# Cost-efficient design of experiments

** Contact person:** Prof. Juha Karvanen

Efficient allocation of resources is desirable in all levels of society. Research is not an exception: scientific studies, whether experimental or observational, may be very expensive to carry out.

The objective is to interpret the design problems encountered in real life research work in the framework of Bayesian optimal design, derive guidelines for cost-efficiency and carry out efficient analysis for the data collected according to the selected design. Here study design refers to all decisions made on the data collection in both observational and experimental setup.

**Sequential design of experiments in brain research, biology and physics**

Design of experiments is a field of statistics that studies optimal allocation of resources in experiments. The designing starts with defining a parametric model that describes the dependence between the controlled variables and the response. The design specifies the optimal values for the controlled variables. Optimality is usually defined as a function of Fisher information of the underlying parametric model. Commonly used optimality criteria are named alphabetically and include A-, c-, D- and E-optimality among others. For example, D-optimality maximizes the determinant of information matrix or equivalently minimizes the generalized variance of the model parameters. The sensitivity to the model assumptions can be reduced by Bayesian or minimax approaches.

In electroencephalography (EEG) and magnetoencephalography (MEG) experiments in brain research, both the number of subjects and the time available per a subject are limited. It is therefore important that the measurements are carried out so that they create as much information as possible. The goal is to develop sequential designs were next the stimulus is determined on the basis of earlier stimuli and their measured responses.

In experiments with pesticides, the optimal allocation of doses leads improved accuracy of the estimated (causal) effects.

Due to the role of statistics as a general methodological science, it is not surprising that the principles of efficient design can be easily transferred across the fields. An example of successful application of sequential design is from switching measurements of Josephson junction circuits in quantum physics. In the experiment, the height of the applied current pulse for the next measurement is determined in real time from a cost-efficient sequential design. The developed measurement procedure has been in daily use in Low Temperature Laboratory at Aalto University and has proven to be about ten times faster than the approach that was previously used. The speed improvement reduces the risk of instability of the measurement system and improves the efficiency of the usage of the measurement equipment.

**Figure 1:** *Using the theory of experimental design, the measurements can be carried out cost-efficiently in quantum physics. The upper panel shows the measurements (red crosses) made to determine the parameters of the response curve (blue) which describes the probability of switching as a function of the height of the current pulse. The lower panel shows the verification measurements for the estimated response curve.***Selected publication:**

J. Karvanen, J. J. Vartiainen, A. Timofeev, J. Pekola, Experimental designs for binary data in switching measurements on superconducting Josephson junctions. Journal of the Royal Statistical Society: Series C (Applied Statistics) 56 (2), 167–181, 2007.

**PhD student:** Santtu Tikka** **

**Collaborators:** Dr. Tiina Parviainen (Jyväskylä Centre for Interdisciplinary Brain Research), Dr. Leena Lindström (Department of Biological and Environmental Science)

**Related projects:** Cost-efficient design of observational studies