Package 'prspace'

Create an event

Description

An Event is a quantity you make probability statements about. Comparing it with a single value (==, !=, <, <=, >, >=) gives a condition such as S_B == 0, which is what you index a PrSpace with. !(X == 0) is the complement X != 0.

The support says which values the event can take, which lets a PrSpace derive and check more. For example, with support = "count", S_B >= 1 is the complement of S_B == 0 and Pr[S_B < 0] is 0.

If name is omitted, it is taken from the variable the event is bound to the first time it is compared, so S_B <- Event() prints as S_B.

Usage

Event(name = NULL, support = NULL)

Arguments

name	Optional label used when printing, a single string.
support	"real" (the default when NULL), "integer", "count" (0, 1, 2, ...), or a vector of the values the event can take, such as c(1, 2, 3) or c("H", "T"). Events with string values can only be compared with == and !=.

Value

A prspace_event object.

See Also

PrSpace

Examples

X <- Event()
X == 0
!(X < 3)
Event("S_B", support = "count")
Event("Coin", support = c("H", "T"))

---

Create a probability space

Description

A PrSpace stores probabilities of conditions built from Events. Assign with Pr[X == 0] <- p (or =) and read back with Pr[X == 0]. Remove a value with Pr[X == 0] <- NULL.

Reading a condition returns, in order: the value assigned to it or to any condition describing the same event; one minus the value assigned to its complement; 0 or 1 if the event's support makes it impossible or certain; and, with derive = TRUE, any value the rules of probability pin down given everything assigned to that event. Otherwise it signals an error of class prspace_undefined whose fields lower and upper give the range the value is known to lie in.

Assigning a condition replaces any stored value for the same event or its complement. With check on, the new value is compared with the range consistent with the other stored values, and a violation signals a condition of class prspace_inconsistent.

A PrSpace has reference semantics: modifying it inside a function modifies the caller's copy.

Usage

PrSpace(check = "warn", derive = TRUE)

Arguments

check	What to do when an assignment is inconsistent with the others: "warn" (store it and warn), "error" (refuse it), or "off".
derive	If TRUE, derive any value the assigned ones determine. If FALSE, only assigned values, their complements, and impossible or certain events are returned.

Value

A prspace_space object.

See Also

Event

Examples

Pr <- PrSpace()
S_B <- Event(support = "count")
n_samples <- choose(19, 10)
for (B in c(100, 1000)) {
  Pr[S_B == 0] <- prod(1 - (0:(B - 1) / n_samples))
  cat("B =", B, "  Pr[S_B >= 1] =", Pr[S_B >= 1], "\n")
}
Pr

X <- Event(support = c(1, 2, 3))
Pr[X == 1] <- 0.2
Pr[X == 2] <- 0.3
Pr[X == 3]

Y <- Event()
Pr[Y < 3] <- 0.6
tryCatch(Pr[Y < 5] <- 0.4, warning = function(w) conditionMessage(w))

---