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If a confidence interval is computed using FIM (or ideally profile-likelihood), for a parameter on log10 or log scale, it can be relevant for users to get the interval on linear scale. This is not a trivial computation, as in a sense we are making a change of distribution, for example for log10 we have for the mean μ and sd σ:
function convert_log10_to_linear(μ_log, σ_log)
μ_log = log(10) * μ_log
σ_log = log(10) * σ_log
μ_lin = exp(μ_log + 0.5 * σ_log^2)
σ_lin = sqrt(exp(2 * μ_log + σ_log^2) * (exp(σ_log^2) - 1))
return μ_lin, σ_lin
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