spectral shift function for trapping energies in the semiclassical limit semiclassical asymptotics of the spectral shift function ssf for schrodinger operator is studied at trapping energies it is shown that the ssf converges to sum of a smooth function and a step function which is essentially the counting function of resonances in particular the weyl asymptotics is proved

eigenvalues of the reference operator and semiclassical resonances we prove that the estimate of the number of the eigenvalues in intervals 0 0 and the number of the positive eigenvalues of l h in we apply this result to obtain a breit wigner approximation of the derivative of the spectral shift function near critical energy levels

residual maximum likelihood reml estimation of a neighbour model for field experiments a spatial analysis of field experiments is proposed which takes account of association between neighbouring plots the residual maximum likelihood reml method of patterson and thompson 1971 biometrika 58 545 554 is used to estimate parameters of a general neighbour model which can be expressed as an autoregressive moving average arma model three data sets are analysed to i highlight the need for a model selection procedure ii illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design and iii illustrate the environmental variation within an experiment using prediction of trend

identification of universally optimal circular designs for the interference model many applications of block designs exhibit neighbor and edge effects a popular remedy is to use the circular design coupled with the interference model the search for optimal or efficient designs has been intensively studied in recent years the circular neighbor balanced designs at distances 1 and 2 cnbd2 including orthogonal array of type i mathrm oa i of strength 2 are the two major designs proposed in literature for the purpose of estimating the direct treatment effects they are shown to be optimal within some reasonable subclasses of designs by using benchmark designs in approximate design theory we show that cnbd2 is highly efficient among all possible designs when the error terms are homoscedastic and uncorrelated however when the error terms are correlated these designs will be outperformed significantly by other designs note that cnbd2 fall into the special catalog of pseudo symmetric designs and they only exist when the number of treatments is larger than the block size and the number of blocks is multiple of some constants in this paper we elaborate equivalent conditions for any design pseudo symmetric or not to be universally optimal for any size of experiment and any covariance structure of the error terms this result is novel for circular designs and sheds light on other similar models in the search for optimal or efficient asymmetric designs

an h likelihood method for spatial mixed linear models based on intrinsic auto regressions summary we consider sparse spatial mixed linear models particularly those described by besag and higdon and develop an h likelihood method for their statistical inference the method proposed allows for singular precision matrices as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model furthermore we generalize the h likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between gaussian intrinsic markov random fields on regular arrays and the de wijs process keeping various applications of spatial mixed linear models in mind we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix free statistical computations we provide two applications the first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation the second application concerns an analysis of a large cotton field which gives a focus to matrix free computations the paper closes with some further considerations such as applications to irregularly spaced data use of the parametric bootstrap and some generalizations to the gaussian matern mixed effect models

breit wigner formula at barrier tops for noncritical energies the asymptotic behavior of the scattering phase and of the time delay are known to be described by a weyl type formula and the breit wigner formula respectively we consider here the case of critical energy levels in dimension 1 we obtain the semiclassical asymptotics of the scattering phase and of the time delay uniformly with respect to the energy in a neighborhood of a critical value

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

zeros of brauer characters and linear actions of finite groups small primes abstract we describe the finite groups whose p brauer character table for p 2 or p 3 does not contain any zero this completes the analysis in 6 where we considered the case p 5

construction of resolvable spatial row column designs resolvable row column designs are widely used in field trials to control variation and improve the precision of treatment comparisons further gains can often be made by using a spatial model or a combination of spatial and incomplete blocking components martin eccleston and gleeson 1993 journal of statistical planning and inference34 433 450 presented some general principles for the construction of robust spatial block designs which were addressed by spatial designs based on the linear variance lv model in this article we define the two dimensional form of the lv model and investigate extensions of the martin et al principles for the construction of resolvable spatial row column designs the computer construction of efficient spatial designs is discussed and some comparisons made with designs constructed assuming an autoregressive variance structure

the linear spatial temporal interaction process and its relation to 1 ω noise if we are to gain an understanding of the evolutionary processes which generate pattern then time cannot be ignored since a purely spatial viewpoint disregards the fundamental generating mechanism of the underlying process we therefore develop a spectral approach based on a general growth interaction model individuals grow at intrinsic rate while two individuals a distance r apart interact at rate a times their size difference special cases considered involve nearest neighbour geometric logarithmic and cauchy type dependence a separate study is made of long term persistence an autoregressive binomial weight structure is used to generate processes with power law spectra d

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

precise estimates of tunneling and eigenvalues near a potential barrier abstract we consider a semiclassical schrodinger operator in one dimension with an analytic potential presenting a barrier between two potential wells we give precise estimates for eigenvalues eigenvalue splittings and avoided crossings of eigenvalues near the barrier level these estimates include bounds of the coefficients in the asymptotic expansions

a neighbour model for field experiments summary a neighbour type model is proposed as an alternative to that of wilkinson et al 1983 for the analysis of field variety trials the model assumes that the varieties are grouped into complete replicates and that the plots within a replicate are side by side a method for the estimation of the variance parameters is developed as an extension of the procedure commonly used in incomplete block designs the model is investigated using data from the 166 cereal variety trials studied by patterson hunter 1983 results show worthwhile gains in efficiency over conventional incomplete block analysis

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

breit wigner formulas for the scattering phase and the total scattering cross section in the semi classical limit in this paper we prove results in resonance scattering for the schrodinger operatorpv h2 v v being a smooth short range potential onrn more precisely for energy near a trapping energy level 0 for the classical system defined by the hamiltonianp x 2 v x we prove that the scattering phase and the scattering cross sections associated to pv p0 have the breit wigner form lorentzian line shape in the limith 0

a modified augmented design for an early stage of plant selection involving a large number of test lines without replication summary in the early stages of a plant selection program field experiments are characterized by having many test lines and a limited amount of material available for each line the present design was proposed to cope with such experimental conditions by using control plots to adjust for environmental heterogeneity the structure is a split plot design where the whole plots can be laid out in any standard design but the arrangements of subplots is always 3 x 3 with the centre point used as a control the shape of subplot needs to be square or nearly square so that the distances between the centre plot and its corresponding eight test plots are relatively uniform the control lines are assigned to the control plots according to the design specification for the whole plots and the test lines are assigned randomly to the noncontrol plots the number of control plots under the present design is approximately 13 17 of the total number of plots the p x p latin square is used as an example to demonstrate the basic idea of the design methods of analysis are also discussed in plant selection programs breeders usually start with a large number of test lines which come either from crossing or through introduction from foreign sources the number of lines can range from several hundred to several thousand to conduct a field experiment for such a large population is extremely difficult for a number of reasons among them that environmental heterogeneity in the field cannot be easily taken into account to complicate the matter further material available for each test line is often limited sometimes being sufficient for only one replication thus designs for variety trials involving large numbers of test lines for example lattice lattice square and quasifactorial designs all of which require replication cannot be used similarly designs such as chain blocks youden and connor 1953 mandel 1954 which require that a substantial number of test lines have at least two replications cannot be applied to circumvent the difficulties arising from nonreplicated experiments federer 1956 proposed a class of design called augmented design the basic idea is to include control lines for which enough material is available and repeat them several times in a standard design each repetition of the control lines is embedded in a block or incomplete block or cell depending on the design used and the test lines are assigned to plots that are not allocated to controls estimation of block effects and plot error is done only with respect to control lines the estimated block effects are used to adjust the observed values of the test lines and the error is used to test the significance of line differences in addition to the above federer and raghavarao 1975 proposed a special square design which we will refer to as the f r design generated from the youden square in this design the control plots are allocated over a square with a constant number of control plots per row and per column and row and column effects are orthogonal to control lines furthermore federer nair and raghavarao

bayesian analysis of agricultural field experiments the paper describes bayesian analysis for agricultural field experiments a topic that has received very little previous attention despite a vast frequentist literature adoption of the bayesian paradigm simplifies the interpretation of the results especially in ranking and selection also complex formulations can be analysed with comparative ease by using markov chain monte carlo methods a key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns this is discussed in detail problems caused by outliers and by jumps in fertility are tackled via hierarchical f formulations that may find use in other contexts the paper includes three analyses of variety trials for yield and one example involving binary data none is entirely straightforward some numerical comparisons with frequentist analyses are made

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

semiclassical representation of the scattering matrix by a feynman integral we study the scattering problem for one dimensional schrodinger equations in the semiclassical limit when the energy level is close to the quadratic maxima of the potential starting from the formula of the scattering matrix obtained by the exact wkb method we represent its principal term in a reduced form of the feynman integral an absolutely convergent sum of suitably defined probability amplitudes over countably many trajectories on generated by classical trajectories and tunneling effects

microlocalization of resonant states and estimates of the residue of the scattering amplitude we obtain some microlocal estimates of the resonant states associated to a resonance z0 of an h differential operator more precisely we show that the normalized resonant states are outside the set of trapped trajectories and are in the incoming area of the phase space as an application we show that the residue of the scattering amplitude of a schrodinger operator is small in some directions under an estimate of the norm of the spectral projector finally we prove such a bound in some examples

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience