Description Usage Arguments Value Author(s) References See Also Examples
View source: R/degross_lpost.R
Log-posterior (with gradient and Fisher information) for given spline parameters, small bin frequencies, tabulated sample moments and roughness penalty parameter. This function is maximized during the M-step of the EM algorithm to estimate the B-spline parameters entering the density specification.
1 2 3 | degross_lpost(phi, tau, n.i, degross.data,
use.moments = rep(TRUE,4), freq.min = 20, diag.only=FALSE,
penalize = TRUE, aa = 2, bb = 1e-6, pen.order = 3)
|
phi |
Vector of K B-spline parameters φ to specify the log-density. |
tau |
Roughness penalty parameter. |
n.i |
Small bin frequencies. |
degross.data |
A degrossData.object created using the degrossData function. |
use.moments |
Vector with 4 logicals indicating which tabulated sample moments to use as soft constraints. Defaults: |
freq.min |
Minimal big bin frequency required to use the corresponding observed moments as soft constraints. Default: |
diag.only |
Logical indicating whether to ignore the off-diagonal elements of the variance-covariance matrix of the sample central moments. Default: FALSE. |
penalize |
Logical indicating whether a roughness penalty of order |
aa |
Positive real giving the first parameter in the Gamma prior for |
bb |
Positive real giving the second parameter in the Gamma prior for |
pen.order |
Integer giving the order of the roughness penalty. Default: |
A list containing :
lpost
, lpost.ni
:
value of the log-posterior based on the given small bin frequencies n.i
and the tabulated sample moments.
lpost.mj
:
value of the log-posterior based on the big bin frequencies degross.data$freq.j
and the tabulated sample moments.
llik.ni
:
multinomial log-likelihood based on the given small bin frequencies n.i
.
llik.mj
:
multinomial log-likelihood based on the big bin frequencies degross.data$freq.j
.
moments.penalty
:
log of the joint (asymptotic) density for the observed sample moments.
penalty
:
\log p(φ|τ) + \log p(τ).
Score
, Score.ni
:
score (w.r.t. φ) of lpost.ni
.
Score.mj
:
score (w.r.t. φ) of lpost.mj
.
Fisher
& Fisher.ni
:
information matrix (w.r.t. φ) of lpost.ni
.
Fisher.mj
:
information matrix (w.r.t. φ) of lpost.mj
.
M.j
:
theoretical moments of the density (resulting from φ) within a big bin.
pi.i
:
small bin probabilities.
ui
:
small bin midpoints.
delta
:
width of the small bins.
gamma.j
:
Big bin probabilities.
tau
:
reminder of the value of the roughness penalty parameter τ.
phi
:
reminder of the vector of spline parameters (defining the density).
n.i
:
reminder of the small bin frequencies given as input.
Philippe Lambert p.lambert@uliege.be
Lambert, P. (2021) Moment-based density and risk estimation from grouped summary statistics. arXiv:2107.03883.
degross_lpostBasic
, degross
, degross.object
.
1 2 3 4 5 6 7 | sim = simDegrossData(n=3500, plotting=TRUE,choice=2) ## Generate grouped data
obj.data = degrossData(Big.bins=sim$Big.bins, freq.j=sim$freq.j, m.j=sim$m.j)
print(obj.data)
obj.fit = degross(obj.data) ## Estimate the underlying density
## Evaluate the log-posterior at convergence
res = with(obj.fit, degross_lpost(phi, tau, n.i, obj.data, diag.only=diag.only))
print(res$Score) ## Score of the log posterior at convergence
|
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