# Density and Cumulative Distribution Function Compute the density and cumulative distribution function of the approximate posterior. The density is approximated on a find grid using a polynomial interpolant. The CDF can't be computed exactly (if it could, you wouldn't be using quadrature!), so a fine grid is laid down and the CDF is approximated at each grid point using a simpler integration rule and a polynomial interpolant. This method tends to work well, but won't always. ```r compute_pdf_and_cdf(obj, ...) ## Default S3 method: compute_pdf_and_cdf( obj, transformation = default_transformation(), finegrid = NULL, interpolation = "auto", ... ) ## S3 method for class 'list' compute_pdf_and_cdf(obj, transformation = default_transformation(), ...) ## S3 method for class 'aghq' compute_pdf_and_cdf(obj, transformation = obj$transformation, ...) ``` ## Arguments - `obj`: Either the output of `aghq::aghq()`, its list of marginal distributions (element `marginals`), or an individual `data.frame` containing one of these marginal distributions as output by `aghq::marginal_posterior()`. - `...`: Used to pass additional arguments. - `transformation`: Optional. Calculate pdf/cdf for a transformation of the parameter whose posterior was normalized using adaptive quadrature. `transformation` is either: a) an `aghqtrans` object returned by `aghq::make_transformation`, or b) a list that will be passed to that function internally. See `?aghq::make_transformation` for details. - `finegrid`: Optional, a grid of values on which to compute the CDF. The default makes use of the values in `margpost` but if the results are unsuitable, you may wish to modify this manually. - `interpolation`: Which method to use for interpolating the marginal posterior, `'polynomial'` (default) or `'spline'`? If `k > 3` then the polynomial may be unstable and you should use the spline, but the spline doesn't work **unless** `k > 3` so it's not the default. See `interpolate_marginal_posterior()`. ## Returns A tbl_df/tbl/data.frame with columns `theta`, `pdf` and `cdf` corresponding to the value of the parameter and its estimated PDF and CDF at that value. ## Examples ```r logfteta2d <- function(eta,y) { # eta is now (eta1,eta2) # y is now (y1,y2) n <- length(y) n1 <- ceiling(n/2) n2 <- floor(n/2) y1 <- y[1:n1] y2 <- y[(n1+1):(n1+n2)] eta1 <- eta[1] eta2 <- eta[2] sum(y1) * eta1 - (length(y1) + 1) * exp(eta1) - sum(lgamma(y1+1)) + eta1 + sum(y2) * eta2 - (length(y2) + 1) * exp(eta2) - sum(lgamma(y2+1)) + eta2 } set.seed(84343124) n1 <- 5 n2 <- 5 n <- n1+n2 y1 <- rpois(n1,5) y2 <- rpois(n2,5) objfunc2d <- function(x) logfteta2d(x,c(y1,y2)) funlist2d <- list( fn = objfunc2d, gr = function(x) numDeriv::grad(objfunc2d,x), he = function(x) numDeriv::hessian(objfunc2d,x) ) opt_sparsetrust_2d <- optimize_theta(funlist2d,c(1.5,1.5)) margpost <- marginal_posterior(opt_sparsetrust_2d,3,1) # margpost for theta1 thepdfandcdf <- compute_pdf_and_cdf(margpost) with(thepdfandcdf,{ plot(pdf~theta,type='l') plot(cdf~theta,type='l') }) ``` ## See Also Other summaries: `compute_quantiles()`, `interpolate_marginal_posterior()`, `marginal_posterior()`

compute_pdf_and_cdf function