Static array multiplied by its adjoint seems to allocate

General Usage Performance
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2

Probably H = @MArray(zeros(length(θ), length(θ))) is type-unstable.
In your code, it looks like length(θ) can only be 3, so try

function HLL(
    θ,
    data
)
    H = zero(SMatrix{3, 3, Float64, 9})
    for obs in data
        X = to_X(obs)
        e = exp(dot(θ, X))
        H += e/(1+e) * X*X'
    end
    return -H / length(data)
end

Hopefully, it’ll be zero allocations.

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