Importance resampling (SIR)

Computes importance weights \(w_i = p(x_i)/g(x_i)\) for draws from a proposal and resamples m of them with probability proportional to the weights (Rubin 1988; Smith and Gelfand 1992). The reported effective sample size \(1/\sum \bar w_i^2\) is the usual diagnostic: it falls towards 1 when a single draw dominates, which is the signal that the proposal is too far from the target for the resample to be usable.

Usage

morie_bayisr(samples, log_target, log_proposal, m, seed = 0)

Arguments

samples

List of draws from the proposal.

log_target, log_proposal

Functions giving the unnormalised log target and the log proposal density.

m

Number of resampled draws.

seed

Seed for the generator shared with the Python arm.

Value

A list with resample, indices (0-based), weights (normalised), ess, n, m, seed, method.

References

Smith, A. F. M. and Gelfand, A. E. (1992). Bayesian statistics without tears. The American Statistician, 46(2), 84-88.

Examples

set.seed(1)
morie_bayisr(samples = as.list(rnorm(100)), log_target = function(x) -0.5 * x^2,
             log_proposal = function(x) -0.5 * x^2, m = 20)
#> $resample
#> $resample[[1]]
#> [1] 0.5566632
#> 
#> $resample[[2]]
#> [1] -0.8356286
#> 
#> $resample[[3]]
#> [1] -0.5732654
#> 
#> $resample[[4]]
#> [1] 1.511781
#> 
#> $resample[[5]]
#> [1] 0.3876716
#> 
#> $resample[[6]]
#> [1] 0.9438362
#> 
#> $resample[[7]]
#> [1] 0.001105352
#> 
#> $resample[[8]]
#> [1] 0.6198257
#> 
#> $resample[[9]]
#> [1] 0.5584864
#> 
#> $resample[[10]]
#> [1] 0.7631757
#> 
#> $resample[[11]]
#> [1] -0.4432919
#> 
#> $resample[[12]]
#> [1] 0.3411197
#> 
#> $resample[[13]]
#> [1] 1.9804
#> 
#> $resample[[14]]
#> [1] 0.4755095
#> 
#> $resample[[15]]
#> [1] -0.6120264
#> 
#> $resample[[16]]
#> [1] -0.1123462
#> 
#> $resample[[17]]
#> [1] -0.4432919
#> 
#> $resample[[18]]
#> [1] 0.9189774
#> 
#> $resample[[19]]
#> [1] 0.5939462
#> 
#> $resample[[20]]
#> [1] 0.3329504
#> 
#> 
#> $indices
#>  [1] 43  2 97 10 32 17 77 24 95 39 76 52 55 70 51 48 76 20 84 85
#> 
#> $weights
#>   [1] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#>  [16] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#>  [31] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#>  [46] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#>  [61] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#>  [76] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#>  [91] 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
#> 
#> $ess
#> [1] 100
#> 
#> $n
#> [1] 100
#> 
#> $m
#> [1] 20
#> 
#> $seed
#> [1] 0
#> 
#> $method
#> [1] "SIR weighted bootstrap (Rubin 1988; Smith-Gelfand 1992)"
#>