Minor wording updates

docs/what_combine_does/fitting_concepts.md

@@ -94,7 +94,7 @@ Frequentist confidence regions are random variables of the observed data.
 These are very often the construction used to define the uncertainties reported on a parameter.
 
 If the same experiment is repeated multiple times, different data will be osbserved each time and a different confidence set $\{ \vec{\theta}\}_{\mathrm{CL}}^{i}$ will be found for each experiment.
-The confidence regions, If the data are generated by the model with some set of values $\vec{\theta}_{\mathrm{gen}}$, then the fraction of the intervals $\{ \vec{\theta}\}_{\mathrm{CL}}^{i}$ which contain the values $\vec{\theta}_{\mathrm{gen}}$ will be equal to the confidence level ${\mathrm{CL}}$. 
+If the data are generated by the model with some set of values $\vec{\theta}_{\mathrm{gen}}$, then the fraction of the regions $\{ \vec{\theta}\}_{\mathrm{CL}}^{i}$ which contain the values $\vec{\theta}_{\mathrm{gen}}$ will be equal to the confidence level ${\mathrm{CL}}$. 
 The fraction of intervals which contain the generating parameter value is referred to as the "coverage".
 
 From first principles, the intervals can be constructed using the [Neyman construction](https://pdg.lbl.gov/2022/web/viewer.html?file=../reviews/rpp2022-rev-statistics.pdf#subsubsection.40.4.2.1).

docs/what_combine_does/introduction.md

@@ -12,7 +12,7 @@ Roughly, combine does three things:
 2. Runs statistical tests on the model and observed data;
 3. Provides tools for validating, inspecting, and understanding the model and the statistical tests.
 
-Combine can be used for analyses in HEP ranging from simple counting experiments, to unfolded measurements, new physics searches, combinations of measurements and EFT fits.
+Combine can be used for analyses in HEP ranging from simple counting experiments, to unfolded measurements, new physics searches,combinations of measurements, and EFT fits.
 
 ## Model Building 
 
@@ -48,7 +48,7 @@ Combine provides tools for [inspecting the model](../../part3/validation/#valida
 
 Methods are provided for comparing pre-fit and postfit results of all values including nuisance parameters, and summaries of the results can produced.
 
-Plotting utilities allow the pre- and post-fit model expectations and their uncertainties to be plotted, as well as plotted summaries of debugging stups such as the nuisance parameter values and likelihood scans.
+Plotting utilities allow the pre- and post-fit model expectations and their uncertainties to be plotted, as well as plotted summaries of debugging steps such as the nuisance parameter values and likelihood scans.
 
 
 

docs/what_combine_does/model_and_likelihood.md

@@ -8,7 +8,7 @@ Combine is designed for counting experiments, where the number of events with pa
 The events can either be binned, as in histograms, or unbinned, where continuous values are stored for each event.
 
 The model consists of a sum over different processes, each processes having its own model defining it.  
-The expected observation is then the sum of the expected observations for each of the processes, $m =\sum_{p} m_{p}$.
+The expected observations are then the sum of the expected observations for each of the processes, $m =\sum_{p} m_{p}$.
 
 The model can also be composed of multiple channels. $\mathcal{M}_{0} = \{ m_{c1}, m_{c2}, .... m_{cN}\}$. 
 The expected observations which define the model is then the union of the sets of expected observations in each individual channel.
@@ -25,7 +25,7 @@ The full model therefore defines the expected observations over all the channels
 
 $$ \mathcal{M} = \{ m_{c1}(\vec{\mu},\vec{\theta}), m_{c2}(\vec{\mu},\vec{\theta}), ..., m_{cN}(\vec{\mu},\vec{\theta}) \} $$
 
-Combine provides tools and interfaces for defining the model as arbitrary functions of the input parameters.
+Combine provides tools and interfaces for defining the model as pre-defined or user-defined functions of the input parameters.
 In practice, however, there are a number of most commonly used functional forms which define how the expected events depend on the model parameters.
 These are discussed in detail in the context of the full likelihood below.
 
@@ -168,7 +168,7 @@ where:
 - $N_{\mathrm{0}}(\theta_{G}) \equiv \frac{\theta_{G}}{\tilde{\theta}_{G}}$, is the normalization effect of a gamma uncertainty. $\tilde{\theta}_{G}$ is taken as the observed number of events in some external control region and $\theta_{G}$ has a constraint pdf $\mathrm{Poiss}(\theta; \tilde{\theta})$
 - $\kappa_{n}^{\theta_{L,n}}$, are log-normal uncertainties specified by a fixed value $\kappa$;
 - $\kappa^{\mathrm{A}}_{a}(\theta_{L(S)}^{a},\kappa^{+}_{a}, \kappa^{-}_{a})^{\theta_{L(S)}^{a}}$ are asymmetric log-normal uncertainties, in which the value of $\kappa^{\mathrm{A}}$ depends on the nuisance parameter and two fixed values $\kappa^{+}_{a}$ and $\kappa^{-}_{a}$. The functions, $\kappa^A$, define a smooth interpolation for the asymmetric uncertainty; and
-- $F_{r}(\vec{\theta}_\rho)$ are arbitrary user-defined functions of the user defined nuisance parameters which may have uniform or gaussian constraint terms.
+- $F_{r}(\vec{\theta}_\rho)$ are user-defined functions of the user defined nuisance parameters which may have uniform or gaussian constraint terms.
 
 The function for the asymmetric normalization modifier, $\kappa^A$ is 
 
@@ -262,10 +262,10 @@ where the indices $i$ and $j$ runs over the Poisson- and Gaussian-constrained pr
 
 #### Customizing the form of $n_{exp}$ 
 
-Although the above likelihood defines some specific functional forms, users are also able to implement [custom functional forms for $M$](../../part2/physicsmodels/#model-building-poop), [ $N$](../../part2/settinguptheanalysis/#rate-parameters), and [ $y_{cbp}$](../../part3/nonstandard/#rooparametrichist-gamman-for-shapes).
-In practice, this makes the functional form almost entirely general. 
+Although the above likelihood defines some specific functional forms, users are also able to implement [custom functional forms for $M$](../../part2/physicsmodels/#model-building), [ $N$](../../part2/settinguptheanalysis/#rate-parameters), and [ $y_{cbp}$](../../part3/nonstandard/#rooparametrichist-gamman-for-shapes).
+In practice, this makes the functional form much more general than the default forms used above. 
 
-However, some constraints, such as the requirement that bin contents be positive, and that the function $M$ only depends on $\vec{\mu}$, whereas $N$, and $y_{cbp}$ only depend on $\vec{\theta}$ do exist.
+However, some constraints do exist, such as the requirement that bin contents be positive, and that the function $M$ only depends on $\vec{\mu}$, whereas $N$, and $y_{cbp}$ only depend on $\vec{\theta}$.
 
 #### Constraint Likelihood terms
 
@@ -351,13 +351,13 @@ The details of the interpolations which are used are found in the section on [no
 
 #### Parameter of Interest Model
 
-As in the template-based case, the parameter of interest model, $M_{cp}(\vec{\mu})$, can take on arbitrary forms [defined by the user](../../part2/physicsmodels/#model-building).
+As in the template-based case, the parameter of interest model, $M_{cp}(\vec{\mu})$, can take on different forms [defined by the user](../../part2/physicsmodels/#model-building).
 The default model is one where $\vec{\mu}$ simply scales the signal processes' normalizations.
 
 #### Shape Morphing Effects
 
-The user may define any number of nuisance parameters which morph the shape of the pdf according to arbitrary functional forms.
-These nuisance parameters are included as $\vec{\theta}_\rho$ uncertainties, which may have gaussian or uniform constraints, and include arbitrary user-defined process normalization effects.
+The user may define any number of nuisance parameters which morph the shape of the pdf according to functional forms defined by the user.
+These nuisance parameters are included as $\vec{\theta}_\rho$ uncertainties, which may have gaussian or uniform constraints, and include user-defined process normalization effects.
 
 
 ### Combining template-based and parametric Likelihoods 

docs/what_combine_does/statistical_tests.md

@@ -29,7 +29,7 @@ Then the value of the test statistic on the actual observed data, $t^{\mathrm{ob
 <!--- this div exists as a convenient link target to the p-value explainer below. It is placed slightly above the explainer, because otherwise the explainer is covered by the page header-->
 </div>
 
-This comparison, which depends on the test in question, will the define the results of the test, which may be simple binary results (e.g. this model point is rejected at a given confidence level), or continuous (e.g. defining the degree to which the data are considered surprising, given the model).
+This comparison, which depends on the test in question, defines the results of the test, which may be simple binary results (e.g. this model point is rejected at a given confidence level), or continuous (e.g. defining the degree to which the data are considered surprising, given the model).
 Often, as either a final result or as an intermediate step, the p-value of the observed test statistic under a given hypothesis is calculated.