sobol              package:sensitivity              R Documentation

_S_o_b_o_l _N_o_n-_l_i_n_e_a_r _S_e_n_s_i_t_i_v_i_t_y _A_n_a_l_y_s_i_s

_D_e_s_c_r_i_p_t_i_o_n:

     'sobol' is the implementation of the Monte Carlo estimation of the
     Sobol indices.

_U_s_a_g_e:

     sobol(method = "sobol93", model = NULL, x1, x2,
           max.order = 1, nboot = 0, conf = 0.95, ...)

_A_r_g_u_m_e_n_t_s:

  method: the method: "sobol93" or "saltelli02"

   model: the model

      x1: the first random sample

      x2: the second random sample

max.order: the maximum order of indices to compute (method "sobol93")

   nboot: the number of bootstrap replicates

    conf: the confidence level for bootstrap confidence intervals

     ...: any other arguments for 'model' which are passed unchanged
          each time it is called

_D_e_t_a_i_l_s:

     Two methods. The method "sobol93" computes all the Sobol indices
     (coming from the HDMR-ANOVA decomposition) from order 1 to order
     given by the argument 'max.order'. The method "saltelli02"
     computes both first order and total indices at a reduced
     computational cost.

     'model' is a function or a predictor (a class with a 'predict'
     method) computing the response 'y' based on the sample given by
     'x'. If no model is specified, the indices will be computed when
     one gives the response.

     The Monte Carlo estimation requires two independent random samples
     'x1' and 'x2'. They must have the same dimensions.

_V_a_l_u_e:

     'sobol' returns an object of class '"sobol"'. An object of class
     '"sobol"' is a list containing the following components:

       x: the factor sample

       y: the response used

       S: the estimations of the Sobol sensitivity indices

      St: the estimations of the total indices (method "saltelli02")

_C_o_m_p_u_t_a_t_i_o_n_a_l _c_o_s_t:

     For the method "sobol93", the number of model evaluations is n *
     (N + 1) where n is the size of the samples 'x1' and 'x2', and N is
     the number of indices to estimate.

     For the method "saltelli02", the number of model evaluations is n
     * (p + 2) where p is the number of factors (for the estimation of
     2p indices).

_R_e_f_e_r_e_n_c_e_s:

     Saltelli, A., Chan, K. and Scott, E. M., 2000, _Sensitivity
     analysis_. Wiley.

     Sobol, I. M., 1993, Sensitivity analysis for non-linear
     mathematical model. _Math. Modelling Comput. Exp._, *1*, 407-414.

     Saltelli, A., 2002, Making best use of model evaluations to
     compute sensitivity indices. _Computer Physics Communication_,
     *145*, 580-297.

_E_x_a_m_p_l_e_s:

     # Test case : the non-monotonic Sobol g-function

     # The method of sobol requires 2 samples
     # There are 8 factors, all following the uniform distribution
     # on [0,1]

     n <- 1000
     x <- data.frame(matrix(nr = 2 * n, nc = 8))
     for (i in 1:8)
       x[, i] <- runif(2 * n)

     # sensitivity analysis

     sa <- sobol(model = sobol.fun, x1 = x[1:n,], x2 = x[(n+1):(2*n),], max.order = 2, nboot = 100)
     print(sa)
     #plot(sa)

