mleB2B: mleB2B Estimates Back-to-Back "Q" and Offsets to a bit error rate function.

Description

Bit error counts modeled as independent binary decisions result in a log-likelihood dependent on the bit error probability. This function inserts the supplied bit error probability function into the binomial log-likelihood function, and passes that to stats4::mle, which ultimately calls stats::optim. The function will optimize a binomial probability of the form $r = N * P( x_1, x_2, ..., x_n, a_1, a_2, ... a_k)$, where the $x_i$ are variables from data, and the $a_j$ are parameters to be estimated.

Usage

mleB2B(data = NULL, Errors, N, f, fparms, start, method = "Nelder-Mead", ...)

Value

An object of class stats4::mle with the parameters identified in start estimated.

Arguments

data: a data frame or list with named components. If a list, each component must be the same length (just like a data frame). This is not checked, so usual rules of recycling will apply. Partial matching not performed, so you must use full column names.
Errors: A vector of error counts, or a string identifying a column of data from which to draw the error counts
N: A single number, or a vector of the same length as data, or a string identifying a column of data specifying the number of trials used to measure the error counts in Errors. If a single number, then that number is used as the number of trials for all error counts.
f: A function that predicts the probability of errors.
fparms: a list of named components that are the arguments of f. Each component can be a string, a single number, or a vector. If a string that names a column of data, that column will be used, otherwise the string will be passed to f. Note the potential for errors if a column name was misspelled. A single number or vector will be passed to f. Between fparms, start, and function defaults, all parameters that need to be supplied to f should be specified, and (except for defaults) not duplicated.
start: Named list of initial values for the parameters of f to be estimated.
method: Optimization method. See stats::optim().
...: Optional arguments to be passed to mle.

Details

The function estimates the parameters identified in start in the constructed call to f. For a function f of the form fun( SNR, x2, x3, B2B, offset) A call of the form

mleB2B( data=df, Errors="r", N="trials", f=fun, fparm=list( SNR="s", x2=1, x3="noise"), start=list(B2B=1, offset=2))

will construct a call to mle of the form:

mle( minuslogl=ll, start=start, nobs=length( Errors), method=method)

where the function ll is defined as

ll <- function( a, b) -sum( dbinom( df$r, df$n, fun( SNR=df$s, x2=1, x3=df$noise, B2B=B2B, offset=offset), log=TRUE))

Examples

Run this code

QPSKdB.B2B <- B2BConvert( QPSKdB)
O1 <- 3
B1 <- 16
s <- 0:20
N <- 1000000
r <- rbinom( length( s), N, QPSKdB.B2B( s, B1, O1))
df <- data.frame( Errors=r, SNR=s, N=N)
llsb2 <- function( b2b, offset)
         -sum( dbinom( r, N, QPSKdB.B2B( s, b2b, offset), log=TRUE))
mle1 <- stats4::mle( llsb2, start=c( b2b=20, offset=0), nobs=length(s),
                     method="Nelder-Mead")
est1 <-  mleB2B( data=df, Errors="Errors", N=N, f=QPSKdB.B2B,
                 fparms=list( x="SNR"), start=c(b2b=20, offset=0))