Find outlying "black swan" jumps in trends

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

Arguments

rotated_modelfit

Output from rotate_trends().

threshold

A probability threshold below which to flag trend events as extreme

plot

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 4.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.41 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> 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: 0.251 seconds (Warm-up)
#> Chain 1:                0.002 seconds (Sampling)
#> Chain 1:                0.253 seconds (Total)
#> Chain 1: 
#> Warning: There were 24 divergent transitions after warmup. See
#> https://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 1.11, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://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
#> https://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
#> https://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]       -1.8  -1.8  -1.8  -1.8 0.0  1.29        4       13
#> x[1,2]       -2.4  -2.4  -2.4  -2.4 0.0  1.29        4       13
#> x[1,3]       -2.9  -2.9  -2.9  -2.9 0.0  1.29        4       13
#> x[1,4]       -3.1  -3.1  -3.1  -3.1 0.0  1.29        4       13
#> x[1,5]       -2.3  -2.3  -2.3  -2.3 0.0  1.29        4       13
#> x[1,6]       -2.5  -2.5  -2.5  -2.5 0.0  1.29        4       13
#> x[1,7]       -2.1  -2.1  -2.0  -2.1 0.0  1.29        4       13
#> x[1,8]       -2.3  -2.3  -2.3  -2.3 0.0  1.29        4       13
#> x[1,9]       -2.3  -2.3  -2.3  -2.3 0.0  1.29        4       13
#> x[1,10]      -1.6  -1.6  -1.6  -1.6 0.0  1.29        4       13
#> x[1,11]      -2.0  -2.0  -2.0  -2.0 0.0  1.29        4       13
#> x[1,12]      -2.8  -2.8  -2.8  -2.8 0.0  1.29        4       13
#> x[1,13]      -0.8  -0.8  -0.8  -0.8 0.0  1.29        4       13
#> x[1,14]      -1.0  -1.0  -1.0  -1.0 0.0  1.29        4       13
#> x[1,15]      -0.3  -0.3  -0.3  -0.3 0.0  1.29        4       13
#> x[1,16]      -1.0  -1.0  -1.0  -1.0 0.0  1.29        4       13
#> x[1,17]      -1.1  -1.1  -1.1  -1.1 0.0  1.29        4       13
#> x[1,18]      -0.4  -0.4  -0.4  -0.4 0.0  1.29        4       13
#> x[1,19]      -0.5  -0.5  -0.5  -0.5 0.0  1.29        4       13
#> x[1,20]       0.6   0.6   0.6   0.6 0.0  1.29        4       13
#> x[1,21]       0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> x[1,22]       0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> x[1,23]       0.6   0.6   0.6   0.6 0.0  1.29        4       13
#> x[1,24]       1.7   1.7   1.7   1.7 0.0  1.29        4       13
#> x[1,25]       2.4   2.4   2.4   2.4 0.0  1.29        4       13
#> x[1,26]       2.4   2.4   2.4   2.4 0.0  1.29        4       13
#> x[1,27]       3.6   3.6   3.6   3.6 0.0  1.29        4       13
#> x[1,28]       4.5   4.5   4.5   4.5 0.0  1.29        4       13
#> x[1,29]       5.6   5.6   5.6   5.6 0.0  1.29        4       13
#> x[1,30]       5.6   5.6   5.6   5.6 0.0  1.29        4       13
#> Z[1,1]       -0.3  -0.3  -0.3  -0.3 0.0  1.29        4       13
#> Z[2,1]       -0.4  -0.4  -0.4  -0.4 0.0  1.29        4       13
#> Z[3,1]       -0.5  -0.5  -0.3  -0.4 0.1  1.29        4       13
#> log_lik[1]    0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[2]    0.0   0.1   0.1   0.0 0.0  1.29        4       13
#> log_lik[3]   -0.1  -0.1   0.1  -0.1 0.1  1.29        4       13
#> log_lik[4]   -0.1  -0.1   0.0  -0.1 0.0  1.29        4       13
#> log_lik[5]   -0.1   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[6]   -0.4  -0.4   0.0  -0.3 0.2  1.29        4       13
#> log_lik[7]    0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[8]   -0.4  -0.2  -0.2  -0.2 0.1  1.29        4       13
#> log_lik[9]   -0.3  -0.3   0.1  -0.2 0.2  1.29        4       13
#> log_lik[10]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[11]  -0.1   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[12]  -0.3  -0.3   0.1  -0.2 0.1  1.29        4       13
#> log_lik[13]   0.0   0.0   0.1   0.1 0.0  1.29        4       13
#> log_lik[14]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[15]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[16]   0.0   0.0   0.1   0.1 0.0  1.29        4       13
#> log_lik[17]  -0.4  -0.2  -0.2  -0.3 0.1  1.29        4       13
#> log_lik[18]  -0.6  -0.6   0.0  -0.4 0.3  1.29        4       13
#> log_lik[19]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[20]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[21]  -0.1   0.1   0.1   0.0 0.1  1.29        4       13
#> log_lik[22]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[23]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[24]  -0.1   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[25]  -0.1  -0.1   0.0   0.0 0.0  1.29        4       13
#> log_lik[26]  -0.1   0.0   0.0  -0.1 0.0  1.29        4       13
#> log_lik[27]  -0.2  -0.2   0.1  -0.1 0.1  1.29        4       13
#> log_lik[28]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[29]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[30]  -0.2   0.1   0.1   0.0 0.1  1.29        4       13
#> log_lik[31]   0.0   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[32]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[33]  -0.3  -0.3   0.1  -0.2 0.1  1.29        4       13
#> log_lik[34]  -0.2   0.0   0.0  -0.1 0.1  1.29        4       13
#> log_lik[35]  -0.3  -0.1  -0.1  -0.1 0.1  1.29        4       13
#> log_lik[36]  -0.8  -0.8   0.0  -0.6 0.3  1.29        4       13
#> log_lik[37]  -1.0  -1.0  -0.9  -1.0 0.0  1.29        4       13
#> log_lik[38]  -0.6  -0.6  -0.5  -0.5 0.0  1.29        4       13
#> log_lik[39]  -0.9  -0.6  -0.6  -0.6 0.1  1.29        4       13
#> log_lik[40]  -0.3  -0.3  -0.2  -0.3 0.0  1.29        4       13
#> log_lik[41]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[42]   0.0   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[43] -26.6 -26.3 -26.3 -26.4 0.1  1.29        4       13
#> log_lik[44]  -0.5  -0.5  -0.4  -0.4 0.0  1.29        4       13
#> log_lik[45]  -0.3  -0.2  -0.2  -0.2 0.0  1.29        4       13
#> log_lik[46]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[47]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[48]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[49]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[50]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[51]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[52]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[53]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[54]  -0.1   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[55]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[56]  -0.3  -0.3  -0.3  -0.3 0.0  1.29        4       13
#> log_lik[57]  -0.1  -0.1   0.0  -0.1 0.0  1.29        4       13
#> log_lik[58]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[59]  -0.1  -0.1  -0.1  -0.1 0.0  1.29        4       13
#> log_lik[60]   0.0   0.1   0.1   0.0 0.0  1.29        4       13
#> log_lik[61]  -0.4  -0.4  -0.4  -0.4 0.0  1.29        4       13
#> log_lik[62]  -0.8  -0.8  -0.8  -0.8 0.0  1.29        4       13
#> log_lik[63]  -1.0  -0.9  -0.9  -0.9 0.0  1.29        4       13
#> log_lik[64]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[65]  -0.2  -0.2  -0.2  -0.2 0.0  1.29        4       13
#> log_lik[66]  -0.4  -0.3  -0.3  -0.3 0.0  1.29        4       13
#> log_lik[67]   0.1   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[68]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[69]  -0.1   0.0   0.0  -0.1 0.0  1.29        4       13
#> log_lik[70]  -0.2  -0.2  -0.1  -0.2 0.0  1.29        4       13
#> log_lik[71]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[72]   0.0   0.1   0.1   0.0 0.0  1.29        4       13
#> log_lik[73]   0.0   0.0   0.0   0.0 0.0  1.29        4       13
#> log_lik[74]   0.0   0.1   0.1   0.1 0.0  1.29        4       13
#> log_lik[75]  -0.1  -0.1   0.1  -0.1 0.1  1.29        4       13
#> log_lik[76]  -0.2  -0.2  -0.1  -0.2 0.1  1.29        4       13
#> log_lik[77]  -0.1  -0.1   0.0  -0.1 0.0  1.29        4       13
#> log_lik[78]  -0.5   0.0   0.0  -0.1 0.2  1.29        4       13
#> log_lik[79]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[80]  -0.1  -0.1   0.0   0.0 0.1  1.29        4       13
#> log_lik[81]  -0.5   0.1   0.1  -0.1 0.3  1.29        4       13
#> log_lik[82]  -0.1  -0.1   0.1   0.0 0.1  1.29        4       13
#> log_lik[83]   0.0   0.0   0.1   0.0 0.0  1.29        4       13
#> log_lik[84]  -0.8   0.1   0.1  -0.1 0.4  1.29        4       13
#> log_lik[85]   0.0   0.1   0.1   0.0 0.0  1.29        4       13
#> log_lik[86]   0.0   0.1   0.1   0.0 0.0  1.29        4       13
#> log_lik[87]  -0.4  -0.4  -0.3  -0.3 0.0  1.29        4       13
#> log_lik[88]  -0.2   0.0   0.0   0.0 0.1  1.29        4       13
#> log_lik[89]   0.0   0.1   0.1   0.0 0.0  1.29        4       13
#> log_lik[90]  -0.5  -0.5  -0.2  -0.4 0.1  1.29        4       13
#> xstar[1,1]    3.7   6.0   7.3   5.7 1.3  1.07        8       13
#> sigma[1]      0.4   0.4   0.4   0.4 0.0  1.29        4       13
#> lp__        -35.4 -35.4 -35.2 -35.4 0.1  1.29        4       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)