Model Classification

Conceptual Model

A conceptual model can be described using various notations, such as UML or OMT for object modelling, or IE or IDEF1X for Entity Relationship Modelling. In UML notation, the conceptual model is often described with a class diagram in which classes represent concepts, associations represent relationships between concepts and role types of an association represent role types taken by instances of the modelled concepts in various situations. In ER notation, the conceptual model is described with an ER Diagram in which entities represent concepts, cardinality and optionalityrepresent relationships between concepts. Regardless of the notation used, it is important not to compromise the richness and clarity of the business meaning depicted in the conceptual model by expressing it directly in a form influenced by design or implementation concerns.








Abstract Model

Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. The starting point for the study of abstract models, which resulted in good examples was Lindström's theorem.










Simulation Model

A simulation model is a mathematical model of a system or process that includes key inputs which affect it and the corresponding outputs that are affected by it. If the model explicitly includes uncertainty, we refer to it as a Monte Carlo simulation model. For example, it can calculate the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment returns, environmental consequences, and the like. Such a model can be created by writing code in a programming language, statements in a simulation modeling language, or formulas in a Microsoft Excel spreadsheet. Regardless of how it is expressed, a simulation model will include:
Model inputs that are uncertain numbers -- we'll call these uncertain variables
Intermediate calculations as required
Model outputs that depend on the inputs -- we'll call these uncertain functions


It's essential to realize that model outputs that depend on uncertain inputs are uncertain themselves -- hence we talk about uncertain variables and uncertain functions. When we perform a simulation with this model, we will test many different numeric values for the uncertain variables, and we'll obtain many different numeric values for the uncertain functions. We'll use statistics to analyze and summarize all the values for the uncertain functions (and, if we wish, the uncertain variables).






Heterogenous Model

The homogeneity hypothesis implies that the substitution process ultimately reaches an equilibrium and it is also assumed that the process was already stationary at the very beginning, i.e., at the root of the phylogeny. If the homogeneity and stationarity assumptions were true, equal nucleotide frequencies would be expected in past and present-day sequences. Actually, we can observe discrepancy's in nucleotide frequencies in many real data sets of present species: model assumptions are clearly violated when using real sequences.


It has been noticed that sequences of similar composition tend to be grouped together irrespective of their real phylogenetic relationships (Lockhart et al., 1994; Tarrio et al., 2001, see e.g., ). In an attempt to avoid this bias, we developed an HETEROGENEOUS model in a Bayesian framework which models coarsely the heterogeneity using a small pool of homogeneous processes. Each branch of the tree ``chooses'' a substitution model among them. The likelihood computation now depends on the position of the root which is why a heterogeneous rooted tree was implemented in PHASE (ultrametricity is optional). The composition observed at this root becomes a free parameter of the model (see, e.g., Yang and Roberts, 1995; Galtier and Gouy, 1998).


Algorithms developed in PHASE are very similar to those implemented in P4 by Peter Foster. PHASE framework might be a bit more general since the full substitution model is allowed vary over the tree. However, you are strongly advised to limit yourself to variation of the composition vector as Foster (2004) did. Unfortunately, we did not have time to implement a way to use a single exchangeability matrix over the whole tree yet. There is a workaround (a bit unsatisfactory): you can start the MCMC chain from a model properly initialized and turn off the perturbation of rate ratios so that they have constant values. Use the same trick to fix the gamma shape parameter and the proportion of invariant sites to a single constant value. (Do not use a +I model with HETEROGENEOUS without constraining the proportion of invariant sites to a constant value).


PHASE is missing an efficient MCMC proposal to modify the position of the root. You are advised to use an outgroup in the TREE block to constrain the position of the common ancestor. Remember that this outgroup can also be a monophyletic cluster.






Model Building Methodology

Model building methodologies are playing an increasingly significant role in many aspects of software engineering activities. Today models are being applied right from requirement conceptualization to the final software installation and maintenance. Traditional methodologies however, fail to cope with increasing complexity and rapidly evolving nature of the software. The need for an efficient model building methodology is quite manifest today. The main objective of this study is to propose and implement a novel Model Building Methodology utilizing Artificial Neural Network (ANN). In order to achieve this objective, information related to regression analysis was reviewed.