The use of an empirical, or sample based, estimator of the covariance of parameter estimates is a useful idea and is gaining popularity. Liang and Zeger (Biometrika 73 (1986) 13–22) suggested a particular empirical estimator called the ‘sandwich’ covariance estimator. This estimator is expected to perform well when the experimental sample size is large. For small and moderately sized samples, it can have large bias. In this paper, we evaluate the performance of the sandwich estimator of the covariance of the quasi-likelihood estimate of regression parameters, in the analysis of count data.

Posterior mode estimators are proposed, which arise from simply expressed prior opinion about expected outcomes, roughly as follows: a conjugate family of prior distributions is determined by a given variance function. Using a conjugate prior, a posterior mode estimator and its estimated (co-)variances are obtained through conventional maximum likelihood computations, by means of small alterations to the observed outcomes and/or to the modelled variance function. Within the conjugate family, for purposes of inference about the regression vector, a reference prior is proposed for a given choice of linear design of the canonical link. The resulting approximate reference inferences approximate the Bayesian inferences which arise from a “minimally informative” reference prior. A set of subjective prior upper and lower percentage points for the expected outcomes can be used to determine a conjugate family member. Alternatively, a set of subjective prior means and standard deviations determines a member. The subfamily of priors determinable by percentage points either includes or approximates the proposed reference prior.

Summary: Résumé: ZusammenfassungSeedlings of wheat (Triticum aestivum L.) and beans (Phaseolus vulgaris L.) were less sensitive to glyphosate when grown in heat‐treated soil than in raw soil. Pythium spp. and Fusarium spp. were not detected in heat‐treated loam or muck soils at the time of glyphosate treatment, although fungi of several other genera were present. The efficacy of glyphosate on wheat or beans grown in heat‐treated loam soil was restored when untreated aqueous soil extracts were added to the heat‐treated soil. Bean seedlings grown in five different soil types varied in their sensitivity to glyphosate. The variation in LD50 among autoclaved soils was lower than that among raw soils. Between 13‐ to 47‐fold more glyphosate was required to kill the bean seedlings in any of the autoclaved soils compared with their corresponding raw soils. This differential effect was not observed on bean seedlings sprayed with either 2, 4‐D or paraquat. LD50 values for glyphosate on apple (Malus domestica Borkh.) seedlings growing in previously sterilized loam soil were reduced by inoculation of the soil with a representative Fusarium sp. or Pythium sp. obtained earlier from apple seedlings treated with glyphosate, but not by a Cylindrocarpon sp. from apple or Pythium ultimum Trow from glyphosate‐treated bean. The efficacy of glyphosate on bean, wheat or apple seedlings can be affected by changes in certain microbial components of the soil. Effet d'un traitement du sol a la chaleur et de la microflore sur l'efficacité du glyphosate sur plantules Des plantules de blé (Triticum aestivum L.) et de haricots (Phaseolus vulgaris L.) ont été moins sensibles au glyphosate quand elles sont cultivées dans des sols traités par la chaleur que dans des sols bruts. Pythium spp et Fusarium spp. n'ont pas été détectés dans la terre traitée à la chaleur ou dans des sols fumés au moment de l'application du glyphosate, bien que des champignons de quelques autres genres aient été présents. L'efficacité du glyphosate sur blé et haricots cultivés en sol traité par la chaleur a été récupérée quand des extraits aqueux de sols non traités ont été additionnés au sol traité. Les plantules de haricots cultivés dans 5 types de sols ont varié dans leur sensibilité au glyphosate. La variation des DL50 pour les sols autoclavés était plus faible en comparaison de celle des sols bruts. Il a fallu de 13 à 47 fois plus de glyphosate pour détruire les plantules de haricot dans tous les sols autoclaves que dans les sols bruts correspondants. Cet effet différentiel n'a pas été observé chez les plantules de haricots traités avec du 2,4 D ou du paraquat. Les valeurs de DL50 pour le glyphosate sur des plantules de pommiers (Malus domestica Borkh.) cultivées sur des sols avec de la terre précédemment stérilisée, ont été réduites par l'innoculation du sol avec un Fusarium sp. ou Pythium sp. obtenu plutôt à partir de plantules de pommier traitées au glyphosate, mais pas avec du Cylindrocarpon du pommier, ou un Pythium ultimum venant d'un haricot traité au glyphosate. L'efficacité du glyphosate sur plantules de haricot, blé ou pommier peut être affecté par des changements de la composition microbiologique du sol. Die Wirkung von Boden‐Hitzesterilisation und Mikroflora auf die Wirksamkeit von Glyphosat auf Keimpflanzen Keimpflanzen von Weizen (Triticum aestivum L.) und Buschbohne (Phaseolus vulgaris L.) waren, in hitzebehandeltem Boden wachsend, gegenüber Glyphosat weniger empfindlich als in unbehandeltem Boden. Pythium spp. und Fusarium spp. wurden in hitzebehandeltem Lehm‐ oder stark organischem Boden zur Glyphosatbehandlung nicht gefunden, obwohl andere Pilzgattungen vorhanden waren. Die Wirksamkeit des Glyphosats auf in hitzebehandeltem Boden gezogenen Weizen‐ oder Bohnenpflanzen stellte sich wieder ein, wenn unbehandelte wäßrige Bodenextrakte dem hitzebehandeltem Boden zugefügt wurden. Bohnenkeimpflanzen zeigten in 5 verschiedenen Bodenarten eine unterschiedliche Empfindlichkeit gegenüber Glyphosat. Die LD50 variierte in autoklavierten Böden weniger als in unbehandelten. Zur Abtötung der Bohnen‐keimpflanzen waren in den autoklavierten Böden 13‐ bis 47mal größere Wirkstoffmengen erforderlich als in den entsprechenden unbehandelten Böden. Diese Wirkungsunterschiede wurden bei mit 2,4‐D oder Paraquat behandelten Bohnenkeimpflanzen nicht beobachtet. Wurden Apfelsämlinge (Malus domestica Borkh.) in sterilisiertem Lehmboden angezogen, so sanken die LD50‐Werte für Glyphosat bei Inokulation des Bodens mit repräsentativen Fusarium‐ oder Pythium‐Arten, die zuvor von Glyphosat‐behandelten Apfelsämlingen gewonnen worden waren, jedoch nicht mit einer Cylindrosporium‐Art von Äpfeln oder Pythium ultimum Trow von Glyphosat‐gehandelteten Bohnen. Die Wirksamkeit von Glyphosat auf Keimpflanzen von Bohnen, Weizen oder Äpfeln kann durch Veränderungen bestimmter mikrobiologischer Bodenkomponenten beeinflußt werden.

Glyphosate is a broad spectrum herbicide that can lead to root rot like damage on crops. This study was undertaken to investigate the effect of glyphosate on the root-colonizing Fusarium spp. The research was conducted at two sites. Site one was densely covered with perennial weeds, and site two with annuals. At site one, spraying the weed cover with glyphosate increased (p < 0.05) the level of colonization by Fusarium spp. in Ranunculus repens and Holcus lanatus, but not in Stellaria media and Plantago lanceolata. At site two, glyphosate enhanced colonization in Spergula arvensis, Stellaria media, Echinochloa crusgalli, and Chenopodium album, but not in Capsella bursa-pastoris and Polygonum persicaria. At both sites, the number of colony-forming units of Fusarium spp. per gram of dried soil was increased by the application of glyphosate. Nevertheless, crops subsequently sown in the field containing the annual weeds were not detrimentally affected by glyphosate treatment of these weeds.

SUMMARY The Bayesian test of a normal mean H 0 : μ = μ0 is revisited. Several interpretations of prior indifference are contrasted; each employs a prior probability for H 0 which in some sense maximizes the information – negative entropy – missing from the prior.

A nonlinear regression model is applied to several sets of enzyme kinetics data, treating the entire regression vector as the parameter of interest. The resulting marginal posterior distributions are presented alongside the usual Student's t posterior distributions implicit in the usual linearized regression. The prior distribution used is that which is minimally informative about the regression vector. In the special case of the linear model this procedure leads to the prior density 1/θ, thereby producing the classical inferences.

Summary A two-stage exchangeable hierarchical model for the lot acceptance problem is described. This is naturally dictated by the need to allow for the possibility of variable quality among the sampling units.