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Probabilistic model
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional
Graphical_model
Notation expressing information under a rule set
defined by a consistent set of rules. A modeling language can be graphical or textual. A graphical modeling language uses a diagramming technique with
Modeling_language
Computer graphics journal
Graphical Models is an academic journal in computer graphics and geometry processing publisher by Elsevier. As of 2021[update], its editor-in-chief is
Graphical_Models
Statistical estimator
independence between the variables therefore implying a Gaussian graphical model. The graphical lasso was originally formulated to solve Dempster's covariance
Graphical_lasso
The Graphical Modeling Framework (GMF) is a framework within the Eclipse platform. It provides a generative component and runtime infrastructure for developing
Graphical_Modeling_Framework
Probabilistic graphical representation of causal relationships
Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies
Bayesian_network
Statistical Markov model
random field) rather than the directed graphical models of MEMM's and similar models. The advantage of this type of model is that it does not suffer from the
Hidden_Markov_model
Graphical models have become powerful frameworks for protein structure prediction, protein–protein interaction, and free energy calculations for protein
Graphical models for protein structure
Graphical_models_for_protein_structure
Form of causal modeling that fit networks of constructs to data
Causal model – Conceptual model in philosophy of science Graphical model – Probabilistic model Judea Pearl Multivariate statistics – Simultaneous observation
Structural_equation_modeling
Subset of artificial intelligence
Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their
Machine_learning
Statistical model for a binary dependent variable
In statistics, a logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent
Logistic_regression
Technique used in statistics
direct-consequence, graphical models are hierarchical. Moreover, being completely determined by its two-factor terms, a graphical model can be represented
Log-linear_analysis
A graphical user interface, or GUI, is a form of user interface that allows users to interact with electronic devices through graphical icons and visual
Graphical_user_interface
Class of statistical models
linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be
Generalized_linear_model
Set of statistical processes for estimating the relationships among variables
In statistical modeling, regression analysis is a statistical method for estimating the relationship between a dependent variable (often called the outcome
Regression_analysis
Software design pattern
controller, the software linking the two. Traditionally used for desktop graphical user interfaces (GUIs), this pattern became popular for designing web
Model–view–controller
Class of statistical survival models
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one
Proportional_hazards_model
Model for generating observable data in probability and statistics
large generative model for musical audio that contains billions of parameters. Mathematics portal Discriminative model Graphical model Three leading sources
Generative_model
Statistical model used in time series analysis
statistical analysis of time series, an autoregressive–moving-average (ARMA) model is used to represent a (weakly) stationary stochastic process by combining
Autoregressive moving-average model
Autoregressive_moving-average_model
Collection of statistical models
experimental units. These include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation
Analysis_of_variance
Time series model
econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Statistical concept
can be added to the graphical model defining the mixture model. For example, in the common latent Dirichlet allocation topic model, the observations are
Mixture_model
Probabilistic problem-solving algorithm
and smoother for non-Gaussian nonlinear state space models". Journal of Computational and Graphical Statistics. 5 (1): 1–25. doi:10.2307/1390750. JSTOR 1390750
Monte_Carlo_method
Type of machine learning model
A large language model (LLM) is a neural network trained on a vast amount of text for natural language processing tasks, especially language generation
Large_language_model
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Type of mathematical model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data
Statistical_model
Probabilistic graphical model
Graphical Models Toolkit (GMTK): an open-source, publicly available toolkit for rapidly prototyping statistical models using dynamic graphical models
Dynamic_Bayesian_network
Technique for the generative modeling of a continuous probability distribution
diffusion models, also known as diffusion-based generative models or score-based generative models, are a class of latent variable generative models. A diffusion
Diffusion_model
Subset of variables that contains all the useful information
variables in the system. This concept is central in probabilistic graphical models and feature selection. If a Markov blanket is minimal—meaning that
Markov_blanket
Unit of information
ISBN 0-471-95820-4. Johanna Drucker (2011). "Humanities Approaches to Graphical Display". Digital Humanities Quarterly. 005 (1). Data at Wikipedia's sister
Data
Branch of statistics
reliability engineering in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis
Survival_analysis
Software development methodology
solution Graphical Modeling Framework (GMF) JetBrains MPS, a metaprogramming system from JetBrains MagicDraw from No Magic Inc MDriven – a UML-based, model-driven
Model-driven_engineering
Measure of variation in statistics
Standard deviation is often used to compare real-world data against a model to test the model. For example, in industrial applications the weight of products
Standard_deviation
Set of random variables
probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by
Markov_random_field
Method of statistical inference
Carlo techniques since complex models cannot be processed in closed form by a Bayesian analysis, while a graphical model structure may allow for efficient
Bayesian_inference
Mathematical visualization
design stages. Graphical modeling tools aim to improve these aspects of design. These tools provide a very generic and unified graphical modeling environment
Model-based_design
Enterprise data modelling or enterprise data modeling (EDM) is the practice of creating a graphical model of the data used by an enterprise or company
Enterprise_data_modelling
Statistical model allowing for frequent zero values
In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent
Zero-inflated_model
Mathematical model used for classification or regression
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification. In machine learning, it typically models the
Discriminative_model
Data visualization
of advantages. First, the box plot enables statisticians to do a quick graphical examination on one or more data sets. Box plots also take up less space
Box_plot
Graphical representation for specifying business processes
Business Process Model and Notation (BPMN) is a graphical representation for specifying business processes in a business process model. Originally developed
Business Process Model and Notation
Business_Process_Model_and_Notation
Statistical concept
researchers to design studies to minimize the occurrence of missing values. Graphical models can be used to describe the missing data mechanism in detail. Values
Missing_data
Range to estimate an unknown parameter
intervals around statistical functionals of a distribution Error bar – Graphical representations of the variability of data Estimation statistics – Data
Confidence_interval
Statistical measure of association
survival analysis Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran–Mantel–Haenszel statistics Multivariate
Cramér's_V
Type of statistical measure over subsets of a dataset
weighting function. One application is removing pixelization from a digital graphical image. This is also known as Anti-aliasing [citation needed] In the financial
Moving_average
Number of values in the final calculation of a statistic that are free to vary
fully determined). The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Middle quantile of a data set or probability distribution
estimator of the population median. If data is represented by a statistical model specifying a particular family of probability distributions, then estimates
Median
Statistical hypothesis test
the Pearson distribution to model the observation and performing a test of goodness of fit to determine how well the model really fits to the observations
Chi-squared_test
Measure of statistical dispersion
preferred to the total range. The IQR is used to build box plots, simple graphical representations of a probability distribution. The IQR is used in businesses
Interquartile_range
American artificial intelligence researcher
Xing's research focuses on statistical machine learning, probabilistic graphical models, and systems for distributed machine learning. He was elected a Fellow
Eric_Xing
Probability distribution
and variance as in the above model. The t distribution is often used as an alternative to the normal distribution as a model for data, which often has heavier
Student's_t-distribution
Fourth standardized moment in statistics
survival analysis Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran–Mantel–Haenszel statistics Multivariate
Kurtosis
Numerical measure of a statistical relationship between variables
well a statistical model fits observations by summarizing the discrepancy between observed values and the values expected under the model Multiple correlation
Correlation_coefficient
Statistical method that summarizes and/or integrates data from multiple sources
developed to simplify the model fitting (e.g., metaBMA and RoBMA) and even implemented in statistical software with graphical user interface (GUI): JASP
Meta-analysis
Statistical hypothesis test
rejected in favor of the alternative hypothesis. Suppose one is fitting the model Y = α + β x + ε , {\displaystyle Y=\alpha +\beta x+\varepsilon ,} where
Student's_t-test
Function of the observed sample results
a result", and "does not provide a good measure of evidence regarding a model or hypothesis" without "context or other evidence". That said, a 2019 task
P-value
Topics referred to by the same term
Graphical language may refer to: Graphical modeling language, graphical types of artificial language to express information or knowledge Visual language
Graphical_language
Type of chart
A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented
Radar_chart
Statistical measure of variability
survival analysis Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran–Mantel–Haenszel statistics Multivariate
Median_absolute_deviation
Type of artificial neural network
In machine learning, a deep belief network (DBN) is a generative graphical model, or alternatively a class of deep neural network, composed of multiple
Deep_belief_network
Variable that is causally influenced by two or more variables
two or more variables. The name "collider" reflects the fact that in graphical models, the arrow heads from variables that lead into the collider appear
Collider_(statistics)
Class of statistical tests
departure from normality (see Anderson Darling coefficient and minitab). A graphical tool for assessing normality is the normal probability plot, a quantile-quantile
Normality_test
Bias in causal inference
doi:10.2307/2337329. JSTOR 2337329. Pearl, J., (1993). "Aspects of Graphical Models Connected With Causality", In Proceedings of the 49th Session of the
Confounding
Measure of the joint variability
producing the g factor. Another is to personality, with models like the five factor model being derived from principal component analysis. Algorithms
Covariance
Net (TAPN) is a time extension of the classical Petri net model (a commonly used graphical model of distributed computations introduced by Carl Adam Petri
TAPAAL_Model_Checker
Statistical property
survival analysis Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran–Mantel–Haenszel statistics Multivariate
Standard_error
Method of data analysis
"Sparse principal component analysis" (PDF). Journal of Computational and Graphical Statistics. 15 (2): 262–286. CiteSeerX 10.1.1.62.580. doi:10.1198/106186006x113430
Principal_component_analysis
Statistical model
Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs)
Maximum-entropy_Markov_model
Approximation method in statistics
best-fit model by minimizing the sum of the squared residuals—the differences between observed values and the values predicted by the model. Least squares
Least_squares
Statistics concept
want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the
Errors_and_residuals
Position that there is no relationship between two phenomena
statistical model corresponding to each candidate hypothesis, and by using model selection techniques to choose the most appropriate model. (The most common
Null_hypothesis
survival analysis Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran–Mantel–Haenszel statistics Multivariate
List_of_statistical_tests
Statistical matching technique
{\displaystyle (r_{0},r_{1})} . Judea Pearl has shown that there exists a simple graphical test, called the back-door criterion, which detects the presence of confounding
Propensity_score_matching
Parametric model in survival analysis
accelerated failure time model (AFT model) is a parametric model that provides an alternative to the commonly used proportional hazards models. Whereas a proportional
Accelerated failure time model
Accelerated_failure_time_model
Design of tasks
discussion of experimental design in the context of model building for models either static or dynamic models, also known as system identification. Laws and
Design_of_experiments
Statistical linear model
general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that
General_linear_model
Diagnostic plot of binary classifier ability
characteristic curve, or ROC curve, is a graphical plot that illustrates the performance of a binary classifier model (although it can be generalized to multiple
Receiver operating characteristic
Receiver_operating_characteristic
Statistical relationship
{\displaystyle [-1,1]} . The odds ratio is generalized by the logistic model to model cases where the dependent variables are discrete and there may be one
Correlation
Plot using the dispersal of scattered dots to show the relationship between variables
Jason (2013). "The Generalized Pairs Plot". Journal of Computational and Graphical Statistics. 22 (1): 79–91. doi:10.1080/10618600.2012.694762. S2CID 28344569
Scatter_plot
Theory and technique of psychological measurement
individuals on nonobservable latent variables are inferred through mathematical modeling based on what is observed from individuals' responses to items on tests
Psychometrics
Type of stochastic recurrent neural network
Boltzmann machine (which is an undirected graphical model), while lower layers form a directed generative model. In a DBM all layers are symmetric and undirected
Boltzmann_machine
Process of using data analysis for predicting population data from sample data
residual analysis, or graphical diagnostics. Inference and interpretation: Finally, based on the estimated parameters and model assessment, statistical
Statistical_inference
Task of selecting a statistical model from a set of candidate models
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context
Model_selection
Tendency to misinterpret statistical experiments involving conditional probabilities
phenomenon in Bayesian networks, and conditioning on a collider in graphical models. This paradox is often illustrated using scenarios from the fields
Berkson's_paradox
Statistical method for handling multiple comparisons
as Bonferroni, Holm or Hochberg. This idea is closely related to the graphical interpretation of the BH procedure. The second paper is by Branko Soric
False_discovery_rate
Statistical hypothesis test for forecasting
other lagged values of the variable jointly add explanatory power to the model according to an F-test. Then the null hypothesis of no Granger causality
Granger_causality
Measure of the asymmetry of random variables
(November 2004). "A Robust Measure of Skewness". Journal of Computational and Graphical Statistics. 13 (4): 996–1017. doi:10.1198/106186004X12632. S2CID 120919149
Skewness
Mathematical methods used in Bayesian inference and machine learning
among the three types of random variables, as might be described by a graphical model. As typical in Bayesian inference, the parameters and latent variables
Variational_Bayesian_methods
Graphical model of computation
Interaction nets are a graphical model of computation devised by French mathematician Yves Lafont in 1989 as a generalisation of the proof structures
Interaction_nets
Gathering information for analysis
survival analysis Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Cochran–Mantel–Haenszel statistics Multivariate
Data_collection
Statistical hypothesis test
two models, 1 and 2, where model 1 is 'nested' within model 2. Model 1 is the restricted model, and model 2 is the unrestricted one. That is, model 1 has
F-test
Class of statistical modeling methods
can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions
Conditional_random_field
Correlation of a signal with a time-shifted copy of itself, as a function of shift
the term is used interchangeably with autocovariance. Various time series models incorporate autocorrelation, such as unit root processes, trend-stationary
Autocorrelation
Type of statistics
Characteristics of a variable's distribution may also be depicted in graphical or tabular format, including histograms and stem-and-leaf display. When
Descriptive_statistics
Metric for fit of statistical models
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy
Goodness_of_fit
Nonparametric measure of rank correlation
coefficient. The coefficient can be used to determine how well data fits a model, like when determining the similarity of text documents. The Spearman correlation
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Graphical model
Dependency networks (DNs) are graphical models, similar to Markov networks, wherein each vertex (node) corresponds to a random variable and each edge captures
Dependency network (graphical model)
Dependency_network_(graphical_model)
Algorithm for modelling sequential data
Translation, which replaced the previous model based on statistical machine translation. The new model was a seq2seq model where the encoder and the decoder
Transformer_(deep_learning)
Algorithm for statistical inference on graphical models
passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates
Belief_propagation
Measure of linear correlation
sum of squares (RSS) over β0 and β1 are equal to 0 in the least squares model, where RSS = ∑ i ( Y i − Y ^ i ) 2 {\displaystyle {\text{RSS}}=\sum _{i}(Y_{i}-{\hat
Pearson correlation coefficient
Pearson_correlation_coefficient
GRAPHICAL MODEL
GRAPHICAL MODEL
Surname or Lastname
English and French
English and French : nickname for a tall person, from Old English lang, long, Old French long ‘long’, ‘tall’ (equivalent to Latin longus).Irish (Ulster (Armagh) and Munster) : reduced Anglicized form of Gaelic Ó Longáin (see Langan).Chinese : from the name of an official treasurer called Long, who lived during the reign of the model emperor Shun (2257–2205 bc). his descendants adopted this name as their surname. Additionally, a branch of the Liu clan (see Lau 1), descendants of Liu Lei, who supposedly had the ability to handle dragons, was granted the name Yu-Long (meaning roughly ‘resistor of dragons’) by the Xia emperor Kong Jia (1879–1849 bc). Some descendants later simplified Yu-Long to Long and adopted it as their surname.Chinese : there are two sources for this name. One was a place in the state of Lu in Shandong province during the Spring and Autumn period (722–481 bc). The other source is the Xiongnu nationality, a non-Han Chinese people.Chinese : variant of Lang.Cambodian : unexplained.
Surname or Lastname
German
German : habitational name from any of several places so named, for example in Westphalia and Switzerland.German : nickname from Middle High German heiden ‘heathen’, Old High German heidano, apparently a derivative of heida ‘heath’, modeled on Latin paganus (see Pain 1). The nickname was sometimes used to refer to a Christian knight who had been on a Crusade to fight in the Holy Land.Jewish (Ashkenazic) : of uncertain origin; possibly a shortened form of any of various ornamental names formed with German Heide- ‘heath’, for example Heidenberg, Heidenkorn, Heidenkrug, Heidenwurzel.English : variant spelling of Hayden.Dutch : shortened form of vanderHeiden.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
English and Dutch
English and Dutch : from the medieval personal name Benedict (Latin Benedictus meaning ‘blessed’). This owed its popularity in the Middle Ages chiefly to St. Benedict of Norcia (c.480–550), who founded the Benedictine order of monks at Monte Cassino and wrote a monastic rule that formed a model for all subsequent rules. No doubt the meaning of the Latin word also contributed to its popularity as a personal name, especially in Romance countries.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Arabic, Muslim
Sample; Model; Paragon
Surname or Lastname
English and Irish (of Norman origin), and northern French
English and Irish (of Norman origin), and northern French : habitational name from any of several places in northern France, such as Nogent-sur-Oise, named with Latin Novientum, apparently an altered form of a Gaulish name meaning ‘new settlement’.The Anglo-Norman family of this name is descended from Fulke de Bellesme, lord of Nogent in Normandy, who was granted large estates around Winchester after the Conquest. His great-grandson was Hugh de Nugent (died 1213), who went to Ireland with Hugh de Lacy, and was granted lands in Bracklyn, County Westmeath. The family formed itself into a clan on the Irish model, of which the chief bore the hereditary title of Uinsheadun (Irish Uinnseadún), from their original seat at Winchester. They have been Earls of Westmeath since 1621. The name is now a common one in Ireland, and has been adopted there by some who have no connection with the clan.
Boy/Male
Tamil
Ayilyam | அயீலà¯à®¯à®®
Model state of india
Ayilyam | அயீலà¯à®¯à®®
Boy/Male
Hindu
Model state of india
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Tamil, Telugu, Traditional
New; Role Model of World; Ever Fresh
Surname or Lastname
English and Scottish
English and Scottish : occupational name for a stonemason, Middle English, Old French mas(s)on. Compare Machen. Stonemasonry was a hugely important craft in the Middle Ages.Italian (Veneto) : from a short form of Masone.French : from a regional variant of maison ‘house’.George Mason (1725–92), the American colonial statesman who framed the VA Bill of Rights and Constitution, which was used as a model by Thomas Jefferson when drafting the Declaration of Independence, was a VA planter, fourth in descent from George Mason (?1629–?86), a royalist soldier of the English Civil War who had received land grants in VA. As well as being prominent in the affairs of VA, the family also produced the first governor of MI.
Boy/Male
Egyptian
To model.
Girl/Female
Czech, Czechoslovakian, Danish, Finnish, German, Hebrew, Irish, Jewish, Polish
Friend; Beautiful; Model of Righteous Convert; Friendship
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Muslim
Model, Example
Boy/Male
Muslim
Sample, Model, Paragon
Girl/Female
Hindu, Indian, Traditional
Model; Idea
Boy/Male
Arabic, Muslim
Model; Example
Girl/Female
Arabic, Muslim
Example; Model; Demo
GRAPHICAL MODEL
GRAPHICAL MODEL
Girl/Female
Indian, Telugu
Fish (in Chineese)
Boy/Male
Hindu, Indian, Tamil
Lord Krishna
Boy/Male
Indian
Nature or beautiful, Figure
Female
Hebrew
(שַׂלְמָה) Hebrew unisex name SALMA means "garment." In the bible, this is a masculine name only, the name of the father of Boaz. Compare with another form of Salma.
Girl/Female
French
Royalty. French royalty title.
Boy/Male
Shakespearean
The Tragedy of Julius Caesar' A senator.
Boy/Male
Hindu, Indian
King; Gold
Boy/Male
Hindu
A friend, Be friendly
Boy/Male
English
Lives on the bare hill.
Girl/Female
Tamil
Hradini | ஹà¯à®°à®¾à®¤à®¿à®¨à¯€
Lightening
GRAPHICAL MODEL
GRAPHICAL MODEL
GRAPHICAL MODEL
GRAPHICAL MODEL
GRAPHICAL MODEL
a.
Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.
a.
Written or engraved; formed of letters or lines.
n.
A pen-shaped pointing device used to specify the cursor position on a graphics tablet.
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
n.
The quality or state of being graphic.
n.
An instrument for recording graphically the variations of temperature, or the indications of a thermometer.
n.
A chart or graphic representation of the average distribution of rain over the surface of the earth.
a.
Of, pertaining to, or resembling, pegmatite; as, the pegmatic structure of certain rocks resembling graphic granite.
a.
Well delineated; clearly and vividly described.
n.
The art or the science of drawing; esp. of drawing according to mathematical rules, as in perspective, projection, and the like.
a.
Of or pertaining to the arts of painting and drawing.
n.
A rock showing under the microscope the structure of a graphic granite (pegmatite).
a.
Alt. of Seraphical
a.
Of or pertaining to a seraph; becoming, or suitable to, a seraph; angelic; sublime; pure; refined.
n.
Hence, any graphic or vivid delineation or description of a person; as, a portrait in words.
n.
An instrument which, when applied over an artery, indicates graphically the movements or character of the pulse. See Sphygmogram.
a.
Of or pertaining to the art of writing.
a.
Alt. of Graphical
n.
Graphic granite. See under Granite.
adv.
In a graphic manner; vividly.