.. _glossary:

Glossary
########


.. glossary::
    :sorted:
    
    confidence intervals
        Ranges in which we can be X% confident that a parameter lies.
        
    fixed effects
        A population-level parameters (usually means) that describe an average from which individuals deviate in a random way, though where the nature of the randomness is known. Signified by |fx| in the model specifications file.
        
    random effects
        Deviation from the population-level fixed parameters, with defined distribution parameters. Signified by |rx| in the model specification file.
        
    covariates
        Measured or observed quantities that are read in from the input data file. Signified by a |cx| in the model specification file (which could also be thought of as an abbreviation of "column"). They include information such as ID, time, weight, and also measurements such as drug concentration.
        
    m parameters
        Person-specific |pkpd| parameters, usually defined as a function of the fixed effects, random effects and measured covariates. Signified by |mx| in the model specification file.
        
    s parameters
        The amount - not concentration - of drug in each compartment of the compartment model. Signified by |sx| in the model specification file.
        
    predictions
        The value the model calculates for a given observations, usually a conversion to concentrations via division by the volumes of the compartments. Signified by |px| in the model specification file.
        
    observations
        The observed values to be modelled, |aka| the dependent variable. These measurements (either synthetic or real) are signified by |cx| in the |predictions| section of a |popy| |script_file|.
           
    solutions
        Solutions are defined by a .pyml file containing links to .csv files that determine a set of |fx|, |rx|, |mx|, |sx|, |px| variables that represent a candidate solution to a |pkpd| model fitting problem.
        
    visual predictive check
        Given a set of |fx| values and a model, new |px| values are simulated which can then be compared with original |cx| data on a graph.
            
    volume of distribution
        The volume (or volume of distribution) is the theoretical volume that a compartment would need to have to give the concentration of drug found in the blood plasma. See :wiki_link:`Volume of Distribution on Wikipedia <Volume_of_distribution>`
        
    clearance
        The :term:`volume<volume of distribution>` of the fluid presented to the :term:`eliminating<elimination>` organ (extractor) that is effectively completely cleared of drug per unit time. (Definition from [RowlandTozer2012]_), also see :wiki_link:`Clearance on Wikipedia <Clearance_(pharmacology)>`
                
    elimination
        The removal of a drug from the body, either by excretion or metabolism.
        
    first pass effect
        A reduction in the amount of drug entering circulation due to it being metabolised by the liver or gut on its way to the blood system. :wiki_link:`First pass effect on Wikipedia <First_pass_effect>`
        
    mixed effect model
        A structural model that uses both |fes| and |res| to model population parameters. In practise, all models contain at least one |fe|, so the key feature is the use of |res| to allow parameters to vary between subjects in the population.
        
    shrinkage
        The tendency to for |res| to shrink towards the mean value when data are sparse.
        
    categorical covariates
        Covariates that indicates membership in one of a set of unordered categories, such as race.
        
    ordinal covariates
        Covariates derived from a discretisation of a continuum such that values have a definite order, such as the East Coast Oncology Group status that ranges from 0 (normal) to 4 (most severe).
        
    structurally identifiable
        A parameter of a model is **structurally identifiable**, if given an infinite amount of data the true underlying parameter value is recoverable. See :wiki_link:`Identifiability Analysis on Wikipedia <Identifiability_analysis#Structural_and_practical_identifiability_analysis>`

    structurally unidentifiable
        A parameter that is |not| :term:`structurally identifiable`
        
    practically identifiable
        A parameter of a model is **practically identifiable** or estimable, if the true value can be estimated from a finite amount of data. See :wiki_link:`Identifiability Analysis on Wikipedia <Identifiability_analysis#Structural_and_practical_identifiability_analysis>`
        
    practically unidentifiable
        A parameter that is |not| :term:`practically identifiable`
        
    symmetric positive definite
        A symmetric positive definite matrix is a matrix whose eigenvalues are all positive. It is the matrix equivalent of having a real valued square root. In |pkpd| models a population covariance matrix is required to be symmetric positive definite. See :wiki_link:`Matrix Definiteness on Wikipedia <Definiteness_of_a_matrix>`
            
    Akaike information criterion
        A method of comparing two similar models by penalising models with a larger number of parameters. See :wiki_link:`Akaike information criterion on Wikipedia <Akaike_information_criterion>`
       
    noise
        Random displacements added to a signal. See :wiki_link:`Signal Processing Noise on Wikipedia <Noise_(signal_processing)>`
        
    variance
        A measure of spread for a random variable. See :wiki_link:`Variance on Wikipedia <Variance>`
          
    covariance matrix
        A measure of spread for multiple random variables that may be correlated. 
        See :wiki_link:`Covariance on Wikipedia <Covariance_matrix>`

    basin of convergence
        A set of initial points that lead to the same local minimum under a given iterative algorithm.
        
    ordinary differential equations
        Multiple differential equations, each with one independent variable. See :wiki_link:`Ordinary differential equation on Wikipedia <Ordinary_differential_equation>`
        
    initial value problem
        The |odes| typically solve a dynamic system which has a defined input state and then the system evolves over time according to the |ode| system. This type of integration problem, typical in |pkpd|, is known as a :wiki_link:`Initial Value Problem<Initial_value_problem>`.
        
    mass balance
        The principal that matter cannot be created or destroyed within a compartment model, apart from deliberate inputs (e.g doses) and sink compartments that model excretion from the body. See :wiki_link:`Mass Balance on Wikipedia<Mass_balance>`.

    objective function
        The |fes| and |res| of a model are estimated by minimising the :term:`objective function`, which is equivalent to maximising the 
        :wiki_link:`likelihood <Likelihood_function>` of the model given the :term:`observations`.
        
    Laplace approximation
        A method of approximating integrals. See :wiki_link:`Laplace method on Wikipedia <Laplace's_method>`. This approximation of the :term:`objective function` is used by |joe|, |foce| and |its| fitting methods.
        
    Likelihood
        The conditional probability, *p(D|M)*, of observing data *D* given a hypothesized model *M*. This expresses the *plausibility* of model *M* given data *D*, but is a probability distribution over *D* rather than *M*. As a result, it cannot be used to compare different models, only different parameter values for the same model. :wiki_link:`Likelihood on Wikipedia <Likelihood_function>`
        
    first order conditional estimation
        |foce| is a fitting method in |nonmem| that uses a first order approximation of the :term:`objective function` conditioned on optimised |res| for each individual in the population.

    hessian
        The :math:`n \times n` matrix of second derivatives of a function of :math:`n` variables. Contains information that describes the shape of the surface at a given point (the minimum, for example).

    iterative two stage
        |its| is a fitting method in |nonmem| that optimises the :term:`objective function` by switching between optimising the |fes| and |res|. The |its| and |foce| methods have the same :term:`objective function`
        
    joint optimisation and estimation
        |joe| is |popy|'s main fitting method see :ref:`fit_methods_joe`, it optimises the same :term:`objective function` as |foce| and |its|.
        
    stochastic approximation expectation maximisation
        |saem| is a probabilistic fitting method originally implemented in |monolix| and also available in |nonmem|. 
        
    importance sampling
        A method of sampling from a complex distribution by first sampling from a simpler distribution and re-weighting with the ratio of the complex and simpler  :wiki_link:`<Probability_density_function>`. See :wiki_link:`Importance Sampling on Wikipedia <Importance_sampling>`. Used by the |imp| fitting method in |nonmem|. 
        
    Graphviz
        Graphviz is open source software used to create :term:`Compartment Diagram` in |popy|. See :wiki_link:`Graphviz on Wikipedia <Graphviz>`

    R
        R is open source statistical software used extensively in the |pkpd| community. See :wiki_link:`R on Wikipedia <R_(programming_language)>`
        
    Nonmem 
        Nonmem (NONlinear Mixed Effect Modelling) is a Fortran based system for |pkpd| modelling. [Bauer2009]_
        
    Monolix 
        Matlab based |pkpd| modelling software. See `http://lixoft.com/products/monolix/`
        
    Python
        Python is a general purpose programming language used in |popy| scripts and to implement |popy| itself. See :wiki_link:`Python on Wikipedia <Python_(programming_language)>`
        
    C++
        C++ is a low level programming language which is automatically used by |popy| for some time critical operations :wiki_link:`C++ on Wikipedia <C%2B%2B>`
        
    YAML
        A simple markup language used by |popy| :ref:`script_formats`. See :wiki_link:`YAML on Wikipedia <YAML>`
        
    Sphinx
        Documentation system used by |popy| and many other |python| projects to generate .html and .pdf files. See :wiki_link:`Sphinx on Wikipedia <Sphinx_(documentation_generator)>`
                
    HTML
        Hyper Text Markup Language used on the web and by |popy| to generate summary output. See :wiki_link:`HTML on Wikipedia <HTML>`
                
    product key
        The |popy| product key is the unique key that identifies the the current licence. It has a form like 'XXXX-XXXX-XXXX-XXXX-XXXX-XXXX-XXXX'. See :ref:`activation`.
        
    dos prompt
        The dos prompt command line in Microsoft Windows. This is the older Windows shell, by default with a black background.
        
    powershell prompt
        The powershell prompt command line in Microsoft Windows. This is the newer Windows shell, by default with a blue background.
        
    Microsoft Windows
        Windows, a popular operating system for personal computers.
        
    DDMoRe
        An online repository of |pkpd| models see `DDMoRe Website <http://repository.ddmore.eu/>`_
        
    LSODA
        Numerical |ode| solver [Radhakrishnan1994]_ available in |popy|, see :ref:`example_ode_solver_scipy_odeint`. 

    Compartment Diagram
        A graphical visualisation of the compartment model, using nodes for compartments and edges for flows between compartments
        
    metabolism
        Process by which drug is chemically transformed into another substance. Takes place primarily in the liver.
                

