From c62c355728286ffd195b5c4f7f7b9406492deab8 Mon Sep 17 00:00:00 2001 From: Claude Date: Fri, 16 Oct 2026 17:16:35 +0000 Subject: [PATCH 1/3] Print the true mean function as mu and the noise term as nu Co-Authored-By: Claude Sonnet 5.5 Claude-Session: https://claude.ai/code/session_01H8gaSFRnPKEfpCbBRqEzZH --- interpretations.tsv | 16 ++++++++-------- macros.qmd | 6 +++--- 2 files changed, 11 insertions(+), 11 deletions(-) diff --git a/interpretations.tsv b/interpretations.tsv index 50a8e874..67e80893 100644 --- a/interpretations.tsv +++ b/interpretations.tsv @@ -1149,8 +1149,8 @@ name interpretation \hcovmat an estimated covariance matrix (prints \hat{\Sigma}) \ecovmat an estimated covariance matrix (forward-looking form) (prints \est{\covmat}) \corpar a correlation parameter (prints \rho) -\noise a model error term (prints \varepsilon) -\vnoise a vector of model error terms (prints \vec{\varepsilon}) +\noise a model error term (prints \nu) +\vnoise a vector of model error terms (prints \vec{\nu}) \rvar a generic value of a random variable in probability expressions (prints x) \Rvar a generic random variable in probability expressions (prints X) \learnrate a learning rate (gradient-descent step size) (prints \eta) @@ -1237,7 +1237,7 @@ name interpretation \midpt an intermediate point in a mean-value or Taylor remainder (prints \tau) \nullity the nullity of a matrix (prints \nu) \lsresid a residual written as epsilon (prints \varepsilon) -\vlsresid a vector of residuals written as epsilon (prints \vec{\varepsilon}) +\vlsresid a vector of residuals written as epsilon (prints \vec{\nu}) \subdiv a subdivision of a region into rectangles (prints \Delta) \universe a universal set (prints \Omega) \lowend the lower endpoint of an interval (prints \alpha) @@ -1314,7 +1314,7 @@ name interpretation \nreps number m of replicates (observations) that share one covariate pattern; written with a pattern index, as \nreps_k \nevents number s of events among the replicates of one covariate pattern; written with a pattern index, as \nevents_k \popdist population distribution P that the data are drawn from -\targetfn target function f: the true relationship between inputs and outcomes +\targetfn target function \mu: the true relationship between inputs and outcomes \dataset data set: the whole collection of labelled observations that the training, validation and test sets are subsets of (prints a calligraphic D) \trainset training set: the labelled data a model is fitted to (prints a calligraphic D with a train subscript) \valset validation set: the held-out observations used to choose among fitted models (prints a calligraphic D with a val subscript) @@ -1322,17 +1322,17 @@ name interpretation \trainidx index set of the training set (prints I with a train subscript) \validx index set of the validation set (prints I with a val subscript) \testidx index set of the test set (prints I with a test subscript) -\targetfnf target function applied to its argument, f(·) +\targetfnf target function applied to its argument, \mu(·) \hmodmem fitted model (hat-wrapped \modmem), legacy form \hmodmemf fitted model applied to its argument (hat-wrapped), h-hat(·) \hmodmemof fitted model with its model family as subscript (hat-wrapped) \htargetfn estimated target function: fitted counterpart of the target function (hat-wrapped), legacy form -\htargetfnf estimated target function applied to its argument (hat-wrapped), f-hat(·) +\htargetfnf estimated target function applied to its argument (hat-wrapped), \mu-hat(·) \emodmem fitted model: estimate of a member of a model family (via \est) \emodmemf fitted model applied to its argument (via \est), h-hat(·) \emodmemof fitted model with its model family as subscript (via \est) -\etargetfn estimated target function: fitted counterpart of the target function (via \est), f-hat -\etargetfnf estimated target function applied to its argument (via \est), f-hat(·) +\etargetfn estimated target function: fitted counterpart of the target function (via \est), \mu-hat +\etargetfnf estimated target function applied to its argument (via \est), \mu-hat(·) \targeterr error of the fitted target function: target function minus its fitted counterpart (the deviation symbol subscripted by the target function) \targeterrf error of the fitted target function at a point (via \targeterr) \codealph alphabet of a block code (the set of symbols codewords use), Sigma diff --git a/macros.qmd b/macros.qmd index db048098..aaebacfe 100644 --- a/macros.qmd +++ b/macros.qmd @@ -191,7 +191,7 @@ \def\nreps{m} \def\nevents{s} \def\popdist{P} -\def\targetfn{f} +\def\targetfn{\mu} \providecommand{\targetfnf}[1]{\targetfn\paren{#1}} \def\dataset{\mathcal{D}} \def\trainset{\mathcal{D}_{\text{train}}} @@ -1206,8 +1206,8 @@ \def\hcovmat{\hat{\Sigma}} \def\ecovmat{\est{\covmat}} \def\corpar{\rho} -\def\noise{\varepsilon} -\def\vnoise{\vec{\varepsilon}} +\def\noise{\nu} +\def\vnoise{\vec{\nu}} \def\rvar{x} \def\Rvar{X} \def\predbar{\bar{\predvar}} From 54e5ce24fe106c36989c3c916058f9249147f7c4 Mon Sep 17 00:00:00 2001 From: Claude Date: Fri, 16 Oct 2026 17:25:26 +0000 Subject: [PATCH 2/3] Alias noise to a new deviation-from-population-mean macro; add two-argument deviation Co-Authored-By: Claude Sonnet 5.5 Claude-Session: https://claude.ai/code/session_01H8gaSFRnPKEfpCbBRqEzZH --- interpretations.tsv | 11 +++++++---- macros.qmd | 9 ++++++--- 2 files changed, 13 insertions(+), 7 deletions(-) diff --git a/interpretations.tsv b/interpretations.tsv index 67e80893..28cb7ec5 100644 --- a/interpretations.tsv +++ b/interpretations.tsv @@ -79,7 +79,7 @@ name interpretation \gg Greek letter gamma (alias for \g) \gd Greek letter delta (δ) \eps varepsilon error term (ε) -\cdev deviation from conditional mean (ε) +\cdev deviation from conditional mean (alias for \popdev) \veps error vector (ε-vector) \epsp ε(·) error function \epsf ε(·) error function (alias for \epsp) @@ -184,6 +184,9 @@ name interpretation \devn deviation symbol (alias for \deviation) \deviationv deviation vector (the vec accent applied to δ) \devnv deviation vector (alias for \deviationv) +\deviationf deviation of the first argument from the reference value in the second, δ_r(z) +\popdev deviation from a population mean, symbol ν +\popdevf deviation of the argument from its population mean, ν_z \Deviation uppercase deviation symbol Δ \Devn uppercase deviation (alias for \Deviation) \residual residual symbol r @@ -1149,8 +1152,8 @@ name interpretation \hcovmat an estimated covariance matrix (prints \hat{\Sigma}) \ecovmat an estimated covariance matrix (forward-looking form) (prints \est{\covmat}) \corpar a correlation parameter (prints \rho) -\noise a model error term (prints \nu) -\vnoise a vector of model error terms (prints \vec{\nu}) +\noise a model error term: the deviation of an outcome from its mean given the input (alias for \popdev) +\vnoise a vector of model error terms (the vec accent applied to \noise) \rvar a generic value of a random variable in probability expressions (prints x) \Rvar a generic random variable in probability expressions (prints X) \learnrate a learning rate (gradient-descent step size) (prints \eta) @@ -1237,7 +1240,7 @@ name interpretation \midpt an intermediate point in a mean-value or Taylor remainder (prints \tau) \nullity the nullity of a matrix (prints \nu) \lsresid a residual written as epsilon (prints \varepsilon) -\vlsresid a vector of residuals written as epsilon (prints \vec{\nu}) +\vlsresid a vector of residuals written as epsilon (the vec accent applied to \noise) \subdiv a subdivision of a region into rectangles (prints \Delta) \universe a universal set (prints \Omega) \lowend the lower endpoint of an interval (prints \alpha) diff --git a/macros.qmd b/macros.qmd index aaebacfe..b0415e22 100644 --- a/macros.qmd +++ b/macros.qmd @@ -80,7 +80,7 @@ \def\gg{\gamma} \def\gd{\delta} \def\eps{\varepsilon} -\def\cdev{\eps} +\def\cdev{\popdev} \def\veps{\vec{\varepsilon}} \providecommand{\epsp}[1]{\eps\paren{#1}} \def\epsf{\epsp} @@ -236,6 +236,9 @@ \def\devn{\deviation} \providecommand{\deviationv}{\vec{\deviation}} \def\devnv{\deviationv} +\providecommand{\deviationf}[2]{\deviation_{#2}\paren{#1}} +\def\popdev{\nu} +\providecommand{\popdevf}[1]{\popdev_{#1}} \def\Deviation{\Delta} \def\Devn{\Deviation} \def\residual{r} @@ -1206,8 +1209,8 @@ \def\hcovmat{\hat{\Sigma}} \def\ecovmat{\est{\covmat}} \def\corpar{\rho} -\def\noise{\nu} -\def\vnoise{\vec{\nu}} +\def\noise{\popdev} +\def\vnoise{\vec{\popdev}} \def\rvar{x} \def\Rvar{X} \def\predbar{\bar{\predvar}} From 99ca7189305c766bb234c10770feda607d28ab60 Mon Sep 17 00:00:00 2001 From: Claude Date: Fri, 16 Oct 2026 17:25:39 +0000 Subject: [PATCH 3/3] Restore the vlsresid interpretation Co-Authored-By: Claude Sonnet 5.5 Claude-Session: https://claude.ai/code/session_01H8gaSFRnPKEfpCbBRqEzZH --- interpretations.tsv | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/interpretations.tsv b/interpretations.tsv index 28cb7ec5..d82f1795 100644 --- a/interpretations.tsv +++ b/interpretations.tsv @@ -1240,7 +1240,7 @@ name interpretation \midpt an intermediate point in a mean-value or Taylor remainder (prints \tau) \nullity the nullity of a matrix (prints \nu) \lsresid a residual written as epsilon (prints \varepsilon) -\vlsresid a vector of residuals written as epsilon (the vec accent applied to \noise) +\vlsresid a vector of residuals written as epsilon (prints \vec{\varepsilon}) \subdiv a subdivision of a region into rectangles (prints \Delta) \universe a universal set (prints \Omega) \lowend the lower endpoint of an interval (prints \alpha)