# mleB2B Estimates Back-to-Back "Q" and Offsets to a bit error rate function. 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. ```r mleB2B(data = NULL, Errors, N, f, fparms, start, method = "Nelder-Mead", ...) ``` ## 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 . ## Returns An object of class stats4::mle with the parameters identified in `start` estimated. ## 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 ```r 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)) ``` ## See Also `stats4::mle()`, `stats::optim()`

mleB2B function