Hello, I’m a new Turing user and I’m not very familiar with probabilistic modeling, but the package is so cool that I couldn’t help trying to implement some of it
Basically I have 2 Bernoulli/Poisson processes (binned spike trains) and I’d like to know if and how much one influences the other.
So my data has this form:
s₁ = [0, 0, 1, 0, 1] s₂ = [1, 0, 0, 0, 1]
and I’ve computed a feature which is the delay of the closest spike of s₂
x = [0, 1, 2, 1, 0]
Then I’ve built the model:
@model my_naive_model(x, y, n, σ²) = begin b0 ~ Normal(0, σ²) b1 ~ Normal(0, σ²) for i = 1:n theta = b0 + b1*x[i, 1] y[i] ~ Bernoulli(sigmoid(theta)) end end;
chain = sample(my_naive_model(x, s₁, length(x), 10), NUTS(200, 0.65), 1500, discard_adapt=false)
And took the predictions with:
function prediction(x::Vector, chain) p0 = mean(chain, :b0) p1 = mean(chain, :b1) r = zeros(size(x, 1)) for i = 1:n theta = p0 + p1*x[i] r[i] = sigmoid(theta) end r end;
And that was awesomely easy, but I’d like to do something a bit more complicated, so these are my questions:
What could be a sensible transformation of x, or how could I figure this out?
For example, I guess I could fit a polynomial, but what about embedding a smoothing spline or another non parametric regression method?
How do I understand the magnitude of the effect that
s₂ has on
s₁? In particular if I’m using a polynomial fit, how can I say that
s₂ is actually having an effect on
This follows directly from the second question: Let’s say that I have a third spike train, and I want to
s₃, and I want to prove that it has no effect at all on
s₁. How do I do that?
Thank you very much in advance, and thanks to all Turing developers for the marvelous work!