From 7e492aac60b9be1a609533de3644f8d0e803e4cb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 16:28:41 +0200 Subject: [PATCH 01/21] Functions for simultaneous confidence bands of ECDF --- R/helpers-ppc.R | 163 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 163 insertions(+) diff --git a/R/helpers-ppc.R b/R/helpers-ppc.R index 1f8ee245..d0258587 100644 --- a/R/helpers-ppc.R +++ b/R/helpers-ppc.R @@ -65,6 +65,32 @@ validate_yrep <- function(yrep, y) { } +#' Validate PIT +#' +#' Checks that `pit` is numeric, doesn't have any NAs, and is either a vector, +#' or a 1-D array with values in [0,1]. +#' +#' @param pit The 'pit' object from the user. +#' @return Either throws an error or returns a numeric vector. +#' @noRd +validate_pit <- function(pit) { + stopifnot(is.numeric(pit)) + + if (!is_vector_or_1Darray(pit)) { + abort("'pit' must be a vector or 1D array.") + } + + if (any(pit > 1) || any(pit < 0)) { + abort("'pit' must only contain values between 0 and 1.") + } + + if (anyNA(pit)) { + abort("NAs not allowed in 'pit'.") + } + + unname(pit) +} + #' Validate group #' #' Checks that grouping variable has same length as `y` and is either a vector or @@ -250,6 +276,143 @@ all_counts <- function(x, ...) { all_whole_number(x, ...) && min(x) >= 0 } + +adjust_gamma <- function(N, + L = 1, + K = N, + prob = 0.99, + M = 1000, + adj_method = "interpolate") { + if (any(c(K, N, L) < 1)) { + abort("Parameters 'N', 'L' and 'K' must be positive integers.") + } + if (prob >= 1 || prob <= 0) { + abort("Value of 'prob' must be in (0,1).") + } + if (L == 1) { + gamma <- adjust_gamma_optimize(N, K, prob) + } + else { + gamma <- adjust_gamma_simulate(N, L, K, prob, M) + } + gamma +} + +# Adjust coverage parameter to find simultaneous confidence intervals for the +# ECDF of a sample from the uniform distribution. +# N - length of samples +# K - number of equally spaced evaluation points, i.e. the right ends of the +# partition intervals. +adjust_gamma_optimize <- function(N, K, prob=0.99) { + target <- function(gamma, prob, N, K) { + z <- 1:(K - 1) / K + z1 <- c(0, z) + z2 <- c(z, 1) + + # pre-compute quantiles and use symmetry for increased efficiency. + x2_lower <- qbinom(gamma / 2, N, z2) + x2_upper <- c(N - rev(x2_lower)[2:K], 1) + + # Compute the total probability of trajectories inside the confidence + # intervals. Initialize the set and corresponding probabilities known + # to be 0 and 1 for the starting value z1 = 0. + x1 <- 0 + p_int <- 1 + for (i in seq_along(z1)) { + tmp <- p_interior( + p_int, x1 = x1, x2 = x2_lower[i]: x2_upper[i], + z1 = z1[i], z2 = z2[i], gamma = gamma, N = N + ) + x1 <- tmp$x1 + p_int <- tmp$p_int + } + abs(prob - sum(p_int)) + } + optimize(target, c(0, 1 - prob), prob, N = N, K = K)$minimum +} + +# Adjust coverage parameter to find silmultaneous confidence intervals for the +# ECDFs of multiple samples (chains) from the uniform distribution. +# N - length of samples (chains). +# L - number of samples (chains). +# K - number of equally spaced evaluation points, i.e. the right ends of the +# partition intervals. +# M - number of simulations used to determine the 'prob' middle quantile. +#' +adjust_gamma_simulate <- function(N, L, K, prob = 0.99, M = 1000) { + gamma <- numeric(M) + z <- (1:(K - 1)) / K + n <- N * (L - 1) + k <- floor(z * N * L) + for (m in seq_len(M)) { + u <- replicate(L, runif(N)) %>% u_scale + scaled_ecdfs <- apply(outer(u, z, "<="), c(2, 3), sum) + gamma[m] <- 2 * min( + apply( + scaled_ecdfs, 1, phyper, m = N, n = n, k = k + ), + apply( + scaled_ecdfs - 1, 1, phyper, m = N, n = n, k = k, lower.tail = FALSE + ) + ) + } + alpha_quantile(gamma, 1 - prob) +} + +p_interior <- function(p_int, x1, x2, z1, z2, gamma, N) { + z_tilde <- (z2 - z1) / (1 - z1) + N_tilde <- rep(N - x1, each = length(x2)) + p_int <- rep(p_int, each = length(x2)) + x_diff <- outer(x2, x1, "-") + p_x2_int <- p_int * dbinom(x_diff, N_tilde, z_tilde) + + list(p_int = rowSums(p_x2_int), x1 = x2) +} + +# 100 * `alpha` percent of the trials are allowed to be rejected. +# In case of ties, return the largest value dominating at most +# 100 * (alpha + tol) percent of the values. +alpha_quantile <- function(gamma, alpha, tol = 0.001) { + a <- unname(quantile(gamma, probs = alpha)) + a_tol <- unname(quantile(gamma, probs = alpha + tol)) + if (a == a_tol) { + if (min(gamma) < a) { + # take the largest value that doesn't exceed the tolerance. + a <- max(gamma[gamma < a]) + } + } + a +} + +# Compute simultaneous confidence intervals for one or more samples from the +# standard uniform distribution. +# N - sample length +# L - number of samples +# K - size of uniform partition defining the ECDF evaluation points. +# gamma - coverage parameter for the marginal distribution (binomial for +# one sample and hypergeometric for multiple rank transformed chains). +#' @noRd +ecdf_intervals <- function(N, L=1, K, gamma) { + lims <- list() + z <- seq(0,1, length.out = K + 1) + if (L == 1) { + lims$lower <- qbinom(gamma / 2, N, z) + lims$upper <- qbinom(1 - gamma / 2, N, z) + } else { + n <- N * (L - 1) + k <- floor(z * L * N) + lims$lower <- qhyper(gamma / 2, N, n, k) + lims$upper <- qhyper(1 - gamma / 2, N, n, k) + } + lims +} + +#' Transform observations in 'x' into their corresponding fractional ranks. +#' @noRd +u_scale <- function(x) { + array(rank(x) / length(x), dim = dim(x), dimnames = dimnames(x)) +} + # labels ---------------------------------------------------------------- create_yrep_ids <- function(ids) paste('italic(y)[rep] (', ids, ")") yrep_label <- function() expression(italic(y)[rep]) From 3a0a61c29134cd23c45a99de17aff58e5bbe0cf9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 16:29:55 +0200 Subject: [PATCH 02/21] Rank ECDF with simultaneous confidence intervals --- R/mcmc-traces.R | 132 ++++++++++++++++++++++++++++++++++++++++++++- man/MCMC-traces.Rd | 31 +++++++++++ 2 files changed, 161 insertions(+), 2 deletions(-) diff --git a/R/mcmc-traces.R b/R/mcmc-traces.R index c23f269b..01427c88 100644 --- a/R/mcmc-traces.R +++ b/R/mcmc-traces.R @@ -63,9 +63,17 @@ #' Ranks from `mcmc_rank_hist()` are plotted using overlaid lines in a #' single panel. #' } +#' \item{`mcmc_rank_ecdf()`}{ +#' The ECDFs of the ranks from `mcmc_rank_hist()` are plotted and +#' simultaneous confidence bands with a coverage determined by +#' `prob` are drawn. By default, the difference between the +#' observed ECDF and the theoretical expectation is drawn. +#' See Säilynoja et al. (2021) for details. +#' } #' } #' #' @template reference-improved-rhat +#' @template reference-uniformity-test #' @examples #' # some parameter draws to use for demonstration #' x <- example_mcmc_draws(chains = 4, params = 6) @@ -316,14 +324,14 @@ mcmc_rank_overlay <- function(x, } else { NULL } - + facet_call <- NULL if (n_param > 1) { facet_args$facets <- ~ parameter facet_args$scales <- facet_args$scales %||% "fixed" facet_call <- do.call("facet_wrap", facet_args) } - + ggplot(d_bin_counts) + aes_(x = ~ bin_start, y = ~ n, color = ~ chain) + geom_step() + @@ -421,6 +429,33 @@ mcmc_rank_hist <- function(x, labs(x = "Rank") } +#' @rdname MCMC-traces +#' @param prob For `mcmc_rank_ecdf()`, a value between 0 and 1 +#' specifying the desired simultaneous confidence of the confidence bands to be +#' drawn for the rank ECDF plots. +#' @param plot_diff For `mcmc_rank_ecdf()`, a boolean specifying it the +#' difference between the observed rank ECDFs and the theoretical expectation +#' should be drawn instead of the unmodified rank ECDF plots. +#' @export +mcmc_rank_ecdf <- + function(x, + pars = character(), + regex_pars = character(), + transformations = list(), + ..., + facet_args = list(), + prob = 0.99, + plot_diff = TRUE) { + check_ignored_arguments(...) + .mcmc_rank_ecdf(x, + pars = pars, + regex_pars = regex_pars, + transformations = transformations, + facet_args = facet_args, + prob = prob, + plot_diff = plot_diff + ) + } #' @rdname MCMC-traces #' @export @@ -604,6 +639,99 @@ mcmc_trace_data <- function(x, yaxis_title(on = n_param == 1) } +.mcmc_rank_ecdf <- function(x, + pars = character(), + regex_pars = character(), + transformations = list(), + facet_args = list(), + ..., + K, + plot_diff = TRUE, + prob = 0.99, + adj_method = "interpolate") { + data <- mcmc_trace_data( + x, + pars = pars, + regex_pars = regex_pars, + transformations = transformations + ) + n_iter <- unique(data$n_iterations) + n_chain <- unique(data$n_chains) + n_param <- unique(data$n_parameters) + + x <- if (missing(K)) { + 0:n_iter / n_iter + } else { + 0:K / K + } + gamma <- adjust_gamma( + N = n_iter, + L = n_chain, + K = if (missing(K)) { + n_iter + } else { + K + }, + conf_level = prob, + ..., + adj_method = adj_method + ) + lims <- ecdf_intervals( + N = n_iter, + L = n_chain, + K = if (missing(K)) { + n_iter + } else { + K + }, + gamma = gamma + ) + data_lim <- data.frame( + upper = lims$upper / n_iter - (plot_diff == TRUE) * x, + lower = lims$lower / n_iter - (plot_diff == TRUE) * x, + x = x + ) + data <- data %>% + group_by(parameter, chain) %>% + dplyr::group_map(~ data.frame( + parameter = .y[1], + chain = .y[2], + ecdf_value = ecdf(.x$value_rank / (n_iter * n_chain))(x) - + (plot_diff == TRUE) * x, + x = x + )) %>% + dplyr::bind_rows() + + mapping <- aes_( + x = ~x, + y = ~ecdf_value, + color = ~chain, + group = ~chain + ) + + scale_color <- scale_color_manual("Chain", values = chain_colors(n_chain)) + + facet_call <- NULL + if (n_param == 1) { + facet_call <- ylab(levels(data$parameter)) + } else { + facet_args$facets <- ~parameter + facet_args$scales <- facet_args$scales %||% "free" + facet_call <- do.call("facet_wrap", facet_args) + } + + ggplot() + + geom_step(data = data_lim, aes_(x = ~x, y = ~upper), show.legend = FALSE) + + geom_step(data = data_lim, aes_(x = ~x, y = ~lower), show.legend = FALSE) + + geom_step(mapping, data) + + bayesplot_theme_get() + + scale_color + + facet_call + + scale_x_continuous(breaks = pretty) + + legend_move(ifelse(n_chain > 1, "right", "none")) + + xaxis_title(FALSE) + + yaxis_title(on = n_param == 1) +} chain_colors <- function(n) { all_clrs <- unlist(color_scheme_get()) diff --git a/man/MCMC-traces.Rd b/man/MCMC-traces.Rd index cd82ec07..aaffe983 100644 --- a/man/MCMC-traces.Rd +++ b/man/MCMC-traces.Rd @@ -7,6 +7,7 @@ \alias{trace_style_np} \alias{mcmc_rank_overlay} \alias{mcmc_rank_hist} +\alias{mcmc_rank_ecdf} \alias{mcmc_trace_data} \title{Trace plots of MCMC draws} \usage{ @@ -64,6 +65,17 @@ mcmc_rank_hist( ref_line = FALSE ) +mcmc_rank_ecdf( + x, + pars = character(), + regex_pars = character(), + transformations = list(), + ..., + facet_args = list(), + confidence_level = 0.99, + difference = TRUE +) + mcmc_trace_data( x, pars = character(), @@ -176,6 +188,14 @@ of rank-normalized MCMC samples. Defaults to \code{20}.} \item{ref_line}{For the rank plots, whether to draw a horizontal line at the average number of ranks per bin. Defaults to \code{FALSE}.} + +\item{confidence_level}{For \code{mcmc_rank_ecdf()}, a value between 0 and 1 +specifying the desired simultaneous confidence of the confidence bands to be +drawn for the rank ECDF plots.} + +\item{difference}{For \code{mcmc_rank_ecdf()}, a boolean specifying it the +difference between the observed rank ECDFs and the theoretical expectation +should be drawn instead of the unmodified rank ECDF plots.} } \value{ The plotting functions return a ggplot object that can be further @@ -212,6 +232,13 @@ See Vehtari et al. (2019) for details. Ranks from \code{mcmc_rank_hist()} are plotted using overlaid lines in a single panel. } +\item{\code{mcmc_rank_ecdf()}}{ +The ECDFs of the ranks from \code{mcmc_rank_hist()} are plotted and +simultaneous confidence bands with a coverage determined by +\code{confidence_level} are drawn. By default, the \code{difference} between the +observed ECDF and the theoretical expectation is drawn. +See Säilynoja et al. (2021) for details. +} } } @@ -300,6 +327,10 @@ mcmc_trace( Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., Bürkner, P. (2019). Rank-normalization, folding, and localization: An improved \emph{R}-hat for assessing convergence of MCMC. \href{https://arxiv.org/abs/1903.08008}{arXiv preprint}. + +Säilynoja, T., Bürkner, P., Vehtari, A. +(2021). Graphical Test for Discrete Uniformity and its Applications in +Goodness of Fit Evaluation and Multiple Sample Comparison \href{https://arxiv.org/abs/2103.10522}{arXiv preprint}. } \seealso{ Other MCMC: From 4085016c6437581f05b1688564f67c2c95b2c293 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 16:31:14 +0200 Subject: [PATCH 03/21] ECDF with simultaneous confidence bands for the PIT values in ppc. --- R/ppc-distributions.R | 147 +++++++++++++++++++++++++++++++++++++++ man/PPC-distributions.Rd | 35 ++++++++++ 2 files changed, 182 insertions(+) diff --git a/R/ppc-distributions.R b/R/ppc-distributions.R index 0cc24c7d..7a5d5b65 100644 --- a/R/ppc-distributions.R +++ b/R/ppc-distributions.R @@ -47,9 +47,16 @@ #' quantiles. `y` is overlaid on the plot either as a violin, points, or #' both, depending on the `y_draw` argument. #' } +#' \item{`ppc_pit_ecdf()`}{ +#' The `100 * prob`% central simultaneous confidence intervals for the ECDF +#' of the empirical PIT values of `y` computed with respect to the +#' corresponding `yrep` values. If 'y' and 'yrep'. Th PIT values can also be +#' provided directly as `pit`. +#' See Säilynoja et al. for more details.} #' } #' #' @template reference-vis-paper +#' @template reference-uniformity-test #' @templateVar bdaRef (Ch. 6) #' @template reference-bda #' @@ -528,6 +535,146 @@ ppc_violin_grouped <- function(y, yrep, group, ..., probs = c(0.1, 0.5, 0.9), bayesplot_theme_get() } +#' @export +#' @rdname PPC-distributions +#' +ppc_pit_ecdf <- function(y, + yrep, + ..., + pit = NULL, + K = NULL, + confidence_level = .99, + difference = TRUE, + adj_method = "interpolate") { + check_ignored_arguments(...) + + if (is.null(pit)) { + pit <- ppc_data(y, yrep) %>% + group_by(y_id) %>% + dplyr::group_map(~ mean(.x$value[.x$is_y] >= .x$value[!.x$is_y])) %>% + unlist() + if (is.null(K)) { + K <- min(length(unique(ppc_data(y, yrep)$rep_id)) + 1, length(pit)) + } + } else { + inform("'pit' specified so ignoring 'y', and 'yrep' if specified.") + pit <- validate_pit(pit) + if (is.null(K)) { + K <- length(pit) + } + } + N <- length(pit) + gamma <- adjust_gamma(N, + K = K, + conf_level = confidence_level, + adj_method = adj_method + ) + lims <- ecdf_intervals(N, K = K, gamma = gamma) + ggplot() + + aes_( + x = 0:K / K, + y = ecdf(pit)(0:K / K) - (difference == TRUE) * 0:K / K, + color = "y" + ) + + geom_step(show.legend = FALSE) + + geom_step(aes( + y = lims$upper / N - (difference == TRUE) * 0:K / K, + color = "yrep" + ), show.legend = FALSE) + + geom_step(aes( + y = lims$lower / N - (difference == TRUE) * 0:K / K, + color = "yrep" + ), show.legend = FALSE) + + yaxis_title(FALSE) + + xaxis_title(FALSE) + + yaxis_ticks(FALSE) + + scale_color_ppc_dist() + + bayesplot_theme_get() +} + +#' @export +#' @rdname PPC-distributions +#' +ppc_pit_ecdf_grouped <- + function(y, + yrep, + group, + ..., + K, + pit, + confidence_level = .99, + difference = TRUE, + adj_method) { + check_ignored_arguments(...) + + if (missing(pit)) { + pit <- ppc_data(y, yrep, group) %>% + group_by(y_id) %>% + dplyr::group_map(~ mean(.x$value[.x$is_y] >= .x$value[!.x$is_y])) %>% + unlist() + if (missing(K)) { + K0 <- length(unique(ppc_data(y, yrep)$rep_id)) + } + } else { + inform("'pit' specified so ignoring 'y', and 'yrep' if specified.") + pit <- validate_pit(pit) + } + N <- length(pit) + + gammas <- lapply(unique(group), function(g) { + N_g <- sum(group == g) + adjust_gamma( + N_g, + K = min(N_g, K0), + conf_level = confidence_level, + adj_method = adj_method + ) + }) + names(gammas) <- unique(group) + + data <- data.frame(pit = pit, group = group) %>% + group_by(group) %>% + dplyr::group_map(~ data.frame( + ecdf_value = ecdf(.x$pit)( + seq(0, 1, length.out = min(nrow(.x) + 1, K0 + 1))), + group = .y[1], + lims_upper = ecdf_intervals( + N = nrow(.x), + K = min(nrow(.x), K0), + gamma = gammas[[unlist(.y[1])]] + )$upper / nrow(.x), + lims_lower = ecdf_intervals( + N = nrow(.x), + K = min(nrow(.x), K0), + gamma = gammas[[unlist(.y[1])]] + )$lower / nrow(.x), + x = seq(0, 1, length.out = min(nrow(.x) + 1, K0 + 1)) + )) %>% + dplyr::bind_rows() + ggplot(data) + + aes_( + x = ~x, + y = ~ ecdf_value - (difference == TRUE) * x, + group = ~group, + color = "y" + ) + + geom_step(show.legend = FALSE) + + geom_step(aes_( + y = ~ lims_upper - (difference == TRUE) * x, + color = "yrep" + ), show.legend = FALSE) + + geom_step(aes_( + y = ~ lims_lower - (difference == TRUE) * x, + color = "yrep" + ), show.legend = FALSE) + + xaxis_title(FALSE) + + yaxis_title(FALSE) + + yaxis_ticks(FALSE) + + bayesplot_theme_get() + + facet_wrap("group") + + scale_color_ppc_dist() + + force_axes_in_facets() + } # internal ---------------------------------------------------------------- scale_color_ppc_dist <- function(name = NULL, values = NULL, labels = NULL) { diff --git a/man/PPC-distributions.Rd b/man/PPC-distributions.Rd index 86de96b0..830dd1e5 100644 --- a/man/PPC-distributions.Rd +++ b/man/PPC-distributions.Rd @@ -13,6 +13,8 @@ \alias{ppc_ecdf_overlay} \alias{ppc_ecdf_overlay_grouped} \alias{ppc_violin_grouped} +\alias{ppc_pit_ecdf} +\alias{ppc_pit_ecdf_grouped} \title{PPC distributions} \usage{ ppc_data(y, yrep, group = NULL) @@ -105,6 +107,29 @@ ppc_violin_grouped( y_alpha = 1, y_jitter = 0.1 ) + +ppc_pit_ecdf( + y, + yrep, + ..., + pit = NULL, + K = NULL, + confidence_level = 0.99, + difference = TRUE, + adj_method = "interpolate" +) + +ppc_pit_ecdf_grouped( + y, + yrep, + group, + ..., + K, + pit, + confidence_level = 0.99, + difference = TRUE, + adj_method +) } \arguments{ \item{y}{A vector of observations. See \strong{Details}.} @@ -211,6 +236,12 @@ variable is plotted as a violin with horizontal lines at notable quantiles. \code{y} is overlaid on the plot either as a violin, points, or both, depending on the \code{y_draw} argument. } +\item{\code{ppc_pit_ecdf()}}{ +The \code{100 * prob}\% central simultaneous confidence intervals for the ECDF +of the empirical PIT values of \code{y} computed with respect to the +corresponding \code{yrep} values. If 'y' and 'yrep'. Th PIT values can also be +provided directly as \code{pit}. +See Säilynoja et al. for more details.} } } @@ -274,6 +305,10 @@ Gelman, A. (2019), Visualization in Bayesian workflow. \href{https://arxiv.org/abs/1709.01449}{arXiv preprint}, \href{https://github.com/jgabry/bayes-vis-paper}{code on GitHub}) +Säilynoja, T., Bürkner, P., Vehtari, A. +(2021). Graphical Test for Discrete Uniformity and its Applications in +Goodness of Fit Evaluation and Multiple Sample Comparison \href{https://arxiv.org/abs/2103.10522}{arXiv preprint}. + Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). \emph{Bayesian Data Analysis.} Chapman & Hall/CRC Press, London, third edition. (Ch. 6) From 979b679e2cd03b91319b612c581aed628a64fe66 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 16:31:36 +0200 Subject: [PATCH 04/21] updated NAMESPACE --- NAMESPACE | 3 +++ 1 file changed, 3 insertions(+) diff --git a/NAMESPACE b/NAMESPACE index c6f52b31..c9cac9da 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -74,6 +74,7 @@ export(mcmc_nuts_treedepth) export(mcmc_pairs) export(mcmc_parcoord) export(mcmc_parcoord_data) +export(mcmc_rank_ecdf) export(mcmc_rank_hist) export(mcmc_rank_overlay) export(mcmc_recover_hist) @@ -127,6 +128,8 @@ export(ppc_loo_pit_data) export(ppc_loo_pit_overlay) export(ppc_loo_pit_qq) export(ppc_loo_ribbon) +export(ppc_pit_ecdf) +export(ppc_pit_ecdf_grouped) export(ppc_ribbon) export(ppc_ribbon_data) export(ppc_ribbon_grouped) From b493f32b43e97055d1336782b9e08a015b2398ad Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 17:04:45 +0200 Subject: [PATCH 05/21] Added documentation to helper functions. --- R/helpers-ppc.R | 64 +++++++++++++++++++++++++++---------------------- 1 file changed, 35 insertions(+), 29 deletions(-) diff --git a/R/helpers-ppc.R b/R/helpers-ppc.R index d0258587..63efeb54 100644 --- a/R/helpers-ppc.R +++ b/R/helpers-ppc.R @@ -276,7 +276,18 @@ all_counts <- function(x, ...) { all_whole_number(x, ...) && min(x) >= 0 } - +#' Obtain the coverage parameter for simultaneous confidence bands for ECDFs +#' +#' @param N Length of sample. +#' @param L Number of chains. Used for MCMC, defaults to 1 for ppc. +#' @param K Number of equally spaced evaluation points (1:K / K). Defaults to N. +#' @param prob Desired simultaneous coverage (0,1). +#' @param M number of simulations to run, if simulation method is used. +#' @param adj_method String defining the desired adjustment method. By default +#' "interpolate" is used. Other available options "optimize" and "simulate". +#' @return The adjusted coverage parameter yielding the desired simultaneous +#' coverage of the ECDF traces. +#' @noRd adjust_gamma <- function(N, L = 1, K = N, @@ -298,11 +309,7 @@ adjust_gamma <- function(N, gamma } -# Adjust coverage parameter to find simultaneous confidence intervals for the -# ECDF of a sample from the uniform distribution. -# N - length of samples -# K - number of equally spaced evaluation points, i.e. the right ends of the -# partition intervals. +# Adjust coverage parameter for single sample using the optimization method. adjust_gamma_optimize <- function(N, K, prob=0.99) { target <- function(gamma, prob, N, K) { z <- 1:(K - 1) / K @@ -321,7 +328,7 @@ adjust_gamma_optimize <- function(N, K, prob=0.99) { for (i in seq_along(z1)) { tmp <- p_interior( p_int, x1 = x1, x2 = x2_lower[i]: x2_upper[i], - z1 = z1[i], z2 = z2[i], gamma = gamma, N = N + z1 = z1[i], z2 = z2[i], N = N ) x1 <- tmp$x1 p_int <- tmp$p_int @@ -331,21 +338,14 @@ adjust_gamma_optimize <- function(N, K, prob=0.99) { optimize(target, c(0, 1 - prob), prob, N = N, K = K)$minimum } -# Adjust coverage parameter to find silmultaneous confidence intervals for the -# ECDFs of multiple samples (chains) from the uniform distribution. -# N - length of samples (chains). -# L - number of samples (chains). -# K - number of equally spaced evaluation points, i.e. the right ends of the -# partition intervals. -# M - number of simulations used to determine the 'prob' middle quantile. -#' +# Adjust coverage parameter for multiple chains using simulation method. adjust_gamma_simulate <- function(N, L, K, prob = 0.99, M = 1000) { gamma <- numeric(M) z <- (1:(K - 1)) / K n <- N * (L - 1) k <- floor(z * N * L) for (m in seq_len(M)) { - u <- replicate(L, runif(N)) %>% u_scale + u <- u_scale(replicate(L, runif(N))) scaled_ecdfs <- apply(outer(u, z, "<="), c(2, 3), sum) gamma[m] <- 2 * min( apply( @@ -359,7 +359,10 @@ adjust_gamma_simulate <- function(N, L, K, prob = 0.99, M = 1000) { alpha_quantile(gamma, 1 - prob) } -p_interior <- function(p_int, x1, x2, z1, z2, gamma, N) { +#' A helper function for 'adjust_gamma_optimize' defining the probability that +#' an ECDF stays within the supplied bounds between z1 and z2. +#' @noRd +p_interior <- function(p_int, x1, x2, z1, z2, N) { z_tilde <- (z2 - z1) / (1 - z1) N_tilde <- rep(N - x1, each = length(x2)) p_int <- rep(p_int, each = length(x2)) @@ -369,9 +372,11 @@ p_interior <- function(p_int, x1, x2, z1, z2, gamma, N) { list(p_int = rowSums(p_x2_int), x1 = x2) } -# 100 * `alpha` percent of the trials are allowed to be rejected. -# In case of ties, return the largest value dominating at most -# 100 * (alpha + tol) percent of the values. +#' A helper function for 'adjust_alpha_simulate' +#' 100 * `alpha` percent of the trials are allowed to be rejected. +#' In case of ties, return the largest value dominating at most +#' 100 * (alpha + tol) percent of the values. +#' @noRd alpha_quantile <- function(gamma, alpha, tol = 0.001) { a <- unname(quantile(gamma, probs = alpha)) a_tol <- unname(quantile(gamma, probs = alpha + tol)) @@ -384,17 +389,17 @@ alpha_quantile <- function(gamma, alpha, tol = 0.001) { a } -# Compute simultaneous confidence intervals for one or more samples from the -# standard uniform distribution. -# N - sample length -# L - number of samples -# K - size of uniform partition defining the ECDF evaluation points. -# gamma - coverage parameter for the marginal distribution (binomial for -# one sample and hypergeometric for multiple rank transformed chains). +#' Compute simultaneous confidence intervals with the given adjusted coverage +#' parameter gamma. +#' @param N Sample length. +#' @param L Number of MCMC-chains. (1 for ppc) +#' @param K Number of uniformly spaced evaluation points. +#' @param gamma Adjusted coverage parameter for the marginal distribution +#' (binomial for PIT values and hypergeometric for rank transformed chains). #' @noRd ecdf_intervals <- function(N, L=1, K, gamma) { lims <- list() - z <- seq(0,1, length.out = K + 1) + z <- seq(0, 1, length.out = K + 1) if (L == 1) { lims$lower <- qbinom(gamma / 2, N, z) lims$upper <- qbinom(1 - gamma / 2, N, z) @@ -407,7 +412,8 @@ ecdf_intervals <- function(N, L=1, K, gamma) { lims } -#' Transform observations in 'x' into their corresponding fractional ranks. +#' Helper for 'adjust_gamma_simulate` +#' Transforms observations in 'x' into their corresponding fractional ranks. #' @noRd u_scale <- function(x) { array(rank(x) / length(x), dim = dim(x), dimnames = dimnames(x)) From 2cc9dff3667c18f508ca9403265eced692d97f6c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 23:27:02 +0200 Subject: [PATCH 06/21] Documentation and examples for ppc-pit-ecdf --- R/ppc-distributions.R | 47 ++++++++++++++++--------- man-roxygen/args-pit-ecdf.R | 11 ++++++ man-roxygen/reference-uniformity-test.R | 4 +++ man/PPC-distributions.Rd | 46 +++++++++++++++++++----- 4 files changed, 82 insertions(+), 26 deletions(-) create mode 100644 man-roxygen/args-pit-ecdf.R create mode 100644 man-roxygen/reference-uniformity-test.R diff --git a/R/ppc-distributions.R b/R/ppc-distributions.R index 7a5d5b65..a7738b6b 100644 --- a/R/ppc-distributions.R +++ b/R/ppc-distributions.R @@ -12,6 +12,7 @@ #' @template args-hist #' @template args-hist-freq #' @template args-dens +#' @template args-pit-ecdf #' @param size,alpha Passed to the appropriate geom to control the appearance of #' the `yrep` distributions. #' @param ... Currently unused. @@ -48,10 +49,10 @@ #' both, depending on the `y_draw` argument. #' } #' \item{`ppc_pit_ecdf()`}{ -#' The `100 * prob`% central simultaneous confidence intervals for the ECDF -#' of the empirical PIT values of `y` computed with respect to the -#' corresponding `yrep` values. If 'y' and 'yrep'. Th PIT values can also be -#' provided directly as `pit`. +#' The ECDF of the empirical PIT values of `y` computed with respect to the +#' corresponding `yrep` values. `100 * prob`% central simultaneous confidence +#' intervals are provided to asses if ´y´ and ´yrep´ originate from the same +#' distribution. The PIT values can also be provided directly as `pit`. #' See Säilynoja et al. for more details.} #' } #' @@ -71,6 +72,11 @@ #' # ppc_ecdf_overlay with continuous data (set discrete=TRUE if discrete data) #' ppc_ecdf_overlay(y, yrep[sample(nrow(yrep), 25), ]) #' } +#' # ECDF and ECDF difference plot of the PIT values of ´y´ compared to ´yrep +#' # with 99% simultaneous confidence bands. +#' ppc_pit_ecdf(y, yrep, prob=0.99, plot_diff=FALSE) +#' ppc_pit_ecdf(y, yrep, prob=0.99) +#' #' #' # for ppc_hist,dens,freqpoly,boxplot definitely use a subset yrep rows so #' # only a few (instead of nrow(yrep)) histograms are plotted @@ -99,6 +105,10 @@ #' #' ppc_ecdf_overlay_grouped(y, yrep[1:25, ], group = group) #' +#' # ECDF difference plots of the PIT values by group +#' # with 99% simultaneous confidence bands. +#' ppc_pit_ecdf_grouped(y, yrep, group=group, prob=0.99) +#' #' # don't need to only use small number of rows for ppc_violin_grouped #' # (as it pools yrep draws within groups) #' color_scheme_set("gray") @@ -536,6 +546,9 @@ ppc_violin_grouped <- function(y, yrep, group, ..., probs = c(0.1, 0.5, 0.9), } #' @export +#' @param pit An optional vector of probability integral transformed values for +#' which the ECDF is to be drawn. If NULL, PIT values are computed to ´y´ with +#' respect to the corresponding values in ´yrep´. #' @rdname PPC-distributions #' ppc_pit_ecdf <- function(y, @@ -543,8 +556,8 @@ ppc_pit_ecdf <- function(y, ..., pit = NULL, K = NULL, - confidence_level = .99, - difference = TRUE, + prob = .99, + plot_diff = TRUE, adj_method = "interpolate") { check_ignored_arguments(...) @@ -566,23 +579,23 @@ ppc_pit_ecdf <- function(y, N <- length(pit) gamma <- adjust_gamma(N, K = K, - conf_level = confidence_level, + conf_level = prob, adj_method = adj_method ) lims <- ecdf_intervals(N, K = K, gamma = gamma) ggplot() + aes_( x = 0:K / K, - y = ecdf(pit)(0:K / K) - (difference == TRUE) * 0:K / K, + y = ecdf(pit)(0:K / K) - (plot_diff == TRUE) * 0:K / K, color = "y" ) + geom_step(show.legend = FALSE) + geom_step(aes( - y = lims$upper / N - (difference == TRUE) * 0:K / K, + y = lims$upper / N - (plot_diff == TRUE) * 0:K / K, color = "yrep" ), show.legend = FALSE) + geom_step(aes( - y = lims$lower / N - (difference == TRUE) * 0:K / K, + y = lims$lower / N - (plot_diff == TRUE) * 0:K / K, color = "yrep" ), show.legend = FALSE) + yaxis_title(FALSE) + @@ -602,9 +615,9 @@ ppc_pit_ecdf_grouped <- ..., K, pit, - confidence_level = .99, - difference = TRUE, - adj_method) { + prob = .99, + plot_diff = TRUE, + adj_method = "interpolate") { check_ignored_arguments(...) if (missing(pit)) { @@ -626,7 +639,7 @@ ppc_pit_ecdf_grouped <- adjust_gamma( N_g, K = min(N_g, K0), - conf_level = confidence_level, + conf_level = prob, adj_method = adj_method ) }) @@ -654,17 +667,17 @@ ppc_pit_ecdf_grouped <- ggplot(data) + aes_( x = ~x, - y = ~ ecdf_value - (difference == TRUE) * x, + y = ~ ecdf_value - (plot_diff == TRUE) * x, group = ~group, color = "y" ) + geom_step(show.legend = FALSE) + geom_step(aes_( - y = ~ lims_upper - (difference == TRUE) * x, + y = ~ lims_upper - (plot_diff == TRUE) * x, color = "yrep" ), show.legend = FALSE) + geom_step(aes_( - y = ~ lims_lower - (difference == TRUE) * x, + y = ~ lims_lower - (plot_diff == TRUE) * x, color = "yrep" ), show.legend = FALSE) + xaxis_title(FALSE) + diff --git a/man-roxygen/args-pit-ecdf.R b/man-roxygen/args-pit-ecdf.R new file mode 100644 index 00000000..875ae54b --- /dev/null +++ b/man-roxygen/args-pit-ecdf.R @@ -0,0 +1,11 @@ +#' @param K An optional integer defining the number of equally spaced evaluation +#' points for the ECDF. If the +#' submitted PIT values are known to be discrete, this should be the number of +#' discrete cases. Defaults to the smaller of length(y) and ncol(yrep). +#' @param prob The desired simultaneous coverage level of the bands around the +#' ECDF. A value in (0,1). +#' @param plot_diff Wether to plot the difference between the observed ECDF and +#' the theoretical expectation when the PIT values are uniform. +#' @param adj_method Method to obtain the simultaneous confidence bands. +#' Possible values: "interpolate", "simulate", "optimize". +#' Defaults to "interpolate". diff --git a/man-roxygen/reference-uniformity-test.R b/man-roxygen/reference-uniformity-test.R new file mode 100644 index 00000000..c18e209a --- /dev/null +++ b/man-roxygen/reference-uniformity-test.R @@ -0,0 +1,4 @@ +#' @references Säilynoja, T., Bürkner, P., Vehtari, A. +#' (2021). Graphical Test for Discrete Uniformity and its Applications in +#' Goodness of Fit Evaluation and Multiple Sample Comparison [arXiv +#' preprint](https://arxiv.org/abs/2103.10522). diff --git a/man/PPC-distributions.Rd b/man/PPC-distributions.Rd index 830dd1e5..9f3cb5fb 100644 --- a/man/PPC-distributions.Rd +++ b/man/PPC-distributions.Rd @@ -114,8 +114,8 @@ ppc_pit_ecdf( ..., pit = NULL, K = NULL, - confidence_level = 0.99, - difference = TRUE, + prob = 0.99, + plot_diff = TRUE, adj_method = "interpolate" ) @@ -126,9 +126,9 @@ ppc_pit_ecdf_grouped( ..., K, pit, - confidence_level = 0.99, - difference = TRUE, - adj_method + prob = 0.99, + plot_diff = TRUE, + adj_method = "interpolate" ) } \arguments{ @@ -190,6 +190,25 @@ horizontal lines. Set to \code{NULL} to remove the lines.} to to the \code{size}, \code{alpha}, and \code{width} arguments of \code{\link[ggplot2:geom_jitter]{ggplot2::geom_jitter()}} to control the appearance of \code{y} points. The default of \code{y_jitter=NULL} will let \strong{ggplot2} determine the amount of jitter.} + +\item{pit}{An optional vector of probability integral transformed values for +which the ECDF is to be drawn. If NULL, PIT values are computed to ´y´ with +respect to the corresponding values in ´yrep´.} + +\item{K}{An optional integer defining the number of equally spaced evaluation +points for the ECDF. If the +submitted PIT values are known to be discrete, this should be the number of +discrete cases. Defaults to the smaller of length(y) and ncol(yrep).} + +\item{prob}{The desired simultaneous coverage level of the bands around the +ECDF. A value in (0,1).} + +\item{plot_diff}{Wether to plot the difference between the observed ECDF and +the theoretical expectation when the PIT values are uniform.} + +\item{adj_method}{Method to obtain the simultaneous confidence bands. +Possible values: "interpolate", "simulate", "optimize". +Defaults to "interpolate".} } \value{ The plotting functions return a ggplot object that can be further @@ -237,10 +256,10 @@ quantiles. \code{y} is overlaid on the plot either as a violin, points, or both, depending on the \code{y_draw} argument. } \item{\code{ppc_pit_ecdf()}}{ -The \code{100 * prob}\% central simultaneous confidence intervals for the ECDF -of the empirical PIT values of \code{y} computed with respect to the -corresponding \code{yrep} values. If 'y' and 'yrep'. Th PIT values can also be -provided directly as \code{pit}. +The ECDF of the empirical PIT values of \code{y} computed with respect to the +corresponding \code{yrep} values. \code{100 * prob}\% central simultaneous confidence +intervals are provided to asses if ´y´ and ´yrep´ originate from the same +distribution. The PIT values can also be provided directly as \code{pit}. See Säilynoja et al. for more details.} } } @@ -256,6 +275,11 @@ ppc_dens_overlay(y, yrep[1:25, ]) # ppc_ecdf_overlay with continuous data (set discrete=TRUE if discrete data) ppc_ecdf_overlay(y, yrep[sample(nrow(yrep), 25), ]) } +# ECDF and ECDF difference plot of the PIT values of ´y´ compared to ´yrep +# with 99\% simultaneous confidence bands. +ppc_pit_ecdf(y, yrep, prob=0.99, plot_diff=FALSE) +ppc_pit_ecdf(y, yrep, prob=0.99) + # for ppc_hist,dens,freqpoly,boxplot definitely use a subset yrep rows so # only a few (instead of nrow(yrep)) histograms are plotted @@ -284,6 +308,10 @@ ppc_dens_overlay_grouped(y, yrep[1:25, ], group = group) ppc_ecdf_overlay_grouped(y, yrep[1:25, ], group = group) +# ECDF difference plots of the PIT values by group +# with 99\% simultaneous confidence bands. +ppc_pit_ecdf_grouped(y, yrep, group=group, prob=0.99) + # don't need to only use small number of rows for ppc_violin_grouped # (as it pools yrep draws within groups) color_scheme_set("gray") From 617a76998a046c4b937c233839a8f2099d831f4b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Tue, 30 Nov 2021 23:27:33 +0200 Subject: [PATCH 07/21] Documentation and example for mcmc-rank-ecdf --- R/mcmc-traces.R | 196 +++++++++++++++++++++------------------------ man/MCMC-traces.Rd | 26 ++++-- 2 files changed, 113 insertions(+), 109 deletions(-) diff --git a/R/mcmc-traces.R b/R/mcmc-traces.R index 01427c88..14803325 100644 --- a/R/mcmc-traces.R +++ b/R/mcmc-traces.R @@ -10,6 +10,7 @@ #' @template args-regex_pars #' @template args-transformations #' @template args-facet_args +#' @template args-pit-ecdf #' @param ... Currently ignored. #' @param size An optional value to override the default line size #' for `mcmc_trace()` or the default point size for `mcmc_trace_highlight()`. @@ -113,6 +114,11 @@ #' mcmc_rank_hist(x, pars = c("alpha", "sigma"), ref_line = TRUE) #' mcmc_rank_overlay(x, "alpha") #' +#' # ECDF difference plots of the ranking of MCMC samples between chains. +#' # Provide 99% simultaneous confidence intervals for the chains sampling from +#' the same distribution. +#' mcmc_rank_ecdf(x, prob = 0.99) +#' #' \dontrun{ #' # parse facet label text #' color_scheme_set("purple") @@ -443,20 +449,96 @@ mcmc_rank_ecdf <- regex_pars = character(), transformations = list(), ..., + K = NULL, facet_args = list(), prob = 0.99, - plot_diff = TRUE) { - check_ignored_arguments(...) - .mcmc_rank_ecdf(x, - pars = pars, - regex_pars = regex_pars, - transformations = transformations, - facet_args = facet_args, - prob = prob, - plot_diff = plot_diff - ) + plot_diff = TRUE, + adj_method = "interpolate") { + check_ignored_arguments(..., ok_args = c("M")) + data <- mcmc_trace_data( + x, + pars = pars, + regex_pars = regex_pars, + transformations = transformations + ) + n_iter <- unique(data$n_iterations) + n_chain <- unique(data$n_chains) + n_param <- unique(data$n_parameters) + + x <- if (is.null(K)) { + 0:n_iter / n_iter + } else { + 0:K / K + } + gamma <- adjust_gamma( + N = n_iter, + L = n_chain, + K = if (is.null(K)) { + n_iter + } else { + K + }, + prob = prob, + ..., + adj_method = adj_method + ) + lims <- ecdf_intervals( + N = n_iter, + L = n_chain, + K = if (is.null(K)) { + n_iter + } else { + K + }, + gamma = gamma + ) + data_lim <- data.frame( + upper = lims$upper / n_iter - (plot_diff == TRUE) * x, + lower = lims$lower / n_iter - (plot_diff == TRUE) * x, + x = x + ) + data <- data %>% + group_by(parameter, chain) %>% + dplyr::group_map(~ data.frame( + parameter = .y[1], + chain = .y[2], + ecdf_value = ecdf(.x$value_rank / (n_iter * n_chain))(x) - + (plot_diff == TRUE) * x, + x = x + )) %>% + dplyr::bind_rows() + + mapping <- aes_( + x = ~x, + y = ~ecdf_value, + color = ~chain, + group = ~chain + ) + + scale_color <- scale_color_manual("Chain", values = chain_colors(n_chain)) + + facet_call <- NULL + if (n_param == 1) { + facet_call <- ylab(levels(data$parameter)) + } else { + facet_args$facets <- ~parameter + facet_args$scales <- facet_args$scales %||% "free" + facet_call <- do.call("facet_wrap", facet_args) } + ggplot() + + geom_step(data = data_lim, aes_(x = ~x, y = ~upper), show.legend = FALSE) + + geom_step(data = data_lim, aes_(x = ~x, y = ~lower), show.legend = FALSE) + + geom_step(mapping, data) + + bayesplot_theme_get() + + scale_color + + facet_call + + scale_x_continuous(breaks = pretty) + + legend_move(ifelse(n_chain > 1, "right", "none")) + + xaxis_title(FALSE) + + yaxis_title(on = n_param == 1) +} + #' @rdname MCMC-traces #' @export mcmc_trace_data <- function(x, @@ -639,100 +721,6 @@ mcmc_trace_data <- function(x, yaxis_title(on = n_param == 1) } -.mcmc_rank_ecdf <- function(x, - pars = character(), - regex_pars = character(), - transformations = list(), - facet_args = list(), - ..., - K, - plot_diff = TRUE, - prob = 0.99, - adj_method = "interpolate") { - data <- mcmc_trace_data( - x, - pars = pars, - regex_pars = regex_pars, - transformations = transformations - ) - n_iter <- unique(data$n_iterations) - n_chain <- unique(data$n_chains) - n_param <- unique(data$n_parameters) - - x <- if (missing(K)) { - 0:n_iter / n_iter - } else { - 0:K / K - } - gamma <- adjust_gamma( - N = n_iter, - L = n_chain, - K = if (missing(K)) { - n_iter - } else { - K - }, - conf_level = prob, - ..., - adj_method = adj_method - ) - lims <- ecdf_intervals( - N = n_iter, - L = n_chain, - K = if (missing(K)) { - n_iter - } else { - K - }, - gamma = gamma - ) - data_lim <- data.frame( - upper = lims$upper / n_iter - (plot_diff == TRUE) * x, - lower = lims$lower / n_iter - (plot_diff == TRUE) * x, - x = x - ) - data <- data %>% - group_by(parameter, chain) %>% - dplyr::group_map(~ data.frame( - parameter = .y[1], - chain = .y[2], - ecdf_value = ecdf(.x$value_rank / (n_iter * n_chain))(x) - - (plot_diff == TRUE) * x, - x = x - )) %>% - dplyr::bind_rows() - - mapping <- aes_( - x = ~x, - y = ~ecdf_value, - color = ~chain, - group = ~chain - ) - - scale_color <- scale_color_manual("Chain", values = chain_colors(n_chain)) - - facet_call <- NULL - if (n_param == 1) { - facet_call <- ylab(levels(data$parameter)) - } else { - facet_args$facets <- ~parameter - facet_args$scales <- facet_args$scales %||% "free" - facet_call <- do.call("facet_wrap", facet_args) - } - - ggplot() + - geom_step(data = data_lim, aes_(x = ~x, y = ~upper), show.legend = FALSE) + - geom_step(data = data_lim, aes_(x = ~x, y = ~lower), show.legend = FALSE) + - geom_step(mapping, data) + - bayesplot_theme_get() + - scale_color + - facet_call + - scale_x_continuous(breaks = pretty) + - legend_move(ifelse(n_chain > 1, "right", "none")) + - xaxis_title(FALSE) + - yaxis_title(on = n_param == 1) -} - chain_colors <- function(n) { all_clrs <- unlist(color_scheme_get()) clrs <- switch( diff --git a/man/MCMC-traces.Rd b/man/MCMC-traces.Rd index aaffe983..4266b254 100644 --- a/man/MCMC-traces.Rd +++ b/man/MCMC-traces.Rd @@ -71,9 +71,11 @@ mcmc_rank_ecdf( regex_pars = character(), transformations = list(), ..., + K = NULL, facet_args = list(), - confidence_level = 0.99, - difference = TRUE + prob = 0.99, + plot_diff = TRUE, + adj_method = "interpolate" ) mcmc_trace_data( @@ -189,13 +191,22 @@ of rank-normalized MCMC samples. Defaults to \code{20}.} \item{ref_line}{For the rank plots, whether to draw a horizontal line at the average number of ranks per bin. Defaults to \code{FALSE}.} -\item{confidence_level}{For \code{mcmc_rank_ecdf()}, a value between 0 and 1 +\item{K}{An optional integer defining the number of equally spaced evaluation +points for the ECDF. If the +submitted PIT values are known to be discrete, this should be the number of +discrete cases. Defaults to the smaller of length(y) and ncol(yrep).} + +\item{prob}{For \code{mcmc_rank_ecdf()}, a value between 0 and 1 specifying the desired simultaneous confidence of the confidence bands to be drawn for the rank ECDF plots.} -\item{difference}{For \code{mcmc_rank_ecdf()}, a boolean specifying it the +\item{plot_diff}{For \code{mcmc_rank_ecdf()}, a boolean specifying it the difference between the observed rank ECDFs and the theoretical expectation should be drawn instead of the unmodified rank ECDF plots.} + +\item{adj_method}{Method to obtain the simultaneous confidence bands. +Possible values: "interpolate", "simulate", "optimize". +Defaults to "interpolate".} } \value{ The plotting functions return a ggplot object that can be further @@ -235,7 +246,7 @@ single panel. \item{\code{mcmc_rank_ecdf()}}{ The ECDFs of the ranks from \code{mcmc_rank_hist()} are plotted and simultaneous confidence bands with a coverage determined by -\code{confidence_level} are drawn. By default, the \code{difference} between the +\code{prob} are drawn. By default, the difference between the observed ECDF and the theoretical expectation is drawn. See Säilynoja et al. (2021) for details. } @@ -281,6 +292,11 @@ mcmc_rank_hist(x, "alpha") mcmc_rank_hist(x, pars = c("alpha", "sigma"), ref_line = TRUE) mcmc_rank_overlay(x, "alpha") +# ECDF difference plots of the ranking of MCMC samples between chains. +# Provide 99\% simultaneous confidence intervals for the chains sampling from +the same distribution. +mcmc_rank_ecdf(x, prob = 0.99) + \dontrun{ # parse facet label text color_scheme_set("purple") From 0545e16b9659f7dfba298f94ad3d2a6b64ce733f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Wed, 5 Jan 2022 16:21:33 +0200 Subject: [PATCH 08/21] preparation for interpolation of adjustments --- R/helpers-ppc.R | 32 +++++++++++++++++------- R/mcmc-traces.R | 10 +++++--- R/ppc-distributions.R | 57 ++++++++++++++++++++++--------------------- 3 files changed, 58 insertions(+), 41 deletions(-) diff --git a/R/helpers-ppc.R b/R/helpers-ppc.R index 63efeb54..874dc2ce 100644 --- a/R/helpers-ppc.R +++ b/R/helpers-ppc.R @@ -293,24 +293,38 @@ adjust_gamma <- function(N, K = N, prob = 0.99, M = 1000, - adj_method = "interpolate") { - if (any(c(K, N, L) < 1)) { + interpolate_adj = FALSE) { + if (any( + c(K, N, L) < 1, + all_counts(c(K, N, L)) + )) { abort("Parameters 'N', 'L' and 'K' must be positive integers.") } if (prob >= 1 || prob <= 0) { abort("Value of 'prob' must be in (0,1).") } if (L == 1) { - gamma <- adjust_gamma_optimize(N, K, prob) - } - else { - gamma <- adjust_gamma_simulate(N, L, K, prob, M) + if (interpolate_adj == TRUE) { + gamma <- 0 + } else { + gamma <- adjust_gamma_optimize(N, K, prob) + } + } else { + if (interpolate_adj == TRUE) { + gamma <- 0 + } else { + gamma <- adjust_gamma_simulate(N, + L, + K, + prob, + M) + } } gamma } # Adjust coverage parameter for single sample using the optimization method. -adjust_gamma_optimize <- function(N, K, prob=0.99) { +adjust_gamma_optimize <- function(N, K, prob) { target <- function(gamma, prob, N, K) { z <- 1:(K - 1) / K z1 <- c(0, z) @@ -339,7 +353,7 @@ adjust_gamma_optimize <- function(N, K, prob=0.99) { } # Adjust coverage parameter for multiple chains using simulation method. -adjust_gamma_simulate <- function(N, L, K, prob = 0.99, M = 1000) { +adjust_gamma_simulate <- function(N, L, K, prob, M) { gamma <- numeric(M) z <- (1:(K - 1)) / K n <- N * (L - 1) @@ -397,7 +411,7 @@ alpha_quantile <- function(gamma, alpha, tol = 0.001) { #' @param gamma Adjusted coverage parameter for the marginal distribution #' (binomial for PIT values and hypergeometric for rank transformed chains). #' @noRd -ecdf_intervals <- function(N, L=1, K, gamma) { +ecdf_intervals <- function(N, L = 1, K, gamma) { lims <- list() z <- seq(0, 1, length.out = K + 1) if (L == 1) { diff --git a/R/mcmc-traces.R b/R/mcmc-traces.R index 14803325..1bb4bc18 100644 --- a/R/mcmc-traces.R +++ b/R/mcmc-traces.R @@ -453,8 +453,10 @@ mcmc_rank_ecdf <- facet_args = list(), prob = 0.99, plot_diff = TRUE, - adj_method = "interpolate") { - check_ignored_arguments(..., ok_args = c("M")) + interpolate_adj = FALSE) { + check_ignored_arguments(..., + ok_args = c("K", "pit", "prob", "plot_diff", "interpolate_adj", "M") + ) data <- mcmc_trace_data( x, pars = pars, @@ -479,8 +481,8 @@ mcmc_rank_ecdf <- K }, prob = prob, - ..., - adj_method = adj_method + interpolate_adj = interpolate_adj, + ... ) lims <- ecdf_intervals( N = n_iter, diff --git a/R/ppc-distributions.R b/R/ppc-distributions.R index a7738b6b..28251f89 100644 --- a/R/ppc-distributions.R +++ b/R/ppc-distributions.R @@ -558,8 +558,9 @@ ppc_pit_ecdf <- function(y, K = NULL, prob = .99, plot_diff = TRUE, - adj_method = "interpolate") { - check_ignored_arguments(...) + interpolate_adj = FALSE) { + check_ignored_arguments(..., + ok_args = c("K", "pit", "prob", "plot_diff", "interpolate_adj")) if (is.null(pit)) { pit <- ppc_data(y, yrep) %>% @@ -578,24 +579,23 @@ ppc_pit_ecdf <- function(y, } N <- length(pit) gamma <- adjust_gamma(N, - K = K, - conf_level = prob, - adj_method = adj_method - ) + K = K, + prob = prob, + interpolate_adj = interpolate_adj) lims <- ecdf_intervals(N, K = K, gamma = gamma) ggplot() + aes_( - x = 0:K / K, - y = ecdf(pit)(0:K / K) - (plot_diff == TRUE) * 0:K / K, + x = 1:K / K, + y = ecdf(pit)(seq(0, 1, length.out = K)) - (plot_diff == TRUE) * 1:K / K, color = "y" ) + geom_step(show.legend = FALSE) + geom_step(aes( - y = lims$upper / N - (plot_diff == TRUE) * 0:K / K, + y = lims$upper[-1] / N - (plot_diff == TRUE) * 1:K / K, color = "yrep" ), show.legend = FALSE) + geom_step(aes( - y = lims$lower / N - (plot_diff == TRUE) * 0:K / K, + y = lims$lower[-1] / N - (plot_diff == TRUE) * 1:K / K, color = "yrep" ), show.legend = FALSE) + yaxis_title(FALSE) + @@ -613,20 +613,21 @@ ppc_pit_ecdf_grouped <- yrep, group, ..., - K, - pit, + K = NULL, + pit = NULL, prob = .99, plot_diff = TRUE, - adj_method = "interpolate") { - check_ignored_arguments(...) + interpolate_adj = FALSE) { + check_ignored_arguments(..., + ok_args = c("K", "pit", "prob", "plot_diff", "interpolate_adj")) - if (missing(pit)) { + if (is.null(pit)) { pit <- ppc_data(y, yrep, group) %>% group_by(y_id) %>% dplyr::group_map(~ mean(.x$value[.x$is_y] >= .x$value[!.x$is_y])) %>% unlist() - if (missing(K)) { - K0 <- length(unique(ppc_data(y, yrep)$rep_id)) + if (is.null(K)) { + K <- length(unique(ppc_data(y, yrep)$rep_id)) + 1 } } else { inform("'pit' specified so ignoring 'y', and 'yrep' if specified.") @@ -638,9 +639,9 @@ ppc_pit_ecdf_grouped <- N_g <- sum(group == g) adjust_gamma( N_g, - K = min(N_g, K0), - conf_level = prob, - adj_method = adj_method + K = min(N_g, K), + prob = prob, + interpolate_adj = interpolate_adj ) }) names(gammas) <- unique(group) @@ -649,26 +650,26 @@ ppc_pit_ecdf_grouped <- group_by(group) %>% dplyr::group_map(~ data.frame( ecdf_value = ecdf(.x$pit)( - seq(0, 1, length.out = min(nrow(.x) + 1, K0 + 1))), + seq(0, 1, length.out = min(nrow(.x), K))), group = .y[1], lims_upper = ecdf_intervals( N = nrow(.x), - K = min(nrow(.x), K0), + K = min(nrow(.x), K), gamma = gammas[[unlist(.y[1])]] - )$upper / nrow(.x), + )$upper[-1] / nrow(.x), lims_lower = ecdf_intervals( N = nrow(.x), - K = min(nrow(.x), K0), + K = min(nrow(.x), K), gamma = gammas[[unlist(.y[1])]] - )$lower / nrow(.x), - x = seq(0, 1, length.out = min(nrow(.x) + 1, K0 + 1)) + )$lower[-1] / nrow(.x), + x = seq(0, 1, length.out = min(nrow(.x), K)) )) %>% dplyr::bind_rows() ggplot(data) + aes_( - x = ~x, + x = ~ x, y = ~ ecdf_value - (plot_diff == TRUE) * x, - group = ~group, + group = ~ group, color = "y" ) + geom_step(show.legend = FALSE) + From 14d183c53fadd8feadf5d336a446b4c29b3e6a7d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Fri, 7 Jan 2022 11:32:57 +0200 Subject: [PATCH 09/21] Fix the use of the all_counts function. --- R/helpers-ppc.R | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/R/helpers-ppc.R b/R/helpers-ppc.R index 874dc2ce..411c955b 100644 --- a/R/helpers-ppc.R +++ b/R/helpers-ppc.R @@ -294,10 +294,7 @@ adjust_gamma <- function(N, prob = 0.99, M = 1000, interpolate_adj = FALSE) { - if (any( - c(K, N, L) < 1, - all_counts(c(K, N, L)) - )) { + if (! all_counts(c(K, N, L))) { abort("Parameters 'N', 'L' and 'K' must be positive integers.") } if (prob >= 1 || prob <= 0) { From a1028b015f1b06eb961783ad97a398b0358efe33 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A4ilynoja=20Teemu?= Date: Fri, 21 Jan 2022 16:07:14 +0200 Subject: [PATCH 10/21] Added adjustment value interpolation -> fast plots --- R/helpers-ppc.R | 73 +++++++++++++++++++++++++++++++++--------- R/mcmc-traces.R | 2 +- R/ppc-distributions.R | 4 +-- R/sysdata.rda | Bin 1646920 -> 1676243 bytes 4 files changed, 61 insertions(+), 18 deletions(-) diff --git a/R/helpers-ppc.R b/R/helpers-ppc.R index 411c955b..d8faa100 100644 --- a/R/helpers-ppc.R +++ b/R/helpers-ppc.R @@ -300,22 +300,16 @@ adjust_gamma <- function(N, if (prob >= 1 || prob <= 0) { abort("Value of 'prob' must be in (0,1).") } - if (L == 1) { - if (interpolate_adj == TRUE) { - gamma <- 0 - } else { - gamma <- adjust_gamma_optimize(N, K, prob) - } + if (interpolate_adj == TRUE) { + gamma <- interpolate_gamma(N, K, prob, L) + } else if (L == 1) { + gamma <- adjust_gamma_optimize(N, K, prob) } else { - if (interpolate_adj == TRUE) { - gamma <- 0 - } else { - gamma <- adjust_gamma_simulate(N, - L, - K, - prob, - M) - } + gamma <- adjust_gamma_simulate(N, + L, + K, + prob, + M) } gamma } @@ -370,6 +364,55 @@ adjust_gamma_simulate <- function(N, L, K, prob, M) { alpha_quantile(gamma, 1 - prob) } +interpolate_gamma <- function(N, K, p, L) { + vals <- get_interpolation_values(N, K, L, p) + N_lb <- max(vals[vals$N <= N, ]$N) + N_ub <- min(vals[vals$N >= N, ]$N) + g_lb <- approx( + x = log(vals[vals$N == N_lb, ]$K), + y = log(vals[vals$N == N_lb, ]$val), + xout = log(K) + )$y + g_ub <- approx( + x = log(vals[vals$N == N_ub, ]$K), + y = log(vals[vals$N == N_ub, ]$val), + xout = log(K) + )$y + if (N_ub == N_lb) { + g <- exp(g_lb) + } else { + g <- exp(approx(x = log(c(N_lb, N_ub)), y = c(g_lb, g_ub), xout = log(N))$y) + } + g +} + +get_interpolation_values <- function(N, K, L, p) { + for (dim in c("L", "prob")) { + if (all(get(if (dim == "L") dim else "p") != bayesplot:::gamma_adj[, dim])) { + stop(paste( + "No precomputed values to interpolate from for '", dim, "' = ", + get(if (dim == "L") dim else "p"), + ".\n", + "Values of '", dim, "' available for interpolation: ", + unique(bayesplot:::gamma_adj[, dim]), + ".", + sep = "" + )) + } + } + vals <- bayesplot:::gamma_adj[bayesplot:::gamma_adj$L == L & bayesplot:::gamma_adj$prob == p, ] + if (K > max(vals[vals$N <= N, ]$K)) { + stop(paste( + "No precomputed values available for interpolation for 'K' = ", + K, + ".\n", + "Try either setting a value of 'K' <= ", + max(vals[vals$N <= N, ]$K), + "or 'interpolate_adj' = FALSE." + )) + } + vals +} #' A helper function for 'adjust_gamma_optimize' defining the probability that #' an ECDF stays within the supplied bounds between z1 and z2. #' @noRd diff --git a/R/mcmc-traces.R b/R/mcmc-traces.R index 1bb4bc18..f0118d17 100644 --- a/R/mcmc-traces.R +++ b/R/mcmc-traces.R @@ -453,7 +453,7 @@ mcmc_rank_ecdf <- facet_args = list(), prob = 0.99, plot_diff = TRUE, - interpolate_adj = FALSE) { + interpolate_adj = TRUE) { check_ignored_arguments(..., ok_args = c("K", "pit", "prob", "plot_diff", "interpolate_adj", "M") ) diff --git a/R/ppc-distributions.R b/R/ppc-distributions.R index 28251f89..0a55c04d 100644 --- a/R/ppc-distributions.R +++ b/R/ppc-distributions.R @@ -558,7 +558,7 @@ ppc_pit_ecdf <- function(y, K = NULL, prob = .99, plot_diff = TRUE, - interpolate_adj = FALSE) { + interpolate_adj = TRUE) { check_ignored_arguments(..., ok_args = c("K", "pit", "prob", "plot_diff", "interpolate_adj")) @@ -617,7 +617,7 @@ ppc_pit_ecdf_grouped <- pit = NULL, prob = .99, plot_diff = TRUE, - interpolate_adj = FALSE) { + interpolate_adj = TRUE) { check_ignored_arguments(..., ok_args = c("K", "pit", "prob", "plot_diff", "interpolate_adj")) diff --git 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