A covering array t-CA(n, k, g), of size n, strength t, degree k and order g, is a k X n array on g symbols such that every t X n sub-array contains every t X 1 vector on g symbols at least once as a column. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening and in areas were interactions of multiple parameters are to be tested. Considering the practical limitations like budget and time in testing process, given fixed values of t=4, k, g and n, we aim to construct covering arrays with largest possible coverage measure. We use group construction method in order to construct covering arrays of strength four with very high coverage measure. We also consider the problem of constructing strength three covering arrays on 3-uniform hypergraphs. In these arrays, only specific choices of three distinct parameters interact and these choices are recorded in hypergraph. We construct optimal (balanced) strength three mixed covering array on 3-uniform interval, specific type of 3-uniform hypertree and fan hypergraph.

Breeding companies continuously pursue lower production costs and better crop yield. The release and recommendation of new commercial varieties requires several breeding trials with potential genotypes obtained from crossing of known varieties. At the initial phases of the breeding program there are many genotypes and little material for planting in experiments, which are usually in large fields, depending on the studied crop (sugarcane, soybean, corn, etc.). To cope with this, all the blocks have commercial varieties which are considered as standard and new varieties can appear in more than one block. In this study, a full-sib progeny was obtained from a bi-parental cross between the elite clone IACSP95-3018 (female parent) and the variety IACSP93-3046 (male parent), which were developed by the Sugarcane Breeding Program at the Instituto Agronômico de Campinas (IAC). IACSP95-3018 is a promising clone used in the IAC Sugarcane Breeding Program, whereas IACSP93-3046 has a high level of sucrose, good tillering and an erect stool habit and is recommended for mechanical harvest. The full-sib progeny and the sugarcane varieties RB835486 and SP81-3250, used as checks, were planted in 2011 in the Ribeirão Preto municipality, São Paulo, Brazil, in a randomized complete block design, with three replicates and plots of 2 meter rows spaced 1.5 meter apart. This trial contained 708 plots in a rectangular array with 59 rows and 12 columns. Both parents and two varieties (SP81-3250 and RB835486) were included four times in each replicate as checks and there were 236 crosses that occurred once in each replicate. The aim is to review the theoretical principles related to block designs, the mixed model approach and spatial analysis of experiments.The experiment will be analyzed as a mixture of treatments as fixed effects (control) and others as random effects (new treatments) and will verify if there is spatial dependence and competition between individuals. The field experiment was carried out in 2012 and the response evaluated was plant weight (kg), where each measurement was obtained from a sample of 10 stalks harvested from each individual plot, according to the methods described in Consecana (2006), for both sugar cane and other ratoon crops. For model selection the REML likelihood ratio test or/and Bayesian Information Criteria (BIC) has been used for each model.

We often want to learn about physical processes described by complex mathematical models implemented as computer simulators. To use a simulator to make predictions about the real physical process, it is necessary to first perform calibration: that is, to use data obtained from a physical experiment to make inference about the values of unknown tuning parameters whilst acknowledging discrepancies between the model and reality. The computational expense of the simulator makes this challenging. Thus, usually in calibration, we use a computationally cheaper approximation to the simulator, called an emulator, which is constructed by fitting a statistical model to the results of a relatively small computer experiment. There is a substantial literature on the design of the computer experiment. However, the problem of designing the physical experiment in calibration is much less well-studied. In this poster, we present some initial considerations on the design of the physical experiment.

Randomization is one of the most important principles in experimental design. When performing an experiment, it is strongly recommended that the experimental observations are made independently, in a random order. The reason for this is that randomization is the best way to protect against any systematic bias due to extraneous factors that are not under control of the experimenter. There are two experimental scenarios, however, in which a complete randomization is not possible.

One scenario involves cases where not all observations can be made under homogeneous conditions. This happens when only a limited number of observations can be made per day, or when different batches of the same material are used to study an industrial process. For theses cases, it is possible to generate experimental designs that explicitly take into account these limitations and allow to perform a more appropriate analysis. This is done by grouping the observations that are made under similar experimental conditions. The correlation of the observations within the groups is modeled by means of a compound symmetric error structure. These types of experiments are called blocked experiments.

Another scenario involves cases where there are factors that are hard, time-consuming or expensive to change. In this scenario, it is common that the person in charge of carrying out the experiment establishes a practical order of observations that avoids changing the levels of these inconvenient factors. Since these factors are not reset every time, the experiment ends up having groups of correlated observations, which should be accounted for in the statistical analysis (again, by means of a compound symmetric error structure). A better design approach is to explicitly consider this correlation structure when setting up the experiment, and generate a design that groups the observations in which the levels of the factors that are inconvenient to change remain constant. Experiments with this characteristic are called split-plot experiments.

A key feature of the traditional analysis of data from block and split-plot experiments is the compound symmetric error structure, which assumes that every pair of observations within a given group has the same correlation. In this presentation, we study experimental scenarios in which not all pairs of observations within each group are correlated to the same extent. This might be expected when the observations are carried out sequentially, or when the experimental conditions are slightly different for each observation within the group. Consider scenarios where, for instance, observations are carried out at different times of a day, or when the experiment involves placing products in an industrial furnace. In this presentation, we consider observations that are closer to each other (either in time or space) to be more correlated than observations that are further apart. This is modeled by assuming that the observations within each group follow an autoregressive process of order one. We generate optimal designs for both blocked and split-plot experiments for that scenario. We compare the statistical efficiency of these designs to that of traditional designs constructed assuming that all observations within a group are correlated to the same extent. Moreover, we study how the optimal grouping configurations of these designs are influenced by the value of the autoregressive parameter considered (or, in other words, by how strongly observations close to each other are correlated).

For paired comparison designs, the optimal designs currently available in the literature for estimation of the main effects, especially for attributes with higher number of levels (say, three or more) are not quite practical since they require respondents to assess too many choice sets. Two new choice design construction methods for the estimation of the main effects, under the indifference assumption of multinomial logit model, are provided. These designs allow for efficient estimation (more than 95% efficient in majority of cases) of the main effects with about more than 30% reduction in number of choice sets and hence are expected to be more useful to practitioners.

Statistical shape analysis plays an important role in various medical imaging applications. In particular, such methods provide tools for registering, deforming, comparing, averaging, and modeling anatomical shapes. In this talk, we focus on a recent method for statistical shape analysis of elastic parametrized surfaces to simulation of realistic endometrial tissue shapes.

Recent advances in medical imaging offer increasingly detailed information on typical anatomical structures. However, there is a lack of validation techniques for automatic image processing strategies, especially for multimodal images, i.e. coming from two different types of imaging equipment. In many medical applications, real data can only be extracted manually by an expert, and then used to validate image processing algorithms. Indeed, scarcity of data for evaluation results in restricted studies.

We present a new statistical framework to generate realistic simulated data that can be used as ground truth when dealing with deformability of endometrial cells. Standard methods to assess an accurate diagnosis use multiple modalities including Trans-Vaginal Ultrasound (TVUS) and Magnetic Resonance Imaging (MRI). However, some limitations due to non-localized endometrial lesions or their infiltration into other organs cannot be directly avoided. An interesting solution is to statistically analyze shapes of real clinical data and provide enough random or simulated samples to validate the TVUS to MRI registration step; registration of these two modalities is key for fusing complementary information for diagnostic purposes.

The clinical real data used in this study are MRI endometrial tissue surfaces, which are used to learn a  statistical shape model. We generate random samples from this model, and apply elastic semi-synthetic deformations to the randomly generated tissue shapes. This provides two types of simulated data: (1) MRI-type endometrial tissue shapes (without deformation) and (2) corresponding TVUS-type endometrial tissue shapes, which undergo a deformation due to the transducer's pressure.

Background: Compared with experiments in engineering and other fields, psychological experiments are considered “nosier” due to the presence of human factors. The assimilation effect and the contrast effect are two well-known carry-over effects that could bias participants’ judgments when they are asked to rate their experiences after receiving multiple treatments or stimuli in a within-subject experiment. Specifically, the assimilation effect might happen due to a positive correlation between the present and the previous experiences, while the contrast effect might produce a bias as a result of a negative correlation between the two. Findings from numerous studies conducted in experimental psychology, social psychology, political science, and consumer research on these two contradictory effects are too diverse to form a consensus. Various remedies, such as random assignment of treatment/stimuli order and the cross-over design, have been proposed. However, random assignment of the sequence is not a viable option in some psychological experiments because certain conceptually related entities must be presented in a sequence. As a compromise related treatments/stimuli can be grouped as a testlet, and only two or several testlets are presented in a cross-over fashion.

Method: 55 university students were split into to two groups to examine the influence of different carry-over effects on ratings of attractiveness. Nine photographs were presented to participants in a cross-over fashion that included: four oddly dressed females, four beautiful females, and one average female. Group 1 looked at the oddly dressed females first, then the average female, and the beautiful females last. Group 2 looked at the photos in a reversed sequence.

Results: Interestingly, neither the hypothesis of assimilation effect nor that of contrast effect was supported by the data. ANOVA repeated measures indicated that the two groups were not significantly different in their ratings; however, a significant time effect was observed. The least-square mean plot indicates that in Group 1 an upward trend in ratings was present, but scores went down near the end. In Group 2 an overall downward trend was observed, except for one spike. The qualitative responses of the students were also revealing. Some students stated they gave a higher or lower score initially but “adjusted” their ratings incrementally. In conclusion, autocorrelation (correlation with time), instead of the carry-over effect, seems to be a serious threat against internal validity, and the cross-over design with testlets might be still problematic due to autocorrelation.

This article discusses D-optimal Bayesian crossover designs for generalized linear models. Crossover trials with $t$ treatments and $p$ periods, for $t<=p$, are considered. The designs proposed in this paper minimize the determinant of the variance of the estimated treatment effects over all possible allocation of the $n$ subjects to the treatment sequences. In the regression model considered for the linear predictor, both direct effect as well as the carryover effect of each treatment are considered. It is assumed that the $p$ observations from each subject are mutually correlated while the observations from different subjects are uncorrelated. The correlation between observations within subjects are modeled using a ``working correlation structure”. The correlation structures are assumed to be either auto-regressive or compound symmetric in nature. Since main interest is in estimating the treatment effects the subject effect is assumed to be nuisance, and generalized estimating equations are used to estimate the marginal means. To address the issue of parameter dependence a Bayesian approach is employed. A prior distribution is assumed on the parameter vector which is then incorporated into the D-optimal design criterion by integrating it over the prior distribution. Two numerical examples, one with binary outcomes in a 4 × 4 trial and another based on count data for a 2 × 2 trial are used to illustrate the proposed method. The effect of choice of prior distributions on the designs are also studied.

Most statistical inference methods such as design of experiments, regression analysis, etc. require normality assumption. Outliers may cause violation of this assumption. In case of non-normality sourcing from the outliers, researchers often use robust methods. The aim of this research is to select the subsets of independent variables, which explain dependent variables in the presence of outliers and possible departures from the normality assumption of the error distribution in robust regression analysis. In this study the robust and classical variable selection methods are compared. The findings are also applied on a data set and the results are interpreted .

One of the most important problems in change point analyzing is to decide the number of change points in the sequence random variables. Many model selection criteria are available in literature such as AIC (Akaike Information Criterion), BIC (Bayesian information criterion), MIC (Modified Information Criterion), DIC (Deviance Information Criterion).In this study we consider multiple change points in the mean of normal distributed sequence and we use binary segmentation algorithm to detect the change point locations in the sequence. The binary segmentation algorithm procedure is compared with the information based criterions, via simulations.

In this presentation, we discuss the construction of optimal designs for an experimental situation that combines elements of a blocked experiment and a split-plot experiment. The split-plot nature of the experiment is caused by the presence of one or more hard-to-change factors whose levels are held constant for a successive number of runs. A blocking factor is involved in the experiment as well, due to a restriction on the number of runs that can be processed together when measuring the output quality.

This problem arises in a specific type of experiment performed in a Belgian company, that studies the adhesion between steel tire cords and rubber. In the experiment, different types of steel cords are produced and subsequently vulcanized into a block of rubber. Next, the effort to pull the cords linearly out of the rubber is measured. The experiment involves one hard-to-change factor which made the experimenters use a split-plot design. An additional complication of the experiment is the fact that there is also a blocking factor, i.e. the block of rubber in which the steel cords are vulcanized.

We will thoroughly discuss the steel tire cord experiment as well as similar experimental situations found in the literature, and compare it to strip-plot experiments. Finally, we use this knowledge to construct an optimal design for this specific ex- perimental situation.

We consider a two-factor experiment of split-block type with b blocks, in which the first factor A occurs at v1 levels and the second factor B occurs at v2 levels. Each block is divided into k1 rows and k2 columns. The levels of the factor A, called row treatments, are randomly assigned to the rows and the levels of the factor B, called column treatments, are randomly assigned to the columns. Such a design is called a split-block design. Here we consider an incomplete split-block design (ISBD) such that k1 < v1 and k2 < v2.

Hering and Mejza (1997, 2002) considered the constructions of ISBDs by the Kronecker product of the incidence matrices of two designs. Ozawa et al. (2000) introduced balanced ISBDs and semi-balanced ISBDs and they gave the necessary conditions for constructing them. Mejza et al. (2001), Kuriki et al. (2005) and Mejza et al. (2009) considered the constructions of ISBDs by a modified Kronecker product (called the semi-Kronecker product) of the incidence matrices of two resolvable designs.

In this talk, we construct an ISBD by the semi-Kronecker product using two affine α- resolvable designs for the row and column treatments. We give the stratum efficiency factors for such an ISBD, which has the general balance property.