Presentation Titles, Abstracts and Slides

References

Breiman, L. (1996) Bagging predictors. Machine Learning.

Efron, B. (2014) Estimation and accuracy after model selection. Journal of the American Statistical Association.

Kabaila, P. and Wijethunga, C. (2019) Confidence intervals centred on bootstrap smoothed estimators. Australian & New Zealand Journal of Statistics.

Kabaila, P. and Wijethunga, C. (2019) On confidence intervals centred on bootstrap smoothed estimators. Stat.

As an alternative to this, an individual genetic variance structure for each of the factors can be fitted, resulting in a separable variance model. This may be a more parsimonious approach to modelling the genetic variance due to estimation of fewer parameters in total, and could provide a more intuitive interpretation of genotype behaviour across environment types. However, separable models have been shown to be less flexible, as they impose more restrictive variance structures.

A set of nematode resistance field trials motivated the exploration of separable variance models, where final nematode counts for each genotype were measured under three different soil depths, two previous nematode population densities resulting from prior crops and three trials. The analysis was first conducted using an overall environment model, where each environment represented a unique combination of soil depth, nematode population and trial. This model showed consistently high genetic correlations between all pairs of environments. The analysis was then performed using a separable genetic variance structure for the three-way factorial. There were substantial differences in the genetic variances and correlations that resulted from the different parameterisation of both models.

In this study, we conducted 6 field trials from 2011 to 2018 in South Australia and Victoria with the objective of providing tolerance ratings of 92 different cereal varieties under high and low levels of pre-established nematode densities in the field. Multi environment trial analyses were used to analyse the data where the term environment refers to each year by location by nematode density combination. Spatial techniques were used to account for the spatial variability in each trial and a factor analytic model was fitted to model the genotype by environment interaction effects.

Multi environment trial analyses revealed high genetic correlation between high and low environments for each of the trials. This indicates that selecting varieties under high levels of CCN is equivalent to select varieties under low levels and thus analogous to select high yielding varieties irrespective of the nematode density. Therefore, a measure to assess the performance of varieties under high levels of nematodes independently of their performance under low levels was defined and named “tolerance index”.

Multi environment trial analyses together with the tolerance index allowed us to select for high yielding varieties as well as give a more useful information to growers in relation to the comparison of varieties between high and low levels of CCN. The definition of the tolerance index and results obtained from this set of trials will be presented in this talk.

A recent publication (Forknall et al. (2019), Phytopathology) describes a method for the statistically robust design and analysis of a single field experiment to quantify the rate of change in yield per unit increase in pathogen burden of five wheat cultivars for the disease crown rot. Using a random regression approach, implemented in a linear mixed model (LMM) framework, response curves describing the relationship between yield and crown rot pathogen burden were estimated for each of the cultivars in the experiment.

This methodology is now extended to an across trials random regression approach, implemented in an LMM framework, which enables the estimation of different response curves for each cultivar in each experiment, where the response of each cultivar is modelled around an overall (average) yield response profile for each experiment. This modelling approach also provides a means of capturing the genetic correlation (covariance) between model parameters, both within and between experiments.

The model is demonstrated by an application to 15 field experiments, estimating the yield response of the same set of five wheat cultivars to crown rot. The analysis revealed variation in the rate of change in yield, or tolerance, of cultivars across experiments, identifying that the tolerance of some cultivars was more influenced by environmental conditions than others. Also presented are graphical tools to assist in unlocking the interaction between cultivars tolerance and environmental conditions.

A fixed effects combined trial analysis for yield response to plant population in a linear mixed model framework is presented. Clustering of the treatments (e.g. hybrid and environment combinations) is performed such that parallel curves are fitted to treatments within the same cluster to i) simplify the interaction and ii) increase the information used for fitting each response function by combining data across treatments within the same cluster. The categorisation of treatments to clusters is considered adequate when there is no significant interaction effect between plant population and treatment within each cluster. This presentation will focus on an objective method for categorising treatments into clusters. Furthermore, a sensitivity analysis will be presented to explore the adequacy of the proposed clustering methodology.

The methodology is applied to a large set of sorghum trials implemented across New South Wales, Australia in two seasons consisting of different hybrids, row spacings and trial locations. Furthermore, it provides a general framework for a fixed effects regression analysis in a linear mixed model framework that can account for i) experimental design terms, ii) separate residual variances and iii) spatial field trend at each trial.

Yoon & Welsh (2019) studied the effect of ignoring clustering in $x$ on fitting LMM, and showed that it can be obtained misleading assessments of both the association between $y$ and $x$ and of the variance components. They also showed that, as the within cluster variance of $x$, $\tau_x$, increases, the likelihood and the REML criterion develop two distinct local maxima and which of these is the global maximum changes at the jump point.

In LMMs for clustered or hierarchical structured data, regressors can be correlated with random effects. When the random effects and regressors independence assumptions are violated, not only regression coefficient estimators but also variance components can be severely biased.

In this study, we investigate how the violation of the random effects and regressors independence assumption could affect on the estimates of parameters and compare the results with the effect of ignoring clustering in $x$ when fitting LMM (Yoon & Welsh). We also extend our study to the case of correlated binary data.

If the shape of the water retention curve is sigmoid, then such data sets can be characterized by several models. The most commonly used model is the van Genuchten model (Soil Sci. Soc. Am. J. 44, 1980, 892-898).

Fitting the van Genuchten model to data sets relating VWC to h involves estimation of four parameters, some of which have a physical significance in understanding soil-water relationships. However typically these data sets only have 8 to 10 (VWC, h) pairs, which leads to difficulty in estimating some of the parameters and, in some cases, the van Genuchten model is difficult to fit.

We fitted the van Genuchten model to VWC vs. h data for 35 water retention curves from semi-arid rangeland soils and seven vineyard soils from the Yass Valley, NSW. We present examples of these fitted models. Some new parameters were derived from the fitted values, and relationships between the four estimated parameters and these derived parameters are also presented. The results from this study show that

(i) On some occasions the van Genuchten model fits poorly or doesn’t fit, so is inappropriate;
(ii) There are strong relationships between some of the estimated and derived parameters, meaning the model is most likely over-parametrized;
(iii) Alternative models should be used when the VWC vs. h relationship is not a distinct sigmoid shape, for example curvilinear or near linear.

Agronomic evaluation of plants – quantity and quality, fertilisers and herbicides and pest control strategies are achieved through agronomic experiments, usually grown in the field, glasshouse or temperature control rooms. During the past three years staff from SAGI-STH training program have developed and run a series of statistical workshops, using adult learning methodologies, to improve the statistical competency of agronomists who conduct these agronomic experiments. The workshops start with an introduction to R, move through design and then analysis of agronomic experiments and end by introducing these scientists to reproducible research through R markdown. The workshops use active learning strategies and real-world examples relevant to the researchers.

On completion of the workshops, participants are then invited to join our community of practice, where we explore their data and work on solving statistical problems as a team. The community of practice is via online meetings, which are recorded so that participants can join synchronously or asynchronously. In this talk we explore the benefits of these workshops and community of practice and what it has meant in practice to the agronomists.

In this presentation we introduce the indirect method for reference interval calculation, based on secondary analysis of administrative data rather than direct identification of a healthy population leading to reference interval calculation. We’ll describe the statistical and biochemical issues that arise from the indirect approach.

We will also investigate the effect of two methods of outlier removal (Tukey elimination and the block method) and three methods of calculation (parametric, non-parametric and robust) on the indirect intervals obtained. The presentation will be illustrated with a large Australian data set relating to serum immunoglobulin A, G and M for males and females across the entire human age range.

The outlier elimination method was more important in the production of the indirect reference intervals than the calculation method. The Tukey elimination procedure consistently eliminated more values than the block method. If Tukey elimination was applied, variation between intervals produced by the different calculation methods was then minimal. The non-parametric intervals were actually more sensitive to outliers which, for certain assays, led to higher and wider intervals for older age groups. There were only minimal differences between robust and parametric reference intervals.

The interaction between outlier elimination and calculation method will be investigated further, and suggestions made for moving forward with indirect intervals in the diagnostic setting.

Many data analysis methods have been developed for compositional data. They make use of log-ratios of counts, but these are problematic in the presence of many zero counts, as is the case for microbiome. We have developed semiparametric rank methods for compositional microbiome data. The methods do not rely on strong distributional assumptions, avoid log-ratios and account for library size variability. The methods make use of either means, rank or sign statistics. False discovery rate control happens through a new permutation method that accounts for the discreteness of the p-value null distributions. Results from a realistic simulation study suggest that the new methods perfom well and that particularly the sign-based methods perform well for overdispersed microbiome data.

The JPS sampling design is implemented with or without replacement, but the SRS sample is always constructed without replacement. The paper presents design-unbiased estimators for the population mean and total, and the variances of these estimators. The efficiency improvement of the sampling designs compared with the SRS sampling design is investigated. The proposed estimator has a smaller variance than a two-stage SRS sample, but the level of improvement in efficiency depends on the intra-cluster correlation coefficient and the choices of the sampling designs in stage I and II of samplings. The paper also presents an approximate confidence interval for the population mean and total. For a fixed cost, the optimal sample sizes for stage I and stage II samples are constructed by maximizing the information content of the sample. The proposed sampling designs and estimators are applied to a two-stage sampling in an agricultural application.

The new method VIVID utilizes feature importance measures via pairwise feature comparisons to identify significant features. We show how the selected features are repeatedly ranked higher and are more stable than other features. Taking advantage of cluster analysis, we construct a set of nested feature groups and then select an optimal group of features from the candidate models. Different methods of visualisation for this resampled information are presented. The computational speed and requirements of VIVID are discussed and how the method is able to deal with data where the number of features is continually increasing.

Approaches for visualizing uncertainty in spatial and spatio-temporal data will be presented. These include the bivariate choropleth map, map pixelation, glyph rotation and exceedance probability maps. Bivariate choropleth maps explore the “blending” of two colour schemes, one representing the estimate and a second representing the margin of error. The second approach uses map pixelation to convey uncertainty. The third approach uses a glyph to represent uncertainty and is what we refer to as glyph rotation. The final map based exploration of uncertainty is through exceedance probabilities.

Vizumap, is an R package that has been developed within Digiscape for visualising uncertainty in spatial and spatio-temporal data. To illustrate the methods, I use an example from the Great Barrier Reef, where sediment loads were quantified from a Bayesian Hierarchical Model (BHM) that assimilated estimates of sediment concentration and flow with modelled output from a catchment model spanning 21 years of daily outputs and 411 spatial locations.

A common approach to genetic association and QTL mapping is to fit uni-variable linear mixed models testing each marker sequentially for associations with phenotype. Population structure is incorporated in the model and the false positive rate is usually controlled through adjustment of the usual 0.05 alpha level for multiple comparisons.

The major disadvantage of this approach is that it does not provide an adjustment for multiple markers or potential gene-gene interactions. Testing of these additional terms can become problematic due to the substantial increase in the number of associations requiring testing compared to the number of sampled observations (the so-called p >> n scenario).

We present an application of Bayesian variable selection for association mapping, implemented in the R package BayesVarSel. The approach of BayesVarSel employs model averaging to provide measures of association of phenotype with predictors (here genetic markers) across multi-variable models and includes functionality for scenarios where p >> n. Additionally this approach explicitly accounts for multiple markers acting simultaneously on the phenotype. We compare the results obtained from BayesVarSel with the traditional uni-variable mixed model methodology through an application of QTL mapping of resistance to net-form-net-blotch (NFNB) in double haploid populations of barley.

In this work we present an efficient multi-step genome wide association analysis pipeline which incorporates a Bayesian variable selection strategy to identify putative QTL. In the initial step of this pipeline, a genomic prediction is conducted to obtain a complete set of marker effects. These effects are then used with a modification of a popular genome wide binning strategy to dramatically reduce the dimensionality of the marker set. With this reduced set of markers, a Bayesian variable selection is conducted to determine a small subset of markers linked to putative QTL. The complete genome wide analysis pipeline is illustrated with phenotypic and genotypic data obtained from a large Australian wheat panel.

However, the genetic structure of lines may not be the only source of variability when trying to understand an output. In this sense, multienvironmental trials poses a mayor challenge adding an underlaying, complex, correlation structure.

In this work we discuss a two steps genome wide association analysis which makes use of a Bayesian variable selection strategy to determine markers significantly linked to a supposed QTL. The method is illustrated with a large Australian wheat panel.

This approach offers an advance upon assignment software such as GeneClass2, and is biologically more interpretable than plots provided by the widely-used software STRUCTURE. The visualization method makes it straightforward to detect features of population structure and to judge the discriminative power of the genetic data for assigning individuals to source populations.

We also propose new methods for quantifying population genetic structure. The measures we propose are closely related to the visualization approach, and enable visual features obvious from the plots to be expressed more formally. One measure is interloper detection probability: for two random genotypes arising from populations A and B, the probability that the one from A has the better fit to A and thus the genotype from B would be correctly identified as the `interloper' in A. Another measure is correct assignment probability: the probability that a random genotype arising from A would be correctly assigned to A rather than B.

Using permutation tests, we can test two populations for significant population structure. These permutation tests are sensitive to subtle population structure, and are particularly useful for eliciting asymmetric features of the populations being studied, e.g. where one population has undergone extensive genetic drift but the other population has remained large enough to retain greater genetic diversity.

We illustrate these methods using microsatellite genotype data from ship rats and southern right whales, and SNP data from human populations.