Bayesian Analysis of Agricultural Field Experiments

Classified as probably not a substantial claim.

Combined effects of pollinator behaviour, out-crossing rates and pollen pool contribution would seem to bestow an advantage on the white allele.

“However, the combined eects of factors, such as pollinator behaviour, out-crossing rates and the contribution to the pollen pool, would seem to bestow an advantage on the white allele (Rausher and Fry, 1993).”

• cites Rausher and Fry, 1993 sourceSupported

May combine two claims.

One-dimensional fertility adjustment is sufficient for the El Batán example but not for the other three applications.

“One-dimensional fertility adjustment is sucient in this example but not in the other three.”

May combine two claims.

The posterior probability that P has maximal effect is 0.38; for P or E it is 0.72; for P, E or V it is 0.87.

“The posterior probability that P has maximal eect is 0.38; for either P or E this probability is 0.72, and for P, E or V it is 0.87.”

The quote only partly states this claim.

The standard errors for the incomplete-block analyses of the corn trials are noticeably larger than the Bayesian posterior standard deviations.

“The standard errors for the incomplete-block analyses are noticeably larger and this may re¯ect the strong row orientation of the blocks.”

May combine two claims.

The locally quadratic Bayesian fertility model produces the same ranking of strawberry varieties, but its posterior means differ a little because it absorbs arbitrary row and column effects.

“the locally quadratic Bayesian fertility model produces the same ranking of varieties but, because it absorbs arbitrary row and column eects, the posterior means are a little dierent”

May combine two claims.

In the morning-glory seed counts, there are 1277 zeros; non-zero counts range from 1 to 1665, with median 98 and mean 197.

“There are 1277 0s, indicated by white pixels.The non-zero counts range between 1 and 1665, with a median of 98 and mean of 197.”

May combine two claims.

Variety 1 has a suspiciously large yield in the final replicate and is therefore penalized by the t-analysis.

“Variety 1 has a suspiciously large yield in the ®nal replicate and hence is penalized by the t-analysis.”

May combine two claims.

Variety 20 has one of the lowest yields in the final replicate but otherwise performs very well, and its mean is enhanced by the t-analysis.

“Variety 20 has one of the lowest yields in the ®nal replicate but otherwise performs very well.Its mean is enhanced by the t-analysis”

May combine two claims.

Variety 4 has posterior probability about 0.5 of being best and probability above 0.9 of being among the top five.

“variety 4 has posterior probability about 0:5 of being best and probability in excess of 0:9 of being among the best ®ve.”

May combine two claims.

For an 18 by 11 lay-out with ρ=1/2, the ratio of maximum to minimum variance of adjacent plot fertility differences is 1.39 without virtual plots; adding borders of widths 2 and 3 reduces it to 1.02 and 1.01.

“As a numerical example, relevant to Section 6, consider an 18 Â 11 lay-out and suppose that 1 2 .Then, without virtual plots, the ratio of the maximum to the minimum of var i À j for i $ j is 1.39.However, with the inclusion of borders of widths 2 and 3 respectively, the ratio drops to 1.02 and 1.01 for the original pairs of plots”

May combine two claims.

Unmeasured plot effects were originally allowed in the morning-glory model but proved negligible and were omitted.

“Originally, we also allowed p to depend on a vector of unmeasured plot eects but these proved to be negligible and were subsequently omitted.”

May combine two claims.

There is a substantial improvement in consistency between individual and combined results when Gaussian rather than uniform variety priors are used, because of additional shrinkage.

“Finally, as we might expect, there is a substantial improvement in consistency between the individual and combined results when Gaussian, rather than uniform, variety priors are used, because of the additional shrinkage.”

May combine two claims.

The t-analysis suggests a fall in fertility in the first replicate between varieties 10 and 11, which demotes variety 10 and promotes variety 11.

“This analysis also suggests a fall in fertility in the ®rst replicate between varieties 10 and 11, which therefore demotes the former and promotes the latter.”

May combine two claims.

There is an almost linear decrease in fertility from left to right in each row, but it is so slight (0.04-0.06) that the adjustment is negligible.

“There is an almost linear decrease in fertility from left to right in each row but this is so slight (0.04±0.06) that the adjustment is negligible.”

May combine two claims.

In the hierarchical-t analysis of the top 15 varieties, posterior means are generally shrunk towards 0 relative to the uniform prior, and this shrinkage is pronounced.

“The means are generally shrunk towards 0 in comparison with corresponding values under the uniform prior.This must always happen but here the eect is quite pronounced”

May combine two claims.

Individual 80% credible intervals for P, E and V are (0.29, 1.26), (0.23, 1.26) and (0.04, 1.01), with simultaneous intervals (0.09, 1.45), (0.02, 1.48) and (-0.16, 1.21).

“Individual 80% credible intervals for P, E and V are (0.29, 1.26), (0.23, 1.26) and (0.04, 1.01) respectively, with corresponding simultaneous intervals (0.09, 1.45), (0.02, 1.48) and (À0:16, 1.21)”

May combine two claims.

The corresponding hierarchical-t analysis rates P best, with V, G and E tying for second, though P is the only variety whose lower 10% point is positive.

“The corresponding hierarchical-t analysis provides some compensation, so that P is rated best, with V, G and E tying for second, though P is the only variety whose lower 10% point is positive.”

May combine two claims.

The corresponding precisions are comparable in the two morning-glory fields, but anisotropy parameters differ considerably, with means 0.74 on the left and 0.39 on the right.

“The corresponding precisions are comparable in the two ®elds but the anisotropy parameters dier considerably, with means 0.74 (left) and 0.39 (right).”

• AssumptionThe authors state this as an assumption: In the morning-glory model, plants produce seeds independently given the centred effects and plot fertilities.
• AssumptionThe authors state this as an assumption: The morning-glory model postulates that seed-production probabilities follow a logistic form with additive centred effects and plot fertilities.

May combine two claims.

In separate Bayesian analyses of the six corn trials, the posterior mean asymmetry parameter varies between 0.3 and 0.8, except in county 4 where the mode is close to 0, corresponding to independent column adjustment.

“The posterior mean for the asymmetry parameter varies between 0.3 and 0.8, except in county 4, where the mode is close to 0, corresponding to independent column adjustment.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Limited experience suggests that the continuum formulation is effectively equivalent to the formulation based on Gaussian random walks.

“Limited experience with this formulation suggests that it is eectively equivalent to that based on Gaussian random walks.”

Probably not a substantial claim: may not pass S3 (load-bearing).

For the data in Section 3, the continuum formulation is effectively equivalent to the Gaussian random walk formulation.

“For example, this holds for the data in Section 3.”

May combine two claims.

Posterior fertility means in the morning-glory analysis show a very strong spatial pattern, with seed-production probability ranging from about 0.1 to 0.9 over the layout.

“The posterior fertility means in the lower panel of Fig. 3 show a very strong spatial pattern, as expected, with the probability of seed production ranging from about 0.1 to 0.9 over the layout.”

• AssumptionThe authors state this as an assumption: In the morning-glory model, plants produce seeds independently given the centred effects and plot fertilities.
• AssumptionThe authors state this as an assumption: The morning-glory model postulates that seed-production probabilities follow a logistic form with additive centred effects and plot fertilities.

May combine two claims.

In county 4 of the corn trials, the geostatistical analysis estimates a very small range of dependence, so fertility corresponds closely to yield and is rather noisy.

“In the geostatistical analysis, the estimated range of dependence is very small, so fertility corresponds closely to yield and is rather noisy.”

May combine two claims.

Shading from a hedge severely delayed crop production in the strawberry trial, making a simple analysis inappropriate.

“As is evident, shading from a hedge severely delayed crop production in its vicinity, so a simple analysis is inappropriate”

May combine two claims.

The variety effects from the Bayesian and geostatistical analyses of the corn trials are very similar, but those from the incomplete-block analysis differ substantially in places.

“The variety eects for the Bayesian and geostatistical analyses are very similar but those for the incomplete-block analysis dier substantially in places.”

May combine two claims.

There is no evidence that colour intensity or seed pool has any effect on whether morning-glory plants produce seeds.

“There is no evidence of main eects, either in Fig. 4 or more formally.”

• Also stated in: § 5.1. Results · plain

  “Thus, we ®nd no evidence that colour intensity or seed pool have any eect in whether plants produce seeds.”

• AssumptionThe authors state this as an assumption: In the morning-glory model, plants produce seeds independently given the centred effects and plot fertilities.
• AssumptionRests on an assumption: Morning-glory plants are susceptible to competition through overtopping, but competition is not an issue at the spacing used in this experiment.
• AssumptionThe authors state this as an assumption: The morning-glory model postulates that seed-production probabilities follow a logistic form with additive centred effects and plot fertilities.

May combine two claims.

Because the combined analysis adjusts each variety effect towards a common combined value, the posterior distribution for each variety effect is shifted slightly left and that for each interaction slightly right.

“However, since the combined analysis adjusts each variety eect t k towards a common combined value k , the posterior distribution for each y is shifted slightly to the left and that for each slightly to the right.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Figs 13(a) and 13(b) indicate a directionally dependent effect for county 1, but Figs 13(c) and 13(d) show no corresponding effect for county 4.

“Figs 13(a) and 13(b) indicate a directionally dependent eect for county 1, but from Figs 13(c) and 13(d) there is no sign of any corresponding eect for county 4, which is very surprising in view of the results in the paper.”

May combine two claims.

In the second North Carolina trial, each of two varieties has its largest yield roughly three times its smallest, with large yields on end plots.

“In the second North Carolina trial, each of two varieties has its largest yield equal to roughly three times its smallest, with the large yields on end plots.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The prior distributions for the degrees of freedom of t-distributions for residual errors and fertility are among the more elaborate features of the authors' models.

“The prior distributions for the degrees of freedom of t-distributions for residual errors and fertility comprise one of the more `elaborate' features of the authors' models.”

May combine two claims.

The North Carolina trial design is a triple lattice but also has a missing piece in one corner.

“The design is a triple lattice (Cochran and Cox (1957), section 10.22) in the sense of Yates (1937), p. 87, but it is also a jigsaw puzzle design, in the sense of Hamleys of Regent Street's Christmas oers, 1998 Ð `complete' with the deliberately missing piece in one corner!”

• cites Cochran and Cox (1957)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Yates (1937)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims. The quote only partly states this claim.

In the El Batán trial, the varieties appear in numerical order in block 1, which suggests that block may not have been randomized.

“In Table 1, giving yields for the El Bata n trial, the varieties appear in numerical order for block 1,”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The standard errors of treatment differences in the strawberry experiment lie in the range (0.53, 0.59), which is marginally better than with the Bayesian analysis presented.

“Also, the standard errors of treatment dierences lie in the range (0.53, 0.59), which is marginally better than with the Bayesian analysis presented.”

May combine two claims.

In the winter wheat trial, credible interval widths vary by a factor of 2 in one analysis, while those in (c) are almost constant.

“However, the widths of the corresponding credible intervals dier from one another by a factor of 2, whereas those in (c) are nearly constant.”

May combine two claims.

With stationary autoregressions, large neighbourhoods are needed but many unexplained structures remain, suggesting non-stationary behaviour.

“With stationary autoregressions we need large neighbourhoods but we still ®nd many unexplained structures in the data, which suggest various kinds of non-stationary behaviour; see KuÈ nsch (1982).”

• cites Künsch (1982)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The El Batán trial used complete blocks of 50 plots.

“The El Bata n trial used complete blocks of 50 plots, even though 50 is evidently too large for the assumption of within-block homogeneity.”

May combine two claims.

In the winter wheat trial, analysis (b) shows negligible shrinkage of variety effects, as the data offer no support for it.

“Note that the shrinkage of the variety eects in (b) is negligible because there is no support for it in the data.”

May combine two claims.

A simple hierarchical-t analysis of the data suggests perhaps three breaks in fertility but no outliers and produces an average posterior standard deviation of variety differences marginally less than the corresponding standard errors in Gilmour et al. (1997).

“A simple hierarchical-t analysis of the data suggests perhaps three breaks in fertility but no outliers and produces an average posterior standard deviation of variety dierences that is marginally less than the corresponding standard errors in Gilmour et al. (1997).”

• cites Gilmour et al., 1997 sourceNot checked — no full text of the source

May combine two claims.

Among the simulations, the visible evidence for non-stationarity is not clear, and for ρ=0.95 there is not much evidence for directional dependence despite strong directionality in the model.

“Among the simulations, the visible evidence for non-stationarity is not at all clear, and for 0:95 in Figs 13(k) and 13(l) there is not much evidence for directional dependence either, despite the strong directionality in the model.”

May combine two claims.

A uniform variety prior yields a defective overall posterior, though variety contrasts generally have a proper distribution.

“Indeed, the uniform variety prior, which we again emphasize was used purely for numerical comparison, produces a defective overall posterior but in general a proper distribution for variety contrasts.”

May combine two claims.

Fig. 5's fertility map indicates that the aberrant row in county 2 is absorbed and that variety effect estimates are largely unaffected.

“The fertility map in Fig. 5 suggests that the aberration is successfully absorbed and that the estimates of variety eects are not much aected.”

May combine two claims.

For intrinsic autoregression (2.5)-(2.6), the true variogram grows roughly logarithmically with distance, matching empirical findings of Fairfield Smith (1938) and Pearce (1976).

“Note that, for the intrinsic autoregression (2.5)±(2.6) in Smith's simulations, the true variogram increases approximately as the logarithm of distance (Besag, 1981;Besag and Kooperberg, 1995), which is in close agreement with the empirical results claimed by Fair®eld Smith (1938) and Pearce (1976).”

• cites Besag, 1981 sourceNot checked — no full text of the source
• cites Besag and Kooperberg, 1995 sourceNot checked — no full text of the source
• cites Fairfield Smith (1938)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Posterior expected loss is about 8% for variety 4 in the El Batán trial; in the spring barley trial, it is about 1% for variety 7 and under 10% for eight others.

“Thus, in the El Bata n trial, the posterior expected loss for variety 4 is about 8%, whereas, in the spring barley trial discussed earlier in the reply, it is about 1% for variety 7 and less than about 10% for eight other varieties.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

Using Bayesian methods makes the interpretation of results simpler, particularly for ranking and selection.

“Adoption of the Bayesian paradigm simpli®es the interpretation of the results, especially in ranking and selection.”

Probably not a substantial claim: may not pass S4 (based).

Complex model formulations can be analysed relatively easily with Markov chain Monte Carlo methods.

“Also, complex formulations can be analysed with comparative ease, by using Markov chain Monte Carlo methods.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Such random walks epitomize non-stationarity in the prior distributions and were first adopted by Besag and Kempton (1986) in frequentist spatial analysis.

“Such random walks epitomize the non-stationarity in our prior distributions and were ®rst adopted by Besag and Kempton (1986) in frequentist spatial analysis.”

• cites Besag and Kempton, 1986 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

If random samples of sizes n and 3n are taken from two independent N(0, sigma) populations, the probability that the n-sample mean is larger in magnitude is 2/3.

“If random samples of sizes n and 3n are taken from two independent N0, populations, there is probability 2 3 that the n-sample mean will be the larger in magnitude.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

For hierarchical-t random walks, blocking ω and λ provides a significant computational improvement.

“Blocking of ! and again provides a signi®cant improvement computationally”

May combine two claims.

As the asymmetry parameter tends to its extremal values, the model yields random walks along rows or columns, which are used for one-dimensional fertility adjustment.

“Also, as the asymmetry parameter P 0, 1 tends to each of its extremal values, we obtain random walks along the rows or along the columns of the trial and these we employ for one-dimensional fertility adjustment.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Information distributed about the corn trials includes the statement that growers are cautioned against making varietal selection decisions based on an individual location in any one year.

“The information distributed about such trials includes the statement `Growers are cautioned against making varietal selection decisions based on an individual location in any one year' (Bowman, 1995).”

• cites Bowman, 1995Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

In either column random walk or locally quadratic fertility modelling, there is a danger of spurious overfitting to some columns because each column has few observations; this danger does not occur with the first-order two-dimensional fertility model.

“In either case, there is the danger of spurious over®tting to some columns, since the number of observations in each is so small.This danger does not occur with the ®rst-order two-dimensional fertility model.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The four-neighbour Gaussian intrinsic autoregression adopted as the base-line representation of two-dimensional fertility variation involves two unknown parameters controlling scale and lateral asymmetry.

“Thus, we have adopted a four-neighbour Gaussian intrinsic autoregression as our base-line representation of two-dimensional variation in fertility.This particular choice involves two unknown parameters, controlling scale and lateral asymmetry”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Continuum models are self-consistent as plot size varies.

“Of course, the main attraction of continuum models is that they are self-consistent as plot size varies.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The conclusion of no main effects in the morning-glory experiment would be strengthened if the uniform treatment prior were replaced by a Gaussian distribution.

“Our conclusion would only be strengthened if the uniform treatment prior were to be replaced by a Gaussian distribution.”

• AssumptionThe authors state this as an assumption: In the morning-glory model, plants produce seeds independently given the centred effects and plot fertilities.
• AssumptionRests on an assumption: Morning-glory plants are susceptible to competition through overtopping, but competition is not an issue at the spacing used in this experiment.
• AssumptionThe authors state this as an assumption: The morning-glory model postulates that seed-production probabilities follow a logistic form with additive centred effects and plot fertilities.

May combine two claims.

The four-neighbour Gaussian intrinsic autoregression has dual interpretations as a limiting version of a first-order stationary Gaussian conditional autoregression and as locally planar stochastic interpolation.

“and has dual interpretations, both as a limiting version of a ®rst-order stationary Gaussian (conditional) autoregression (Besag, 1974) and as locally planar stochastic interpolation.”

• cites Besag, 1974 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The order of updating λ_y and β is crucial.

“Note that here the order of updating y and is crucial.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The geostatistical formulation does not allow for uncertainty in estimating the parameters in expression (6.1), though this could be corrected in a fully Bayesian analysis.

“Finally, note that the geostatistical formulation does not allow for uncertainty in estimating the parameters in expression (6.1), though this could be corrected in a corresponding fully Bayesian analysis (Diggle et al., 1998).”

• cites Diggle et al., 1998Not checked — no full text of the source

May combine two claims.

The authors considered such differencing unsuitable in a prior distribution because it absorbs arbitrary row and column effects and is therefore highly degenerate.

“There, we considered such dierencing unsuitable in a prior distribution because it absorbs arbitrary row and column eects and is therefore highly degenerate.”

May combine two claims.

t-distributions provide an exception to the usual posterior complications, allowing a simple Gibbs sampler.

“Although non-Gaussian components in the prior and in the likelihood generally lead to complications in the posterior that are best handled via Hastings rather than Gibbs steps, t-distributions provide an exception.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Gilmour et al. (1997) reached an analogous frequentist conclusion that double differencing is inefficient because it loses too many degrees of freedom.

“Gilmour et al. (1997) reached an analogous frequentist conclusion that double dierencing is inecient because it loses too many degrees of freedom.”

• cites Gilmour et al., 1997 sourceNot checked — no full text of the source

May combine two claims.

In a Gaussian formulation, a few anomalies spread uncertainty among all effects, whereas the t-formulation anticipates occasional aberrations.

“In a Gaussian formulation, the existence of a few anomalies spreads uncertainty among all eects, whereas the t-formulation anticipates occasional aberrations.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The resulting analysis is closely related to frequentist methods developed by Cullis and Gleeson (1991) and investigated empirically by Kempton et al. (1994).

“The resulting analysis has close ties with the frequentist methods developed by Cullis and Gleeson (1991) and investigated empirically by Kempton et al. (1994).”

• cites Cullis and Gleeson (1991) sourceNot checked — no full text of the source
• cites Kempton et al. (1994) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The order of updating ω and λ is again important.

“so that order is again important.”

May combine two claims.

When ρ equals 1, the model yields independent random walks along the columns, and when ρ equals 0, along the rows.

“When 1 in equation (2.5), we obtain a set of independent random walks along the columns of the array, each with an N0, 1= increment distribution, and similarly along the rows if 0.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The device of adding layers can also be applied to non-Gaussian formulations for fertility.

“The device of adding layers can also be applied to non-Gaussian formulations for but, in the Gaussian case, there are simpli®cations in the evaluation of the eigenvalues of W that can be used to speed up the computations and hence introduce a continuous prior for ; see Section 2.5.”

May combine two claims.

In natural populations of morning-glory in south-eastern USA, the W-locus is generally polymorphic, with at least two pigment intensities present and white allele frequency typically below 40%.

“In natural populations in south-eastern USA, the W-locus is generally polymorphic, so at least two of the pigment intensities are present, with the frequency of the white allele being typically less than 40% (Epperson and Clegg, 1988).”

• cites Epperson and Clegg, 1988 sourceNot checked — no full text of the source

May combine two claims.

The papers on lattice-based fertility models all support parsimony but differ in their detailed conclusions; the first two favour differencing and non-stationarity, while the third promotes the stationary AR(1) x AR(1) process.

“The papers all support parsimony, with which we concur, but dier in their detailed conclusions.Thus, the ®rst two favour dierencing as a component and hence non-stationarity but the third promotes the (stationary) AR(1) Â AR(1) or doubly geometric process”

• cites Martin, 1979Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Martin, 1990 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Unusually small posterior means of ω_ij suggest the locations of fertility jumps.

“also !ij s with unusually small posterior means suggest the locations of fertility jumps.”

Probably not a substantial claim: may not pass S3 (load-bearing).

For locally quadratic interpolation, restricting the infinite lattice process to a q1 by q2 array is straightforward.

“Curiously, the restriction of the in®nite lattice process to a q 1 Â q 2 array is now straightforward, with j G exp”

May combine two claims.

For variety 20, the most notable change under the t-analysis is an increase in the width of its credible interval, which indicates model uncertainty.

“but the most notable change is the increase in the width of its credible interval, which is an indication of model uncertainty.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Blocking with λ_y can yield a significant computational improvement.

“Moreover, a signi®cant computational improvement can be made by blocking with y , as below.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The larger standard errors for the incomplete-block analyses may reflect the strong row orientation of the blocks.

“The standard errors for the incomplete-block analyses are noticeably larger and this may re¯ect the strong row orientation of the blocks.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In the spatial mixture model for El Batán, the prior probability that two plots are allocated to the same component decreases as they become further apart.

“Within each column, the use of a limiting case of a logistic autonormal multinomial allocation scheme, controlled by a smoothing parameter h > 0, ensures that the prior probability that two plots are allocated to the same component decreases as they become further”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In well-designed experiments, the benefits of Bayesian analysis will be reduced and may disappear completely.

“Presumably in welldesigned experiments the bene®ts of the Bayesian analysis will be reduced and may disappear completely.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

In hierarchical modelling, the data may carry little information about hyperparameters, so the usual assumption that prior input is swamped by the data likelihood may be unjustified.

“Unfortunately, it is quite possible that the data will carry little information about such hyperparameters and the usual assumption that the prior input will be swamped by the data likelihood may be unjusti®ed.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Wavelet methods would allow the priors in Section 2.3 to be generalized to allow for intermittent effects.

“Wavelet methods would allow the priors in Section 2.3 of the paper to be generalized, to allow for such intermittent eects; for some discussion of the range of possible behaviour of functions generated from priors over wavelet coecients see, for example, Abramovich et al. (1998).”

• cites Abramovich et al. (1998) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

If Z1 and Z2 are independent white noises on Z2, then conditionally on the sums over all loops being zero, they have the same second moments as the increments of a first-order intrinsic autoregression.

“This is indeed true: if Z 1 and Z 2 are two independent white noises on Z 2 , then, conditionally on the sums over all loops being 0, Z 1 , Z 2 has the same second moments as the increments of a ®rst-order intrinsic autoregression.”

• cites Priestley (1981)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The vast majority of intrinsic autoregressions do not suffer from severe degeneracy, including the one proposed, which has a single desirable rank deficiency producing non-stationarity.

“However, the vast majority of intrinsic autoregressions do not suer from severe degeneracy and this includes the one that we propose, with its single (desirable) de®ciency in rank producing non-stationarity, as in one-dimensional dierencing.”

May combine two claims.

Intrinsic autoregressions serve as limiting cases of stationary models and can be interpreted as local smoothers.

“These are not only the limiting forms of corresponding stationary models but also have an interpretation as local smoothers, as noted by Ferna ndez and Green.”

• cites Fernández and GreenNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Repeated ploughing over a very long period would reduce local variations in fertility.

“One might expect that repeated ploughing over a very long period would reduce the local variations in fertility.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The practical simplicity of Fisher's scheme of design and analysis of agricultural field experiments was quickly appreciated worldwide.

“It is a historical fact that the practical simplicity of Fisher's scheme of design and analysis of agricultural ®eld experiments was quickly appreciated worldwide.”

Probably not a substantial claim: may not pass S3 (load-bearing).

On the basis of the Wiener process assumption, Jones could make a considerable reduction in the errors in contrasts.

“On the basis of this assumption Jones could make a considerable reduction in the errors in contrasts.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

50 plots is too large for the assumption of within-block homogeneity.

“The El Bata n trial used complete blocks of 50 plots, even though 50 is evidently too large for the assumption of within-block homogeneity.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

Bean yields were affected by worms in the soil whose breeding habits suggested that fertility along a row could be represented by a Wiener process with positive autocorrelation.

“It was known that the bean yields were aected by worms in the soil whose breeding habits suggested that fertility along a row could reasonably be represented by a Wiener process with positive autocorrelation.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Fisher's simplicity was linked with his identification of the analysis with the design.

“This simplicity was linked with Fisher's identi®cation of the analysis with the design.”

Probably not a substantial claim: may not pass S3 (load-bearing).

A random walk is represented by a linear graph with no constraints.

“Note that a random walk corresponds to a linear graph and the absence of any constraints.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Dr A. E. Jones studied fertility variations of rows of bean plants at Rothamsted.

“Dr A. E.Jones, who was killed in a lift accident in 1948, studied fertility variations of rows of bean plants at Rothamsted.”

May combine two claims.

Traditional analysis of covariance requires a regression coefficient below 1; its adjustment is attenuated and resembles stationarity rather than being strictly local.

“Note that, in the traditional analysis of covariance, the regression coecient must be less than 1 and the corresponding adjustment is not strictly local as claimed by Pearce (1998) and here in the discussion but is attenuated and more akin to that obtained under stationarity.”

• cites Pearce (1998) sourceNot checked — no full text of the source

May combine two claims.

A Gaussian prior for variety effects makes Bayesian analysis non-additive; its shrinkage produces near-perfect results that do not generalize.

“However, Bayesian analysis, with a Gaussian prior for variety eects, is non-additive and shrinkage will produce results that are close to perfect but that do not generalize.”

May combine two claims.

The variogram results probably support the use of a non-stationary model, but the evidence is not strong.

“If these results show anything, they probably support the use of a non-stationary model, but the Downloaded from https://academic.oup.com/jrsssb/article/61/4/691/7083194 by guest on 19 December 2023 evidence is not strong.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

Practitioners are reluctant to implement either new designs or new methods of analysis.

“In my experience, practitioners are reluctant to implement either new designs or new methods of analysis.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Attention to short-range soil variation has grown considerably since field experimentation extended to regions such as Australia and North America, where land has been under plough for shorter periods than at Rothamsted.

“I think that it is true that attention to short-range soil variation has grown considerably since ®eld experimentation has been extended to regions such as Australia and much of North America, where the land involved has been under the plough for much shorter periods than the land at Rothamsted.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Null results in small samples sometimes misled an experimenter into believing that no real effects existed.

“In particular, `null' results in small samples sometimes misled an experimenter into believing that no real eects existed.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Fertility is intrinsically an intermittent phenomenon.

“Fertility is intrinsically an intermittent phenomenon.”

• AssumptionThe authors state this as an assumption: Fertility is intrinsically an intermittent phenomenon.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Bayesians who claim that their approach covers all inference ignore the rejection of their approach by many scientists and philosophers.

“Bayesians who claim that their approach covers all inference ignore the rejection of their approach by many scientists and philosophers (see, for example, Mayo (1996)).”

• cites Mayo (1996) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The spatial mixture methodology is directly applicable to arbitrary graphs.

“Although here we apply a one-dimensional adjustment, our methodology is directly applicable to arbitrary graphs.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

The choice of hyperpriors is rather arbitrary and the rescaling of the data is inelegant, though neither has produced practical problems in analyses of many data sets.

“Among many other topics given scant attention, we note the rather arbitrary choice of hyperpriors and the inelegant rescaling of the data, though neither has produced any practical problems in the analysis of many dierent data sets, so far as we know.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The result can be extended so that non-zero ωij values may differ.

“An obvious extension permits the non-zero !ij s to be unequal.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Replacing the squares in equation (2.4) by a Huber function can preserve sharp edges without increasing computational difficulty too much.

“In KuÈ nsch (1994) I also showed that replacing the squares in equation (2.4) by a Huber function can preserve sharp edges without increasing the computational diculty too much.”

• cites Künsch (1994)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

In one dimension, a first-order intrinsic autoregression means that the first differences are white noise.

“For instance, in one dimension, a ®rst-order intrinsic autoregression simply means that the ®rst dierences are white noise.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Using t increments preserves a useful Gaussian interpretation for any specified degrees of freedom.

“In fact, the switch to t increments retains a useful Gaussian interpretation for any given , as noted in Section 2.5.”

May combine two claims.

The authors' approach already incorporates some model uncertainty, both in the basic formulation where values close to extremes produce essentially one-dimensional adjustment, and in the hierarchical-t representation through variation in degrees of freedom.

“However, our approach already incorporates some model uncertainty, both in the basic formulation (2.8), where values of close to its extremes produce essentially one-dimensional adjustment, and in the hierarchical-t representation, through variation in the degrees of freedom.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

Randomization has some problems for frequentists, notably in small samples, but its role for a Bayesian is much less clear.

“Randomization has some problems for frequentists, notably in small samples, but its role for a Bayesian is much less clear.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Errors in copying and arithmetic are all too frequent in agricultural and horticultural trial data.

“Errors in copying and in arithmetic are all too frequent.”

Probably not a substantial claim: may not pass S2 (checkable).

It is extremely difficult to find simple models that give a good fit to uniformity trials.

“Finally, I would like to con®rm that it is extremely dicult to ®nd simple models which give a good ®t to uniformity trials.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In other areas of statistical research where stochastic processes are used, likelihood-based methods of inference for non-location parameters do not always perform well.

“Certainly, in other areas of statistical research where stochastic processes are used, likelihood-based methods of inference for non-location parameters do not always perform well.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Even with Bayesian analysis, a well-designed experiment will still perform better than a badly designed experiment.

“However, even with the Bayesian analysis, a well-designed experiment will still perform better than a badly designed experiment.”

May combine two claims.

Direct variogram fitting lacks an explicit class of allowable functions, and invalid choices sometimes occur.

“In direct ®tting, which is often employed for geological data, the class of allowable variogram functions is not known explicitly and sometimes an invalid choice is made, as discussed by Gneiting (1996).”

• cites Gneiting (1996)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

A benefit of spatial analysis is that special-purpose design criteria affect its efficiency less.

“One advantage of spatial analysis is that its eciency is less aected by special purpose design criteria.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Because the analysis is non-additive, its results do not generalize.

“Such examples were omitted from the paper because they are somewhat ambiguous: the Gaussian prior for variety eects provides desirable shrinkage, also advocated by Patterson in his contribution, but the non-additivity of the analysis implies that the results do not generalize.”