Y | x ~ Poisson(exp(f(x))) with f a finite random series. The log
link keeps the rate positive without constraining the coefficients,
and gradient ascent on the MAP objective recovers the log-rate; the
reported error is the mean absolute deviation of the fitted f from the
truth f0(x) = 1 + 0.8 cos(pi x) over a uniform grid.
Usage
Ghosalfrspoireg(n = 800, K = 3, seed = 42)
Arguments
- n
Sample size.
- K
Number of basis terms.
- seed
Seed for the deterministic draws.
Value
List with estimate (mean absolute error of the fitted
log-rate), beta, method.
Details
Formula: grad_k = sum_i (y_i - exp(min(f(x_i), 5))) phi_k(x_i),
beta <- beta + step grad - decay beta.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 10.4.4.
Examples
Ghosalfrspoireg()
#> $estimate
#> [1] 0.03708307
#>
#> $beta
#> [1] 0.98893976 0.60547045 -0.01954952
#>
#> $method
#> [1] "series Poisson regression (GvdV 2017 sec. 10.4.4)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
