BayesMassBal (version 1.1.0)

mainEff: Main Effects

Description

Calculates the main effect of a variable, which is independent of process performance, on a function.

Usage

mainEff(
  BMBobj,
  fn,
  rangex,
  xj,
  N = 50,
  res = 100,
  hdi.params = c(1, 0.95),
  ...
)

Arguments

BMBobj

A BayesMassBal object originally obtained from the BMB function. See BMB.

fn

A character string naming a function with arguments of BMBobj$ybal and independent random variables X. See Details and examples for more on function requirements.

rangex

A numeric matrix. Each column of rangex contains the minimum and maximum value of uniformly distributed random values making up vector \(x\).

xj

Integer indexing which element in \(x\) is used for conditioning for \(E_x\lbrack f(x,y)|x_j\rbrack\). If a vector is supplied the marginal main effect of each element is calculated sequentially. The integers supplied in xj are equivalent to the indices of the columns in rangex.

N

Integer specifying the length of the sequence used for xj. Larger N trades a higher resolution of the main effect of xj for longer computation time and larger RAM requirements.

res

Integer indicating the number of points to be used for each Monte-Carlo integration step. Larger res reduces Monte-Carlo variance as the expense of computation time.

hdi.params

Numeric vector of length two, used to calculate Highest Posterior Density Interval (HPDI) of the main effect xj using hdi. hdi.params[1] = 1 indicates hdi is used, and the mean and HPDI bounds are returned instead of the every sample from the distribution of \(E_x\lbrack f(x,y)|x_j\rbrack\). The second element of hdi is passed to the credMass argument in the hdi function. The default, hdi.params = c(1,0.95), returns 95% HPDI bounds.

...

Extra arguments passed to the named fn

Value

A list of length(xj) list(s). Each list specifies output for the main effect of a xj

g

The grid used for a particular xj

fn.out

A matrix giving results on \(E_x\lbrack f(x,y)|x_j\rbrack\). If hdi.params[1] = 1, the mean and Highest Posterior Density Interval (HPDI) bounds of \(E_x\lbrack f(x,y)|x_j\rbrack\) are returned. Otherwise, samples of \(E_x\lbrack f(x,y)|x_j\rbrack\) are returned. The index of each column of fn.out corresponds to the the value of g at the same index.

fn

Character string giving the name of the function used. Same value as argument fn.

xj

Integer indicating the index of \(x\) corresponding to a grouped fn.out and g.

Details

The mainEff function returns a distribution of \(E_x\lbrack f(x,y)|x_j\rbrack\), marginalized over the samples of BMBobj$ybal, giving the distribution of \(E_x\lbrack f(x,y)|x_j\rbrack\) which incorporates uncertainty of a chemical or particulate process.

In the current implementation of mainEff in the BayesMassBal package, only uniformly distributed values of \(x\) are supported.

The \(f(x,y)\) is equivalent to the supplied function named in mainEff(fn). For the arguments of fn, ybal is structured in a similar manner as BMBobj$ybal. The only difference being individual columns of each matrix are used at a time, and are vectorized. Note the way ybal is subset in the example function fn_example. The supplied X is a matrix, with columns corresponding to each element in \(x\). The output to fn must be a vector of length nrow(x). The first argument of fn must be X, the second argument must be BMBobj$ybal. Order of other arguments passed to fn through ... does not matter. Look at the example closely for details!

Examples

# NOT RUN {
## Importing Data, generating BMB object
y <- importObservations(file = system.file("extdata", "twonode_example.csv",
                                    package = "BayesMassBal"),
                   header = TRUE, csv.params = list(sep = ";"))

C <- matrix(c(1,-1,0,-1,0,0,1,-1,0,-1), byrow = TRUE, ncol = 5, nrow = 2)
X <- constrainProcess(C = C)

BMB_example <- BMB(X = X, y = y, cov.structure = "indep",
                   BTE = c(10,200,1), lml = FALSE, verb=0)

fn_example <- function(X,ybal){
    cu.frac <- 63.546/183.5
    feed.mass <- ybal$CuFeS2[1] + ybal$gangue[1]
    ## Concentrate mass per ton feed
    con.mass <- (ybal$CuFeS2[3] + ybal$gangue[3])/feed.mass
    ## Copper mass per ton feed
    cu.mass <- (ybal$CuFeS2[3]*cu.frac)/feed.mass
    gam <- c(-1,-1/feed.mass,cu.mass,-con.mass,-cu.mass,-con.mass)
    f <- X %*% gam
    return(f)
    }

rangex <- matrix(c(4.00 ,6.25,1125,1875,3880,9080,20,60,96,208,20.0,62.5),
                  ncol = 6, nrow = 2)

mE_example <- mainEff(BMB_example, fn = "fn_example",rangex =  rangex,xj = 3, N = 15, res = 4)

# }