Calculate posterior probabilities

This function calculates the posterior probability Pr(Y | X, data), where Y and X are two (non overlapping) sets of joint variate values. If X is omitted or NULL, then the posterior probability Pr(Y | data) is calculated. The function also gives quantiles about the possible variability of the probability Pr(Y | X, newdata, data) that we could have if more learning data were provided, as well as a number of samples of the possible values of such probabilities. If several joint values are given for Y or X, the function will create a 2D grid of results for all possible compbinations of the given Y and X values. This function also allows for base-rate or other prior-probability corrections: If a prior (for instance, a base rate) for Y is given, the function will calculate the Pr(Y | X, data, prior) from Pr(X | Y, data) and the prior by means of Bayes's theorem. Each variate in each argument Y, X can be specified either as a point-value Y = y or as a left-open interval Y ≤ y or as a right-open interval Y ≥ y, through the argument tails.

Usage

Pr(
  Y,
  X = NULL,
  learnt,
  tails = NULL,
  priorY = NULL,
  nsamples = "all",
  quantiles = c(0.055, 0.25, 0.75, 0.945),
  parallel = NULL,
  silent = FALSE,
  keepYX = TRUE
)

Arguments

Y: Matrix or data.table: set of values of variates of which we want the joint probability of. One variate per column, one set of values per row.
X: Matrix or data.table or NULL (default): set of values of variates on which we want to condition the joint probability of Y. If NULL, no conditioning is made (except for conditioning on the learning dataset and prior assumptions). One variate per column, one set of values per row.
learnt: Either a character with the name of a directory or full path for a 'learnt.rds' object, produced by the learn() function, or such an object itself.
tails: Named vector or list, or NULL (default). The names must match some or all of the variates in arguments Y and X. For variates in this list, the probability arguments are understood in an semi-open interval sense: Y ≤ y or Y ≥ y, an so on. This is true for variates on the left and on the right of the conditional sign \|. A left-open interval Y ≤ y is indicated by the values '<=' or 'left' or -1; a right-open interval Y ≥ y is indicated by the values '>=' or 'right' or +1. Values NULL, '==', 0 indicate that a point value Y = y (not an interval) should be calculated. NB: the semi-open intervals always include the given value; this is important for ordinal or rounded variates. For instance, if Y is an integer variate, then to calculate P(Y < 3) you should require P(Y <= 2); for this reason we also have that P(Y <= 2) and P(Y >= 2) generally add up to more than 1.
priorY: Numeric vector with the same length as the rows of Y, or TRUE, or NULL (default): prior probabilities or base rates for the Y values. If TRUE, the prior probabilities are assumed to be all equal.
nsamples: Integer or NULL or 'all' (default): desired number of samples of the variability of the probability for Y. If NULL, no samples are reported. If 'all' (or Inf), all samples obtained by the learn() function are used.
quantiles: Numeric vector, between 0 and 1, or NULL: desired quantiles of the variability of the probability for Y. Default c(0.055, 0.25, 0.75, 0.945), that is, the 5.5%, 25%, 75%, 94.5% quantiles (these are typical quantile values in the Bayesian literature: they give 50% and 89% credibility intervals, which correspond to 1 shannons and 0.5 shannons of uncertainty). If NULL, no quantiles are calculated.
parallel: Logical or positive integer or cluster object. TRUE: use roughly half of available cores; FALSE: use serial computation; integer: use this many cores. It can also be a cluster object previously created with parallel::makeCluster(); in this case the parallel computation will use this object.
silent: Logical, default FALSE: give warnings or updates in the computation?
keepYX: Logical, default TRUE: keep a copy of the Y and X arguments in the output? This is used for the plot method.

Value

A list of class probability, consisting of the elements values, quantiles (possibly NULL), samples (possibly NULL), values.MCaccuracy, quantiles.MCaccuracy (possibly NULL), Y, X. Element values: a matrix with the probabilities P(Y|X,data,assumptions), for all combinations of values of Y (rows) and X (columns). Element quantiles: an array with the variability quantiles (3rd dimension of the array) for such probabilities. Element samples: an array with the variability samples (3rd dimension of the array) for such probabilities. Elements values.MCaccuracy and quantiles.MCaccuracy: arrays with the numerical accuracies (roughly speaking a standard deviation) of the Monte Carlo calculations for the values and quantiles elements. Elements Y, X: copies of the Y and X arguments.