Fundamentals of rice crop science

THE best adjective to describe this work is \"sweep11 ing.\" The range of subject matter is so broad that it can almost be described as containing everything except fuzzy set theory. Included are explicit discussions of the basics of probability (relegated to an appendix); the practice of problem solving; testing hypotheses about statistical parameters; calculating and interpreting confidence limits; tolerance limits and prediction limits; setting up and interpreting control charts; design of experiments; analysis of variance; line and surface fitting; and maximum likelihood procedures. If you can think of something that is not in this list, then it probably means I have overlooked it.

Experiments: Planning, Analysis, and Parameter Design Optimization

In recent years developments in plant phenomic approaches and facilities have gradually caught up with genomic approaches. An opportunity lies ahead to dissect complex, quantitative traits when both genotype and phenotype can be assessed at a high level of detail. This is especially true for the study of natural variation in photosynthetic efficiency, for which forward genetics studies have yielded only a little progress in our understanding of the genetic layout of the trait. High-throughput phenotyping, primarily from chlorophyll fluorescence imaging, should help to dissect the genetics of photosynthesis at the different levels of both plant physiology and development. Specific emphasis should be directed towards understanding the acclimation of the photosynthetic machinery in fluctuating environments, which may be crucial for the identification of genetic variation for relevant traits in food crops. Facilities should preferably be designed to accommodate phenotyping of photosynthesis-related traits in such environments. The use of forward genetics to study the genetic architecture of photosynthesis is likely to lead to the discovery of novel traits and/or genes that may be targeted in breeding or bio-engineering approaches to improve crop photosynthetic efficiency. In the near future, big data approaches will play a pivotal role in data processing and streamlining the phenotype-to-gene identification pipeline.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/tpj.14190

Converging phenomics and genomics to study natural variation in plant photosynthetic efficiency.

Summary One attractive feature of optimum design criteria, such as D- and A-optimality, is that they are directly related to statistically interpretable properties of the designs that are obtained, such as minimizing the volume of a joint confidence region for the parameters However, the assumed relationships with inferential procedures are valid only if the variance of experimental units is assumed to be known If the variance is estimated, then the properties of the inferences depend also on the number of degrees of freedom that are available for estimating the error variance Modified optimality criteria are defined, which correctly reflect the utility of designs with respect to some common types of inference For fractional factorial and response surface experiments, the designs that are obtained are quite different from those which are optimal under the standard criteria, with many more replicate points required to estimate error The optimality of these designs assumes that inference is the only purpose of running the experiment, but in practice interpretation of the point estimates of parameters and checking for lack of fit of the treatment model assumed are also usually important Thus, a compromise between the new criteria and others is likely to be more relevant to many practical situations Compound criteria are developed, which take account of multiple objectives, and are applied to fractional factorial and response surface experiments The resulting designs are more similar to standard designs but still have sufficient residual degrees of freedom to allow effective inferences to be carried out The new procedures developed are applied to three experiments from the food industry to see how the designs used could have been improved and to several illustrative examples The design optimization is implemented through a simple exchange algorithm

Optimum design of experiments for statistical inference

Summary. Two simple pilot procedures are proposed for avoiding the problem of dealing with a disconnected experimental design. Both procedures should be carried out on the selected design before any experimentation is considered. The first procedure is a check that the suggested design is connected with respect to treatments. This makes use of the information matrix for the model and provides feed-back on a disconnected design. The second procedure specifies which observations are influential in causing a connected design to become disconnected, with respect to any set of parameter effects, if these observations are lost during the experimental period. This specification is found by examining the projection matrix for the model. These pilot procedures are illustrated by several examples.

Simple pilot procedures for the avoidance of disconnected experimental designs

Statistical designs for two-color microarray experiments involving technical replication

Due to the lack of a replication-based estimate for the experimental error variance, unreplicated orthogonal main-effect plans (OMEPs) usually appear to be unsatisfactory in screening active factors, when there are certain interactions likely to be non-negligible. In this study, partially replicated designs constructed through two-level orthogonal arrays are recommended to compensate for this deficiency. A compound criterion called the extended minimum aberration (EMA) is proposed for choosing the twice-replicated fractions. According to the EMA criterion, sufficient conditions for constructing the minimal two-level OMEPs with partial replication are proposed, and a series of EMA designs with practical run-sizes is provided for practical applications. The Canadian Journal of Statistics 42: 168–183; 2014 © 2014 Statistical Society of Canada

Selection of partial replication on two‐level orthogonal arrays

Minimum breakdown designs in blocks of size two

Two-color cDNA or oligonucleotide-based spotted microarrays have been commonly used in measuring the expression levels of thousands of genes simultaneously. To realize the immense potential of this powerful new technology, budgeted within limited resources or other constraints, practical designs with high efficiencies are in demand. In this study, we address the design issue concerning the arrangement of the mRNA samples labeled with fluorescent dyes and hybridized on the slides. A normalization model is proposed to characterize major sources of systematic variation in a two-color microarray experiment. This normalization model establishes a connection between designs for two-color microarray experiments with a particular class of classical row-column designs. A heuristic algorithm for constructing A-optimal or highly efficient designs is provided. Statistical optimality results are found for some of the designs generated from the algorithm. It is believed that the constructed designs are the best or very close to the best possible for estimating the relative gene expression levels among the mRNA samples of interest.

Statistical designs for two-color spotted microarray experiments.

When designing a two-level factorial experiment, a cost-effective com- promise for obtaining a replication-based estimate of the error variance is to con- duct a partial replication on unreplicated designs. In this article, based on the D-optimality criterion, we focus on selecting a partial replication from the orthog- onal designs derived from Hadamard matrices. It is shown that the augmented designs, composed of the chosen partial replication and the orthogonal designs, are highly efficient. We obtain (i) sufficient conditions for the augmented designs to be D-optimal over their corresponding classes; (ii) a construction method for the desired designs.

/pdf/d-optimal-partially-replicated-two-level-factorial-designs-1dsqgupaea.pdf

Shin-Fu Tsai

Papers

Statistical designs for two-color microarray experiments involving technical replication

Selection of partial replication on two‐level orthogonal arrays

Minimum breakdown designs in blocks of size two

Statistical designs for two-color spotted microarray experiments.

D-optimal partially replicated two-level factorial designs