# Dr Bernard Torsney

**Honorary Research Fellow**(School of Mathematics & Statistics)

**email**:
Bernard.Torsney@glasgow.ac.uk

Mathematics Building

## Research interests

I have a long standing interest in the area of optimal regression design or optimal designs for models with both qualitative and quantitative inputs. This covers both linear and non-linear models. These designs need to be determined numerically. I have proposed algorithms for determining optimal design weights; i.e. the proportions of observations to be taken at given design points. These are multiplicative in form, neatly ensuring the constraints which weights must satisfy. I have applied these methods to other examples of this kind of problem, including various maximum likelihood estimation problems. A current interest is paired comparisons and ranking data. There is scope for developing a rich class of models for such data, whose parameters can be taken to be weights. Numerical techniques are needed to determine maximum likelihood estimates. Other examples arise in sampling problems.

In the design context too these algorithms can be used to determine the design points at which observations should be taken. In the one design variable case these must lie in a finite design interval under a linear model. The design points therefore split the design interval into sub-intervals, which form proportions of the whole interval. Determining these proportions optimally determines the design points. A similar problem arises in determining cut-points for survey questions on items or variables such as income, given an assumed distribution for the variable. This in fact is an extension of optimal designing for binary response models to multinomial ones. Particular applications arise in Contingent Valuation or Willingness To Pay studies.

In almost of these areas there also arise problems in which several optimising distributions are sought. A recent example is that of determining optimal conditional designs when there is control over only some terms in a model, while the others are known prior to experimenting. Designs conditional on these known values are sought. Examples also arise in the paired comparisons and ranking data context when comparisons are made in respect of several attributes. Also the relaxation labelling approach to pixel categorisation (of each pixel) in image analysis is of a similar flavour. Our class of algorithm readily extends to this scenario.