Data along the time axis

[Dashadower]

If we're integrating from time 0 to T, say we want some variable X where we know the observed values for each discrete timestep. Stan needs the variable to be defined along the entire [0, T] real interval meaning some interpolation is necessary.

The obvious solution to this is to just use piecewise linear approximation much like LOOKUP. The minor problem/inconvenience would be the number of conditional branches being as man￦ as the number of discrete timesteps.

[hyunjimoon]

Would the following Juho's explanation prevent us from LOOKUP function implementation?

functions {
  vector one_comp_mm_elim_abs(real t,
                              vector y,
                              real k_a, // Dosing rate in 1/day
                              real K_m, // Michaelis-Menten constant in mg/L
                              real V_m, // Maximum elimination rate in 1/day
                              real D,
                              real V) {
    vector[1] dydt;

    real dose = 0;
    real elim = (V_m / V) * y[1] / (K_m + y[1]);

    if (t > 0)
      dose = exp(- k_a * t) * D * k_a / V;

    dydt[1] = dose - elim;

    return dydt;
  }
}

vector[1] mu_C[N_t] = ode_bdf(one_comp_mm_elim_abs, C0, t0, times,
                                k_a, K_m, V_m, D, V);

If you want to pass a vector to one_comp_mm_elim_abs then the signature for the argument is just vector D . You cannot index that with t because t is the continuous time value. The function one_comp_mm_elim_abs will be called with various t values when solving the ODE and those values are different from the output time points. If your D is a function of t then you can just write the function inside one_comp_mm_elim_abs . If you only know the value of D at the output time points and have it in a vector D then you need to somehow interpolate so that you can get D in arbitrary time points.