quite, although usually you’ll have a model f(x,y)=aXY+bX+cY+d. I’m actually underselling this approach, because if I had two variables X, and Y which can be observed between (-1,1), and only have two observations to do it in then we’re much better going (X,Y)=(-1,1) and (1,-1) rather than (0,1),(1,0), because we’re gathering more information.
We always want to design in the location with the most variance, because thats the hardest place to predict. Given that the model we’re looking at is linear in both the parameters and the variables then we know the places where we get the most variation will be at the extremes. Obviously we have no information if we think there might be some kind of quadratic terms here, but one of the nice things about design for linear models is you can build your experimentation to iteratively build up information.
Typically in an industrial setting we’ll have a few dozen different factors which we think might affect our outcome, so we can design to eliminate down to a handful by using a very basic linear model in a screening experiment, then use a more sophisticated design called a central composite design.
Now if we want a mechanistic model, something based on what we know on the physics of the situation (say we have some differential equations describing the reaction), then designing becomes harder, which is where my research is.
quite, although usually you’ll have a model f(x,y)=aXY+bX+cY+d. I’m actually underselling this approach, because if I had two variables X, and Y which can be observed between (-1,1), and only have two observations to do it in then we’re much better going (X,Y)=(-1,1) and (1,-1) rather than (0,1),(1,0), because we’re gathering more information.
We always want to design in the location with the most variance, because thats the hardest place to predict. Given that the model we’re looking at is linear in both the parameters and the variables then we know the places where we get the most variation will be at the extremes. Obviously we have no information if we think there might be some kind of quadratic terms here, but one of the nice things about design for linear models is you can build your experimentation to iteratively build up information.
Typically in an industrial setting we’ll have a few dozen different factors which we think might affect our outcome, so we can design to eliminate down to a handful by using a very basic linear model in a screening experiment, then use a more sophisticated design called a central composite design.
Now if we want a mechanistic model, something based on what we know on the physics of the situation (say we have some differential equations describing the reaction), then designing becomes harder, which is where my research is.