Weighted Statistical A-optimal Designs for Two-variable Poisson Regression Model with Application to Fertility Studies

This research extends design optimization to model involving count data. A two-variable Poisson regression model was investigated for A-optimality on a constrained design space and the weights of the optimal design points were obtained. The constructed designs were verified to be A-optimal at 4-point design through the general equivalence theorem. The efficiency of the constructed optimal design was found to be 100% A-efficient. The concept of weighted optimal designs for Poisson regression model was applied to fertility studies. Approximate A-optimal design weights of educational level of women were obtained for each marriage duration period with respect to their places of residence. The study revealed that the numbers of women with secondary education and above were found to be consistently more than that of women with no education, lower primary education and upper primary education, respectively for all the marriage duration periods considered and at each place of residence. The only exclusion is the marriage duration of 0–4 years at Suva where the proportion of women with no education was more than other educational levels. Keywords: A-optimality; Design Point; Fisher Information Matrix; Imperialist Competitive Algorithm; Poisson Regression Model

R-optimal designs for second-order Scheffé model with qualitative factors

<abstract><p>Considering a mixture model with qualitative factors, the $ R $-optimal design problem is investigated when the levels of the qualitative factor interact with the mixture factors. In this paper, the conditions for $ R $-optimality of designs with mixture and qualitative factors are presented. General analytical expressions are also derived for the decision function under the $ R $-optimal designs, in order to verify that the resulting designs satisfy the general equivalence theorem. In addition, the relative efficiency of the $ R $-optimal design is discussed.</p></abstract>

Computable and Continuous Partial Homomorphisms on Metric Partial Algebras

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations.