for measuring echo threshold the third experiment demonstrated that both lead and lag stimuli must be presented during the conditioning train in order to produce the buildup of suppression when only the lead sound was presented during the conditioning train the perceptibility of the lag sound during the test burst appeared to be enhanced

psychometric functions for level discrimination to determine the form of psychometric functions for 2i 2afc level discrimination ten increment levels were presented in random order within blocks of 100 trials stimuli were chosen to encompass a wide range of conditions and difference limens eight 10 ms tones had frequencies of 0 25 1 8 or 14 khz and levels of 30 60 or 90 db spl two 500 ms stimuli also were tested a 1 khz tone at 90 db spl and a white noise at 63 db spl for each condition at least 20 blocks were presented in mixed order results for three normal listeners show that the sensitivity d is nearly proportional to l 20 log p p p where p is pressure over the entire range of difference limens when d is plotted against weber fractions for pressure p p or intensity i i exponents of the best fitting power functions decrease with increasing difference limens and are less than one for large difference limens these results indicate that the transformation from stimulus intensity to decision variable may be approximately lo

picard groups and infinite matrix rings we describe a connection between the picard group of a ring with local units t and the picard group of the unital overring end tt using this connection we show that the three groups pic r pic fm r and pic rfm r are isomorphic for any unital ring r furthermore eaclh ele ment of pic rfm r arises from an automorphism of rfm r which yields an isomorphsm between pic rfm r and out rfm r as one applica tion we extend a classical result of rosenberg and zelinsky by showing that the group outr rfm r is abelian for any commutative unital ring r

automorphisms of certain lie algebras of upper triangular matrices over a commutative ring abstract letrbe an arbitrary commutative ring with identity denote bytthe lie algebra overrconsisting of all upper triangularnbynmatrices overrand letbbe the lie subalgebra oftconsisting of all matrices of trace 0 the aim of this paper is to give an explicit description of the automorphism group of the lie algebrat which extends a result given by dokovic in addition we explicitly describe the automorphism group of the lie algebrabwhennis a unit ofr

graded equivalence theory with applications we develop the foundations for graded equivalence theory and apply them to investigate properties such as primeness finite representation type and vertex theory of graded rings the key fact that we prove is that for any two g graded rings r and s such that there is a category equivalence from gr r to gr s that commutes with suspensions then for any subgroup h of g the categories gr h g r and gr h g s of modules graded by the g set of right cosets are also equivalent