Find outlying "black swan" jumps in trends

find_swans(rotated_modelfit, threshold = 0.01, plot = FALSE)

## Arguments

rotated_modelfit Output from rotate_trends(). A probability threshold below which to flag trend events as extreme Logical: should a plot be made?

## Value

Prints a ggplot2 plot if plot = TRUE; returns a data frame indicating the probability that any given point in time represents a "black swan" event invisibly.

## References

Anderson, S.C., Branch, T.A., Cooper, A.B., and Dulvy, N.K. 2017. Black-swan events in animal populations. Proceedings of the National Academy of Sciences 114(12): 3252–3257. https://doi.org/10.1073/pnas.1611525114

## Examples

set.seed(1)
s <- sim_dfa(num_trends = 1, num_ts = 3, num_years = 30)
s$y_sim[1, 15] <- s$y_sim[1, 15] - 6
plot(s$y_sim[1, ], type = "o") abline(v = 15, col = "red") # only 1 chain and 250 iterations used so example runs quickly: m <- fit_dfa(y = s$y_sim, num_trends = 1, iter = 50, chains = 1, nu_fixed = 2)
#>
#> SAMPLING FOR MODEL 'dfa' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 3.8e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds.
#> Chain 1:
#> Chain 1:
#> Chain 1: WARNING: There aren't enough warmup iterations to fit the
#> Chain 1:          three stages of adaptation as currently configured.
#> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of
#> Chain 1:          the given number of warmup iterations:
#> Chain 1:            init_buffer = 3
#> Chain 1:            adapt_window = 20
#> Chain 1:            term_buffer = 2
#> Chain 1:
#> Chain 1: Iteration:  1 / 50 [  2%]  (Warmup)
#> Chain 1: Iteration:  5 / 50 [ 10%]  (Warmup)
#> Chain 1: Iteration: 10 / 50 [ 20%]  (Warmup)
#> Chain 1: Iteration: 15 / 50 [ 30%]  (Warmup)
#> Chain 1: Iteration: 20 / 50 [ 40%]  (Warmup)
#> Chain 1: Iteration: 25 / 50 [ 50%]  (Warmup)
#> Chain 1: Iteration: 26 / 50 [ 52%]  (Sampling)
#> Chain 1: Iteration: 30 / 50 [ 60%]  (Sampling)
#> Chain 1: Iteration: 35 / 50 [ 70%]  (Sampling)
#> Chain 1: Iteration: 40 / 50 [ 80%]  (Sampling)
#> Chain 1: Iteration: 45 / 50 [ 90%]  (Sampling)
#> Chain 1: Iteration: 50 / 50 [100%]  (Sampling)
#> Chain 1:
#> Chain 1:  Elapsed Time: 0.175159 seconds (Warm-up)
#> Chain 1:                0.00241 seconds (Sampling)
#> Chain 1:                0.177569 seconds (Total)
#> Chain 1: #> Warning: There were 25 divergent transitions after warmup. See
#> http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.#> Warning: Examine the pairs() plot to diagnose sampling problems#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> http://mc-stan.org/misc/warnings.html#r-hat#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> http://mc-stan.org/misc/warnings.html#bulk-ess#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> http://mc-stan.org/misc/warnings.html#tail-ess#> Inference for the input samples (1 chains: each with iter = 25; warmup = 12):
#>
#>                Q5   Q50   Q95  Mean  SD  Rhat Bulk_ESS Tail_ESS
#> x[1,1]       -1.3  -1.3  -1.3  -1.3 0.0  1.00       13       13
#> x[1,2]       -1.9  -1.9  -1.9  -1.9 0.0  1.00       13       13
#> x[1,3]       -2.2  -2.2  -2.2  -2.2 0.0  1.00       13       13
#> x[1,4]       -2.4  -2.4  -2.4  -2.4 0.0  1.00       13       13
#> x[1,5]       -2.7  -2.7  -2.7  -2.7 0.0  1.00       13       13
#> x[1,6]       -2.1  -2.1  -2.1  -2.1 0.0  1.00       13       13
#> x[1,7]       -2.1  -2.1  -2.1  -2.1 0.0  1.00       13       13
#> x[1,8]       -2.3  -2.3  -2.3  -2.3 0.0  1.00       13       13
#> x[1,9]       -2.1  -2.1  -2.1  -2.1 0.0  1.00       13       13
#> x[1,10]      -1.8  -1.8  -1.8  -1.8 0.0  1.00       13       13
#> x[1,11]      -1.8  -1.8  -1.8  -1.8 0.0  1.00       13       13
#> x[1,12]      -1.4  -1.4  -1.4  -1.4 0.0  1.00       13       13
#> x[1,13]      -1.1  -1.1  -1.1  -1.1 0.0  1.00       13       13
#> x[1,14]      -0.8  -0.8  -0.8  -0.8 0.0  1.00       13       13
#> x[1,15]      -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> x[1,16]      -0.7  -0.7  -0.7  -0.7 0.0  1.00       13       13
#> x[1,17]      -1.0  -1.0  -1.0  -1.0 0.0  1.00       13       13
#> x[1,18]      -0.6  -0.6  -0.6  -0.6 0.0  1.00       13       13
#> x[1,19]      -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> x[1,20]       0.2   0.2   0.2   0.2 0.0  1.00       13       13
#> x[1,21]       1.3   1.3   1.3   1.3 0.0  1.00       13       13
#> x[1,22]       1.1   1.1   1.1   1.1 0.0  1.00       13       13
#> x[1,23]       0.8   0.8   0.8   0.8 0.0  1.00       13       13
#> x[1,24]       1.8   1.8   1.8   1.8 0.0  1.00       13       13
#> x[1,25]       1.9   1.9   1.9   1.9 0.0  1.00       13       13
#> x[1,26]       3.1   3.1   3.1   3.1 0.0  1.00       13       13
#> x[1,27]       4.1   4.1   4.1   4.1 0.0  1.00       13       13
#> x[1,28]       4.9   4.9   4.9   4.9 0.0  1.00       13       13
#> x[1,29]       5.5   5.5   5.5   5.5 0.0  1.00       13       13
#> x[1,30]       5.5   5.5   5.5   5.5 0.0  1.00       13       13
#> Z[1,1]       -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> Z[2,1]       -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> Z[3,1]       -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[1]   -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> log_lik[2]   -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[3]   -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[4]   -0.6  -0.6  -0.6  -0.6 0.0  1.00       13       13
#> log_lik[5]    0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[6]    0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[7]   -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[8]    0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[9]   -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[10]  -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> log_lik[11]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[12]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[13]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[14]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[15]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[16]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[17]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[18]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[19]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[20]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[21]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[22]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[23]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[24]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[25]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[26]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[27]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[28]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[29]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[30]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[31]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[32]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[33]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[34]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[35]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[36]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[37]  -0.7  -0.7  -0.7  -0.7 0.0  1.00       13       13
#> log_lik[38]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[39]  -0.5  -0.5  -0.5  -0.5 0.0  1.00       13       13
#> log_lik[40]  -0.5  -0.5  -0.5  -0.5 0.0  1.00       13       13
#> log_lik[41]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[42]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[43] -22.6 -22.6 -22.6 -22.6 0.0  1.00       13       13
#> log_lik[44]  -0.5  -0.5  -0.5  -0.5 0.0  1.00       13       13
#> log_lik[45]  -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> log_lik[46]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[47]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[48]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[49]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[50]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[51]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[52]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[53]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[54]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[55]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[56]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[57]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[58]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[59]  -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> log_lik[60]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[61]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[62]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[63]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[64]  -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> log_lik[65]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[66]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[67]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[68]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[69]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[70]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[71]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[72]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[73]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[74]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[75]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[76]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[77]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[78]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[79]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[80]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[81]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[82]  -0.1  -0.1  -0.1  -0.1 0.0  1.00       13       13
#> log_lik[83]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[84]  -0.4  -0.4  -0.4  -0.4 0.0  1.00       13       13
#> log_lik[85]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> log_lik[86]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[87]  -0.3  -0.3  -0.3  -0.3 0.0  1.00       13       13
#> log_lik[88]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[89]   0.0   0.0   0.0   0.0 0.0  1.00       13       13
#> log_lik[90]  -0.2  -0.2  -0.2  -0.2 0.0  1.00       13       13
#> xstar[1,1]    4.1   5.8   7.8   5.9 1.3  1.07       13       13
#> sigma[1]      0.4   0.4   0.4   0.4 0.0  1.00       13       13
#> lp__        -29.7 -29.7 -29.7 -29.7 0.0  1.00       13       13
#>
#> For each parameter, Bulk_ESS and Tail_ESS are crude measures of
#> effective sample size for bulk and tail quantities respectively (an ESS > 100
#> per chain is considered good), and Rhat is the potential scale reduction
#> factor on rank normalized split chains (at convergence, Rhat <= 1.05).r <- rotate_trends(m)
p <- plot_trends(r) #+ geom_vline(xintercept = 15, colour = "red")
print(p)
# a 1 in 1000 probability if was from a normal distribution:
find_swans(r, plot = TRUE, threshold = 0.001)