Misspecified Turing.jl model?

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1

hi everyone - I’m thinking I may have miss-specified a Turing model :thinking:

I want to combine measurements of X, from 2 tests:
test A, has a known precision (test_A_error)
test B has an unknown precision (test_B_error) and bias (test_B_bias_pr)

I’m expecting that increasing the amount of data from test A and from test B should reduce uncertainty in all my parameters: mean_X, sd_X, X, test_B_bias and test_B_error

…however, this is not the case. Specifically, mean_X, sd_X, X , do not appear to be shifting from their (weakly informative) prior.

I will continue to investigate, but would like to knof if anyone sees anything fundamentally wrong with the model:

@model function test_model(test_A_data, test_A_error, test_B_data)  

    # priors
    mean_X ~ mean_X_pr 
    sd_X ~ sd_X_pr 

    test_B_bias ~ test_B_bias_pr
    test_B_error ~ test_B_error_pr

    # Likelihood for the test data
    X ~ Normal(mean_X, sd_X)

    for test_A_id in eachindex(test_A_data)
        test_A_data[test_id] ~ Normal(X, test_A_error)
    end
    
    for test_B_id in eachindex(test_B_data)
        test_B_data[test_B_id] ~ Normal(X + test_B_bias, test_B_error)
    end
        
end
2

I thought I would include the solution here, just incase anyone would benefit:

The issue was that X wasn’t vectorising as I had assumed in the model code. I needed to explicitly create an X for each measurement:

X = Vector{Real}(undef, Nx)
for i in 1:Nx
    X[i] ~ Normal(mean_X, sd_X)
end

and then reference that particular X in the likelihoods:

for test_A_id in eachindex(test_A_data)
    test_A_data[test_A_id] ~ Normal(X[test_A_id], test_A_error)
end

…where

Nx = max(length(test_A_data), length_test_B_data))
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3

I think what you wanted was

X ~ MvNormal(...)

Which will also be faster than the looped version.

1 Like