lnorm_p1_lmn

One component of the second derivative of the normalized log-likelihood

Generates predictive distributions based on calibrating priors
for various commonly used statistical models, including models with
predictors. Routines for densities, probabilities, quantiles, random
deviates and the parameter posterior are provided. The predictions are
generated from the Bayesian prediction integral, with priors chosen to
give good reliability (also known as calibration). For homogeneous models,
the prior is set to the right Haar prior, giving predictions which are
exactly reliable. As a result, in repeated testing, the frequencies of
out-of-sample outcomes and the probabilities from the predictions agree.
For other models, the prior is chosen to give good reliability. Where
possible, the Bayesian prediction integral is solved exactly. Where exact
solutions are not possible, the Bayesian prediction integral is solved
using the Datta-Mukerjee-Ghosh-Sweeting (DMGS) asymptotic expansion.
Optionally, the prediction integral can also be solved using posterior
samples generated using Paul Northrop's ratio of uniforms sampling package
('rust'). Results are also generated based on maximum likelihood, for
comparison purposes. Various model selection diagnostics and testing
routines are included. Based on "Reducing reliability bias in assessments
of extreme weather risk using calibrating priors", Jewson, S., Sweeting, T.
and Jewson, L. (2024); <doi:10.5194/ascmo-11-1-2025>.

Stephen Jewson

fitdistcp

Distribution Fitting with Calibrating Priors for Commonly Used
Distributions

lnorm_p1_lmn function

<dl><dt>x</dt>
<dd>a vector of training data values</dd>
<dt>t</dt>
<dd>a vector or matrix of predictors</dd>
<dt>v1</dt>
<dd>first parameter</dd>
<dt>d1</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>
<dt>v2</dt>
<dd>second parameter</dd>
<dt>d2</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>
<dt>v3</dt>
<dd>third parameter</dd>
<dt>fd3</dt>
<dd>the fractional delta used in the numerical derivatives with respect to the parameter</dd>
<dt>mm</dt>
<dd>an index for which derivative to calculate</dd>
<dt>nn</dt>
<dd>an index for which derivative to calculate</dd></dl>

Arguments

One component of the second derivative of the normalized log-likelihood — lnorm_p1_lmn

<dl>

<dt>x</dt>
<dd>a vector of training data values</dd>


<dt>t</dt>
<dd>a vector or matrix of predictors</dd>


<dt>v1</dt>
<dd>first parameter</dd>


<dt>d1</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>


<dt>v2</dt>
<dd>second parameter</dd>


<dt>d2</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>


<dt>v3</dt>
<dd>third parameter</dd>


<dt>fd3</dt>
<dd>the fractional delta used in the numerical derivatives with respect to the parameter</dd>


<dt>mm</dt>
<dd>an index for which derivative to calculate</dd>


<dt>nn</dt>
<dd>an index for which derivative to calculate</dd>

</dl>

lnorm_p1_lmn: One component of the second derivative of the normalized log-likelihood

Description

Usage

Value

Arguments