redist_ci: Confidence Intervals for SMC and MCMC Estimates

In redist: Simulation Methods for Legislative Redistricting

Confidence Intervals for SMC and MCMC Estimates

Description

Builds a confidence interval for a quantity of interest. If multiple runs are available, uses the between-run variation to estimate the standard error. If only one run is available, uses information on the SMC particle/plan genealogy to estimate the standard error, using a variant of the method of Olson & Douc (2019). The multiple-run estimator is more reliable, especially for situations with many districts, and should be used when parallelism is available. All reference plans are ignored.

Usage

redist_ci(plans, x, district = 1L, conf = 0.9, by_chain = FALSE)

redist_smc_ci(plans, x, district = 1L, conf = 0.9, by_chain = FALSE)

redist_mcmc_ci(plans, x, district = 1L, conf = 0.9, by_chain = FALSE)

Arguments

plans	a redist_plans object.
x	the quantity to build an interval for. Tidy-evaluated within plans.
district	for redist_plans objects with multiple districts, which district to subset to. Set to NULL to perform no subsetting.
conf	the desired confidence level.
by_chain	Whether the confidence interval should indicate overall sampling uncertainty (FALSE) or per-chain sampling uncertainty (TRUE). In the latter case the intervals will be wider by a factor of sqrt(runs).

Value

A tibble with three columns: X, X_lower, and X_upper, where X is the name of the vector of interest, containing the mean and confidence interval. When used inside summarize() this will create three columns in the output data.

Functions

• redist_smc_ci(): Compute confidence intervals for SMC output.

• redist_mcmc_ci(): Compute confidence intervals for MCMC output.

References

Lee, A., & Whiteley, N. (2018). Variance estimation in the particle filter. Biometrika, 105(3), 609-625.

Olsson, J., & Douc, R. (2019). Numerically stable online estimation of variance in particle filters. Bernoulli, 25(2), 1504-1535.

H. P. Chan and T. L. Lai. A general theory of particle filters in hidden Markov models and some applications. Ann. Statist., 41(6):2877–2904, 2013.

Examples

library(dplyr)
data(iowa)

iowa_map <- redist_map(iowa, existing_plan = cd_2010, pop_tol = 0.05)
plans <- redist_mergesplit_parallel(iowa_map, nsims = 200, chains = 2, silent = TRUE) %>%
    mutate(dem = group_frac(iowa_map, dem_08, dem_08 + rep_08)) %>%
    number_by(dem)
redist_smc_ci(plans, dem)

redist documentation built on April 3, 2023, 5:46 p.m.