**Bayesian**- Hierarchical Bayesian extensions of MPT models explicitly account for participant heterogeneity by assuming that the individual parameters follow a continuous hierarchical distribution. (springer.com)
- Instead, we use a hierarchical Bayesian approach which enforces sharing of statistical strength across the different parts of the model. (ed.ac.uk)
- To make computations with the model efficient, and to better model the power-law statistics often observed in sequence data, we use a Bayesian nonparametric prior called the Pitman-Yor process as building blocks in the hierarchical model. (ed.ac.uk)
- The performance of these manifold Monte Carlo methods is assessed on Mixture models, logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. (ed.ac.uk)
- Continuous-Time Bayesian networks is a compact modeling language for multi-component processes that evolve continuously over time. (ed.ac.uk)
- This statistical model enables us to counterbalance the variability induced by small sample sizes and to embed the estimation in a Bayesian framework. (irit.fr)
- The multifractal analysis of multivariate images is then addressed by generalizing this Bayesian framework to hierarchical models able to account for the assumption that multifractal properties evolve smoothly in the dataset. (irit.fr)
- In the Bayesian approach to implementing, testing, and using cognitive models, assumptions can influence both the likelihood function of the model, usually corresponding to assumptions about psychological processes, and the prior distribution over model parameters, usually corresponding to assumptions about the psychological variables that influence those processes. (springer.com)
- The specification of the prior is unique to the Bayesian context, but often raises concerns that lead to the use of vague or non-informative priors in cognitive modeling. (springer.com)
- The Bayesian approach offers the additional possibility of expressing assumptions in the prior distribution over the parameters. (springer.com)
- Even those who advocate Bayesian methods in cognitive modeling sometimes regard the need to specify a prior as a cost that must be borne to reap the benefits of complete and coherent inference. (springer.com)
- non-parametric hierarchical Bayesian models, such as models based on the Dirichlet process, which allow the number of latent variables to grow as necessary to fit the data, but where individual variables still follow parametric distributions and even the process controlling the rate of growth of latent variables follows a parametric distribution. (wikipedia.org)
- Empirical Bayes requires a hierarchical observation model, in which higher levels can be regarded as providing prior constraints on lower levels: In neuroimaging observations of the same effect over voxels provides a natural, two-level hierarchy that enables an empirical Bayesian approach. (ucl.ac.uk)
- Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. (wikipedia.org)
- Frequentist statistics, the more popular foundation of statistics, has been known to contradict Bayesian statistics due to the Bayesian treatment of the parameters as random variables and its use of subjective information in establishing assumptions on these parameters. (wikipedia.org)
- Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. (wikipedia.org)

**independently and identically distributed**- Traditionally, data are aggregated across participants and analyzed under the assumption of independently and identically distributed observations. (springer.com)

**probability**- For both data-analytic and cognitive models, the likelihood is the function that gives the probability of observed data for a given set of parameter values. (springer.com)
- These include, among others: distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. (wikipedia.org)
- Posterior probability maps (PPMs) represent a complementary alternative to statistical parametric maps (SPMs) that are used to make classical inferences. (ucl.ac.uk)
- Numerous statistical applications involve multiple parameters that can be regarded as related or connected in such a way that the problem implies dependence of the joint probability model for these parameters. (wikipedia.org)
- In order to make updated probability statements about θ j {\displaystyle \theta _{j}} , given the occurrence of event y, we must begin with a model providing a joint probability distribution for θ j {\displaystyle \theta _{j}} and y. (wikipedia.org)
- In this model, the probability for an event to trigger another one primarily depends on their separating space and time distances, as well as on the magnitude of the triggering event, so that seismicity is then governed by a set of seven parameters. (wikipedia.org)
- The research presented cuts across the disciplines of Operations Management, Operations Research, System and Control Theory, Industrial Engineering, Probability and Statistic, and Applied Mathematics. (wikipedia.org)
- Each of these components is modeled by a probability distribution function and its coding length is computed as follows: The boundary encoding leverages the fact that regions in natural images tend to have a smooth contour. (wikipedia.org)
- It appears that children can detect the statistical probability of certain sounds occurring with one another, and use this to parse out word boundaries. (wikipedia.org)

**Markov-chain**- TreeBUGS reads standard MPT model files and obtains Markov-chain Monte Carlo samples that approximate the posterior distribution. (springer.com)
- We set up a transmission model for which parameters are estimated from the data via Markov chain Monte Carlo sampling. (pnas.org)
- Here, we set up a transmission model for which parameters are estimated from the data via Markov chain Monte Carlo sampling and data augmentation techniques ( Materials and Methods and SI Materials and Methods ). (pnas.org)
- The authors develop binomial-beta hierarchical models for ecological inference using insights from the literature on hierarchical models based on Markov chain Monte Carlo algorithms and King's ecological inference model. (harvard.edu)

**Inference**- We introduce a general technique for making statistical inference from clustering tools applied to gene expression microarray data. (pnas.org)
- Statistical inference is based on the application of a randomization technique, bootstrapping. (pnas.org)
- However, another question that is at least as important has received less attention: How does one make statistical inference based on the results of clustering? (pnas.org)
- Ecological inference is a large and very important area for applications that is especially rich with open statistical questions. (harvard.edu)
- Nonparametric statistics includes both descriptive statistics and statistical inference. (wikipedia.org)
- In this talk, I will explain the key differences between associational and causal models and describe some of the recent technical developments in causal inference. (microsoft.com)

**regression**- We've done some work on the logistic regression ("3-parameter Rasch") model , and it might be helpful to see some references to other approaches. (andrewgelman.com)
- Data analysis typically relies on a standard set of statistical models, especially Generalized Linear Models (GLMs) that form the foundations of regression and the analysis of variance. (springer.com)
- Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. (harvard.edu)
- This model, which provides a tool for comparative politics research analagous to that which regression analysis provides in the American two-party context, can be used to explain or predict how geographic distributions of electoral results depend upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or aggregate areas. (harvard.edu)
- These techniques include, among others: non-parametric regression, which refers to modeling where the structure of the relationship between variables is treated non-parametrically, but where nevertheless there may be parametric assumptions about the distribution of model residuals. (wikipedia.org)
- They are different from statistical models (for example linear regression) whose aim is to empirically estimate the relationships between variables. (wikipedia.org)

**hypothesis**- Topics include an introduction to the basic two-level model for continuous outcomes, assessment of fit, checking model assumptions, single and multiparameter hypothesis testing, the extension to three-level models, and nonlinear models for binary outcomes. (umich.edu)
- Data Analysis : Data Analysis is the process of inspecting, cleaning and modelling data with the objective of discovering useful information, arriving at conclusion Statistics : Statistical Analysis enables to validate the assumptions, hypothesis and test them using standard statistical models. (wikipedia.org)
- A second hypothesis of Soar's theory is that although only a single operator can be selected at each step, forcing a serial bottleneck, the processes of selection and application are implemented through parallel rule firings, which provide context-dependent retrieval of procedural knowledge. (wikipedia.org)
- The efficient coding hypothesis was proposed by Horace Barlow in 1961 as a theoretical model of sensory coding in the brain. (wikipedia.org)
- A key prediction of the efficient coding hypothesis is that sensory processing in the brain should be adapted to natural stimuli. (wikipedia.org)
- One assumption used in testing the Efficient Coding Hypothesis is that neurons must be evolutionarily and developmentally adapted to the natural signals in their environment. (wikipedia.org)

**Markovian**- As opposed to most other sequence models, our model does not make any Markovian assumptions. (ed.ac.uk)
- Kalman-Bucy or particle) filtering, generalized filtering eschews Markovian assumptions about random fluctuations. (wikipedia.org)

**distributions**- However, flexible and user-friendly software is not yet available to analyze MPT models with continuous hierarchical distributions. (springer.com)
- nonparametric statistics (in the sense of a statistic over data, which is defined to be a function on a sample that has no dependency on a parameter), whose interpretation does not depend on the population fitting any parameterised distributions. (wikipedia.org)
- In these techniques, individual variables are typically assumed to belong to parametric distributions, and assumptions about the types of connections among variables are also made. (wikipedia.org)
- By assuming different distributions of y ∣ u {\displaystyle y\mid u} and u {\displaystyle u} , and using different functions of g {\displaystyle g} and ' v {\displaystyle v} , we will be able to obtain different models. (wikipedia.org)
- In hierarchical generalized linear models, the distributions of random effect u {\displaystyle u} do not necessarily follow normal distribution. (wikipedia.org)

**human cognition**- This assumption better reflects the characteristics of human cognition because cognitive processes usually do not work in isolation but function within a network of interrelated competencies and skills. (wikipedia.org)
- Recently, the emphasis on Soar has been on general AI (functionality and efficiency), whereas the emphasis on ACT-R has always been on cognitive modeling (detailed modeling of human cognition). (wikipedia.org)
- Bootstrapping has a strong link to connectionist theories which model human cognition as a system of simple, interconnected networks. (wikipedia.org)

**critical assumptions**- The assumptions underlying each analysis are emphasized, and the reader is shown how to test the critical assumptions using SPSS or SAS. (ecampus.com)
- According to Pinker, semantic bootstrapping requires two critical assumptions to hold true: A child must be able to perceive meaning from utterances. (wikipedia.org)

**theoretical**- My experience is that anything too data-driven in this field tends to run into trouble within political science because it while it is one thing to toss more elaborate statistical setups at the roll call data, they tend to lack the clear theoretical underpinnings of the Euclidean spatial voting model. (andrewgelman.com)
- They provide a way of formalizing available information and making theoretical assumptions, enabling the evaluation of the assumptions by empirical evidence, and applying what is learned to make more complete model-based inferences and predictions. (springer.com)
- The directional and proximity models offer dramatically different theories for how voters make decisions and fundamentally divergent views of the supposed microfoundations on which vast bodies of literature in theoretical rational choice and empirical political behavior have been built. (harvard.edu)
- We demonstrate here that the empirical tests in the large and growing body of literature on this subject amount to theoretical debates about which statistical assumption is right. (harvard.edu)
- Sornette's group has contributed significantly to the theoretical development and study of the properties of the now standard Epidemic Type Aftershock Sequence (ETAS) model. (wikipedia.org)

**priors**- We survey several sources of information that can help to specify priors for cognitive models, discuss some of the methods by which this information can be formalized in a prior distribution, and identify a number of benefits of including informative priors in cognitive modeling. (springer.com)
- We believe failing to give sufficient attention to specifying priors is unfortunate, and potentially limits what cognitive modeling can achieve. (springer.com)
- Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. (wikipedia.org)

**stochastic processes**- This is a ubiquitous measure of roughness in the theory of stochastic processes. (wikipedia.org)

**parameters**- Moreover, fitting separate models per participant is often not possible due to insufficient numbers of individual responses, which prevents a reliable estimation of model parameters. (springer.com)
- From signals, the statistical descriptive parameters are obtained and a map of its distribution is calculated. (google.de)
- The first limitation is tackled by introducing a generic statistical model for the logarithm of wavelet leaders, parametrized by multifractal parameters of interest. (irit.fr)
- The key difference is the interpretation of the model likelihood and parameters. (springer.com)
- In these models, parameters have generic interpretations, like locations and scales. (springer.com)
- It is natural to interpret the parameters in cognitive models as psychological variables like memory capacities, attention weights, or learning rates. (springer.com)
- Even when a cognitive model uses a likelihood function consistent with GLMs-for example, modeling choice probabilities as weighted linear combinations of stimulus attributes-it is natural to interpret the likelihood as corresponding to cognitive processes, because of the psychological interpretability of the parameters. (springer.com)
- We develop an augmentation to MFVB that delivers accurate estimates of posterior uncertainty for model parameters. (microsoft.com)
- In order to make the model identifiable, we need to impose constraints on parameters. (wikipedia.org)
- Sornette's group is currently pushing the model to its limits by allowing space and time variations of its parameters. (wikipedia.org)
- Generalized filtering furnishes posterior densities over hidden states (and parameters) generating observed data using a generalized gradient descent on variational free energy, under the Laplace assumption. (wikipedia.org)

**parameter**- 2) our setup maps directly onto the 2 parameter IRT model from educational testing, about which much is known… In this sense our approach is a little more model-driven than data-driven (i.e., contrast naive MDS or factor analysis or clustering etc). (andrewgelman.com)
- Traditionally, MPT models are fitted using data aggregated across participants (i.e., summed response frequencies) to obtain a sufficiently large number of observations for parameter estimation and for a high statistical power of goodness-of-fit tests. (springer.com)
- The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. (ed.ac.uk)
- In the standard frequentist approach, assumptions can only be used to specify the likelihood, and, less commonly, the bounds of the parameter space. (springer.com)
- Thus taking reliable account of parameter and model uncertainty is crucial, perhaps even more so than for standard statistical models, yet this is an area that has received little attention from statisticians. (wikipedia.org)
- There are different ways to obtain parameter estimates for a hierarchical generalized linear model. (wikipedia.org)
- The difficulty parameter is called b. the two important assumptions are local independence and unidimensionality. (wikipedia.org)
- They are one parameter logistic model, two parameter logistic model and three parameter logistic model. (wikipedia.org)

**data**- Just a couple of general comments: (1) Any model that makes probabilistic predictions can be judged on its own terms by comparing to actual data. (andrewgelman.com)
- The paper is mostly about computation but it has an interesting discussion of some general ideas about how to model this sort of data. (andrewgelman.com)
- What behavioral/political assumptions or processes suggest that we ought to do this when we model the data? (andrewgelman.com)
- Multinomial processing tree (MPT) models are a class of measurement models that account for categorical data by assuming a finite number of underlying cognitive processes. (springer.com)
- However, the aggregation of data is only justified under the assumption that observations are identically and independently distributed (i.i.d.) for all participants and items. (springer.com)
- Evaluating the impact of different social networks on the spread of respiratory diseases has been limited by a lack of detailed data on transmission outside the household setting as well as appropriate statistical methods. (pnas.org)
- or time-use data) but then makes assumptions about how transmission rates change with the type of interaction (e.g., as a function of the setting and the spatial or social distance between individuals, etc. (pnas.org)
- Validating these assumptions can be challenging due to the scarcity of appropriate epidemiological data. (pnas.org)
- Printouts with annotations from SAS or SPSS show how to process the data for each analysis. (ecampus.com)
- Although this phenomenon is appreciated by many population geneticists, many modern statistical approaches for analyzing genotype data ignore one of these two components. (genetics.org)
- In this talk I will present a new approach to modelling sequence data called the sequence memoizer. (ed.ac.uk)
- One way to think of cognitive modeling is as a natural extension of data analysis. (springer.com)
- Both involve developing, testing, and using formal models as accounts of brain and behavioral data. (springer.com)
- For data-analytic models, these likelihoods typically follow from GLMs. (springer.com)
- Their more elaborate interpretation means that cognitive models aim to formalize and use richer information and assumptions than data-analytic models do. (springer.com)
- Our statistical approach, hd-MI, is based on imputation for samples without available RNA-seq data that are considered as missing data but are observed on the secondary dataset. (deepdyve.com)
- The large amount of generated data has created a need for multiple bioinformatics and statistical post-processing of the raw experimental data. (deepdyve.com)
- RNA-seq expression data are count data and are thus discrete so standard GGM models usually used for network inferrence and that are based on Gaussianity assumption are not suited to such data. (deepdyve.com)
- Having a large number of observations is thus a key point for ensuring reliable results in statistical analyses of RNA-seq data Liu et al. (deepdyve.com)
- To illustrate our recommendations, we replicate the results of several published works, showing in each case how the authors' own conclusions can be expressed more sharply and informatively, and, without changing any data or statistical assumptions, how our approach reveals important new information about the research questions at hand. (harvard.edu)
- This article also provides an example of a hierarchical model in which the statistical idea of "borrowing strength" is used not merely to increase the efficiency of the estimates but to enable the data analyst to obtain estimates. (harvard.edu)
- We then specified a model without this unrealistic assumption and we found that the assumption was not supported, and that all evidence in the data for platforms causing government budgets evaporated. (harvard.edu)
- The key statistical assumptions have not been empirically tested and, indeed, turn out to be effectively untestable with exiting methods and data. (harvard.edu)
- We also develop diagnostics for checking the fit of the imputation model based on comparing imputed data to nonimputed data. (harvard.edu)
- Typically, the model grows in size to accommodate the complexity of the data. (wikipedia.org)
- This problem can be eschewed by using empirical Bayes in which prior variances are estimated from the data, under some simple assumptions' about their form. (ucl.ac.uk)
- In the model a control stream replaces the instruction and data streams of the real system. (wikipedia.org)
- Predictive analytics encompasses a variety of statistical techniques from predictive modelling, machine learning, and data mining that analyze current and historical facts to make predictions about future or otherwise unknown events. (wikipedia.org)
- In business, predictive models exploit patterns found in historical and transactional data to identify risks and opportunities. (wikipedia.org)
- Scoring models process a customer's credit history, loan application, customer data, etc., in order to rank-order individuals by their likelihood of making future credit payments on time. (wikipedia.org)
- It is important to note, however, that the accuracy and usability of results will depend greatly on the level of data analysis and the quality of assumptions. (wikipedia.org)
- Generally, the term predictive analytics is used to mean predictive modeling, "scoring" data with predictive models, and forecasting. (wikipedia.org)
- These disciplines also involve rigorous data analysis, and are widely used in business for segmentation and decision making, but have different purposes and the statistical techniques underlying them vary. (wikipedia.org)
- The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. (wikipedia.org)
- However, Bayesians argue that relevant information regarding decision making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. (wikipedia.org)
- Statistical Methods for psychology include development and application statistical theory and methods for modeling psychological data. (wikipedia.org)
- Texture is encoded by lossy compression in a way similar to minimum description length (MDL) principle, but here the length of the data given the model is approximated by the number of samples times the entropy of the model. (wikipedia.org)

**ANOVA**- Analysis of variance (ANOVA): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests. (wikipedia.org)

**Bayes**- Bridge sampling is an impoverished method that only gives Bayes factors for overlapping models. (ed.ac.uk)
- In the model, this circuit computes probabilities that considered alternatives are correct, according to Bayes' theorem. (ed.ac.uk)

**Poisson**- Recent works have considered using a generalized linear model (GLM) based on the Poisson distribution [log-linear graphical model Allen and Liu (2012) or hierarchical Poisson log-normal model Gallopin et al. (deepdyve.com)
- For example, if the distribution of y ∣ u {\displaystyle y\mid u} is Poisson with certain mean, the distribution of u {\displaystyle u} is Gamma, and canonical log link is used, then we call the model Poisson conjugate HGLM. (wikipedia.org)

**robust**- This point is relevant even to something as seemingly innocuous as hierarchical modeling or robust fitting. (andrewgelman.com)
- Also, due to the reliance on fewer assumptions, non-parametric methods are more robust. (wikipedia.org)
- A key benefit of this approach is the aggregation of information leading to a higher statistical power and more robust point estimate than is possible from the measure derived from any individual study. (wikipedia.org)

**empirically**- The model and some extensions have been empirically tested and are widely used in the marketing literature. (wikipedia.org)

**methods**- As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. (wikipedia.org)
- Under Race to the Top and other programs advocating for better methods of evaluating teacher performance, districts have looked to value-added modeling as a supplement to observing teachers in classrooms. (wikipedia.org)
- Louisiana legislator Frank A. Hoffmann introduced a bill to authorize the use of value-added modeling techniques in the state's public schools as a means to reward strong teachers and to identify successful pedagogical methods, as well as providing a means to provide additional professional development for those teachers identified as weaker than others. (wikipedia.org)
- Here it is convenient to follow the terminology used by the Cochrane Collaboration, and use "meta-analysis" to refer to statistical methods of combining evidence, leaving other aspects of 'research synthesis' or 'evidence synthesis', such as combining information from qualitative studies, for the more general context of systematic reviews. (wikipedia.org)
- Structured sparsity regularization is a class of methods, and an area of research in statistical learning theory, that extend and generalize sparsity regularization learning methods. (wikipedia.org)
- Both sparsity and structured sparsity regularization methods seek to exploit the assumption that the output variable Y {\displaystyle Y} (i.e., response, or dependent variable) to be learned can be described by a reduced number of variables in the input space X {\displaystyle X} (i.e., the domain, space of features or explanatory variables). (wikipedia.org)
- Structured sparsity regularization methods generalize and extend sparsity regularization methods, by allowing for optimal selection over structures like groups or networks of input variables in X {\displaystyle X} . Common motivation for the use of structured sparsity methods are model interpretability, high-dimensional learning (where dimensionality of X {\displaystyle X} may be higher than the number of observations n {\displaystyle n} ), and reduction of computational complexity. (wikipedia.org)
- Moreover, structured sparsity methods allow to incorporate prior assumptions on the structure of the input variables, such as overlapping groups, non-overlapping groups, and acyclic graphs. (wikipedia.org)
- Examples of uses of structured sparsity methods include face recognition, magnetic resonance image (MRI) processing, socio-linguistic analysis in natural language processing, and analysis of genetic expression in breast cancer. (wikipedia.org)
- This can lead to a stack of substates, where traditional problem methods, such as planning or hierarchical task decomposition, naturally arise. (wikipedia.org)
- These models use the genetic information already obtained through methods such as phylogenetics to determine the route that evolution has taken and when evolutionary events occurred. (wikipedia.org)

**displaystyle**- The usual starting point of a statistical analysis is the assumption that the n values y n {\displaystyle y_{n}} are exchangeable. (wikipedia.org)
- In this hierarchical generalized linear model, the fixed effect is described by β {\displaystyle \beta } , which is the same for all observations. (wikipedia.org)
- If the distribution of u {\displaystyle u} is normal and the link function of v {\displaystyle v} is the identity function, then hierarchical generalized linear model is the same as GLMM. (wikipedia.org)
- If y ∣ u {\displaystyle y\mid u} follows binomial distribution with certain mean, u {\displaystyle u} has the conjugate beta distribution, and canonical logit link is used, then we call the model Beta conjugate model. (wikipedia.org)
- This intersection of complements selection criteria implies the modeling choice that we allow some coefficients within a particular group g {\displaystyle g} to be set to zero, while others within the same group g {\displaystyle g} may remain positive. (wikipedia.org)
- m ) {\displaystyle p({\tilde {s}}(t)\vert m)} to compare different models. (wikipedia.org)

**correlations**- The spatial and temporal correlations of the map are modeled as well as their dependence on experimental covariables. (google.de)
- In this situation, using generalized linear models and ignoring the correlations may cause problems. (wikipedia.org)

**estimates**- Conceptually, a meta-analysis uses a statistical approach to combine the results from multiple studies in an effort to increase power (over individual studies), improve estimates of the size of the effect and/or to resolve uncertainty when reports disagree. (wikipedia.org)

**dependence**- Mutual information is a measure of the inherent dependence expressed in the joint distribution of X and Y relative to the joint distribution of X and Y under the assumption of independence. (wikipedia.org)

**framework**- This model provides a framework for designing diagnostic items based on attributes, which links examinees' test performance to specific inferences about examinees' knowledge and skills. (wikipedia.org)
- The hierarchical linear model (HLM) provides a conceptual framework and a flexible set of analytic tools to study a variety of social, political, and developmental processes. (umich.edu)
- Dynare - when the framework is deterministic, can be used for models with the assumption of perfect foresight. (wikipedia.org)

**procedure**- Aleks Jakulin has come up with his own procedure for hierarchical classification of legislators using roll-call votes and has lots of detail and cool pictures on his website. (andrewgelman.com)

**unified theory**- I don't have any unified theory of these models, and I don't really have any good reason to prefer any of these models to any others. (andrewgelman.com)

**Moreover**- Moreover, the generalized linear mixed model (GLMM) is a special case of the hierarchical generalized linear model. (wikipedia.org)
- Moreover, the mixed linear model is in fact the normal conjugate HGLM. (wikipedia.org)

**computational**- During this talk I will present computational models describing decision making process in the cortico-basal ganglia circuit. (ed.ac.uk)
- The hierarchical form of analysis and organization helps in the understanding of multiparameter problems and also plays an important role in developing computational strategies. (wikipedia.org)

**descriptive**- However, people are increasingly using the term to refer to related analytical disciplines, such as descriptive modeling and decision modeling or optimization. (wikipedia.org)

**observation**- The development of cognitive models involves the creative scientific formalization of assumptions, based on theory, observation, and other relevant information. (springer.com)
- In a hierarchical model, observations are grouped into clusters, and the distribution of an observation is determined not only by common structure among all clusters but also by the specific structure of the cluster where this observation belongs. (wikipedia.org)

**analysis**- if you don't know about it, Doug Rivers has a very nice paper on identification for multidimensional item-response models (with roll call analysis as a special case). (andrewgelman.com)
- The AHM also differs from the RSM with respect to the identification of the cognitive attributes and the logic underlying the diagnostic inferences made from the statistical analysis. (wikipedia.org)
- Principled test design encompasses 3 broad stages: cognitive model development test development psychometric analysis. (wikipedia.org)
- Psychometric analysis comprises the third stage in the test design process. (wikipedia.org)
- The approach utilizes an analysis of variance model to achieve normalization and estimate differential expression of genes across multiple conditions. (pnas.org)
- Value-added modeling (also known as value-added analysis and value-added assessment) is a method of teacher evaluation that measures the teacher's contribution in a given year by comparing the current test scores of their students to the scores of those same students in previous school years, as well as to the scores of other students in the same grade. (wikipedia.org)
- A meta-analysis is a statistical analysis that combines the results of multiple scientific studies. (wikipedia.org)
- The statistical theory surrounding meta-analysis was greatly advanced by the work of Nambury S. Raju, Larry V. Hedges, Harris Cooper, Ingram Olkin, John E. Hunter, Jacob Cohen, Thomas C. Chalmers, Robert Rosenthal, Frank L. Schmidt, and Douglas G. Bonett. (wikipedia.org)
- A meta-analysis is a statistical overview of the results from one or more systematic reviews. (wikipedia.org)

**latent**- We also propose and implement novel statistical extensions to include continuous and discrete predictors (as either fixed or random effects) in the latent-trait MPT model. (springer.com)
- The modern test theory is based on latent trait model. (wikipedia.org)

**explicitly**- I will explain why many existing machine learning tasks are really causal reasoning in disguise, why an increasing number of machine learning tasks will explicitly require causal models, and why researchers and practitioners who understand causal reasoning will succeed where others fail. (microsoft.com)

**approach**- In contrast, the AHM uses an a priori approach to identifying the attributes and specifying their interrelationships in a cognitive model. (wikipedia.org)
- In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner. (harvard.edu)
- This approach captures the modeling situation where variables can be selected as long as they belong at least to one group with positive coefficients. (wikipedia.org)

**observations**- A summary of commonly used models are: Hierarchical generalized linear models are used when observations come from different clusters. (wikipedia.org)

**classification**- The RSM using statistical pattern classification where examinees' observed response patterns are matched to pre-determined response patterns that each correspond to a particular cognitive or knowledge state. (wikipedia.org)
- Notwithstanding these distinctions, the statistical literature now commonly applies the label "non-parametric" to test procedures that we have just termed "distribution-free", thereby losing a useful classification. (wikipedia.org)

**mathematical**- The architecture system design of the present invention allows for information gathering independent of the mathematical models used and takes into account security settings in the network hosts. (google.com)
- In mathematical modeling, deterministic simulations contain no random variables and no degree of randomness, and consist mostly of equations, for example difference equations. (wikipedia.org)

**psychological**- Cognitive models often use likelihoods designed to formalize assumptions about psychological processes, such as the encoding of a stimulus in memory, or the termination of search in decision making. (springer.com)
- The classical test theory or true score theory or reliability theory in statistics is a set of statistical procedures useful for development of psychological tests and scales. (wikipedia.org)

**parametric**- The second meaning of non-parametric covers techniques that do not assume that the structure of a model is fixed. (wikipedia.org)

**different**- Unfortunately, these assumptions are also crucial since changing them leads to different conclusions about voter processes. (harvard.edu)
- Hierarchical modeling is used when information is available on several different levels of observational units. (wikipedia.org)
- So a random effect component, different for different clusters, is introduced into the model. (wikipedia.org)
- There are different techniques to fit a hierarchical generalized linear model. (wikipedia.org)
- Since its beginnings in 1983 as John Laird's thesis, it has been widely used by AI researchers to create intelligent agents and cognitive models of different aspects of human behavior. (wikipedia.org)
- As a process, bootstrapping can be divided into different domains, according to whether it involves semantic bootstrapping, syntactic bootstrapping, prosodic bootstrapping, or pragmatic bootstrapping. (wikipedia.org)

**approaches**- In recent years, several approaches have been developed to account for heterogeneity in MPT models. (springer.com)

**cognitive model**- To generate a diagnostic skill profile, examinees' test item responses are classified into a set of structured attribute patterns that are derived from components of a cognitive model of task performance. (wikipedia.org)
- The cognitive model contains attributes, which are defined as a description of the procedural or declarative knowledge needed by an examinee to answer a given test item correctly. (wikipedia.org)
- The AHM differs from Tatsuoka's Rule Space Method (RSM) with the assumption of dependencies among the attributes within the cognitive model. (wikipedia.org)
- As such, the attribute hierarchy serves as a cognitive model of task performance designed to represent the inter-related cognitive processes required by examinees to solve test items. (wikipedia.org)
- Cognitive model development comprises the first stage in the test design process. (wikipedia.org)
- During this stage, the cognitive knowledge, processes, and skills are identified and organized into an attribute hierarchy or cognitive model. (wikipedia.org)
- This stage also encompasses validation of the cognitive model prior to the test development stage. (wikipedia.org)
- During this stage, items are created to measure each attribute within the cognitive model while also maintaining any dependencies modeled among the attributes. (wikipedia.org)
- During this stage, the fit of the cognitive model relative to observed examinee responses is evaluated to ascertain the appropriateness of the model to explain test performance. (wikipedia.org)

**usually**- Researchers use statistical processes on a student's past test scores to predict the student's future test scores, on the assumption that students usually score approximately as well each year as they have in past years. (wikipedia.org)
- Deterministic simulation models are usually designed to capture some underlying mechanism or natural process. (wikipedia.org)
- Crucially, the precision (inverse variance) of high order derivatives fall to zero fairly quickly, which means it is only necessary to model relatively low order generalized motion (usually between two and eight) for any given or parameterized autocorrelation function. (wikipedia.org)

**make**- Hierarchical feedback control policies, on the other hand, offer the promise of being able to handle realistically complex manufacturing systems in a tractable fashion to make their management more efficient. (wikipedia.org)

**results**- We show state-of-the-art results on language modelling and text compression. (ed.ac.uk)
- In the first part I will review models describing how speed and accuracy of decisions is controlled in the cortico-basal-ganglia circuit, and present results of a recent experiment attempting to distinguish between these models. (ed.ac.uk)
- Social Scientists rarely take full advantage of the information available in their statistical results. (harvard.edu)
- Deployment : Predictive model deployment provides the option to deploy the analytical results into everyday decision making process to get results, reports and output by automating the decisions based on the modelling. (wikipedia.org)
- Model Monitoring : Models are managed and monitored to review the model performance to ensure that it is providing the results expected. (wikipedia.org)

**estimate**- Design: A set of experimental runs which allows you to fit a particular model and estimate your desired effects. (wikipedia.org)

**standard**- First, accepting their entire statistical model, and correcting only an algebraic error (a mistake in how they computed their standard errors), we showed that their hypothesized relationship holds up in fewer than half the tests they reported. (harvard.edu)
- With Taylor ED's open architecture, software users can access standard libraries of atoms to build models. (wikipedia.org)

**distribution**- The Distribution of Species Range Size: a Stochastic Process Proceedings. (jove.com)

**contrast**- In contrast, the RSM makes no assumptions regarding the dependencies among the attributes. (wikipedia.org)
- Cognitive models, in contrast, aim to afford more substantive interpretations. (springer.com)

**statistics**- Simulation of the system model yields the timing and resource usage statistics needed for performance evaluation, without the necessity of emulating the system. (wikipedia.org)
- In statistics, hierarchical generalized linear models (HGLM) extend generalized linear models by relaxing the assumption that error components are independent. (wikipedia.org)
- The group is active in the modelling of earthquakes, landslides, and other natural hazards, combining concepts and tools from statistical physics, statistics, tectonics, seismology and more. (wikipedia.org)
- This over-simplified assumption has recently relaxed by coupling the statistics of ETAS to genuine mechanical information. (wikipedia.org)

**test**- In the second part of the talk, I will present a model assuming that the cortico-basal-ganglia circuit performs statistically optimal test that maximizes speed of decisions for any required accuracy. (ed.ac.uk)
- Naively, these associations can be found by use of a simple statistical test. (microsoft.com)
- In this way, value-added modeling attempts to isolate the teacher's contributions from factors outside the teacher's control that are known to strongly affect student test performance, including the student's general intelligence, poverty, and parental involvement. (wikipedia.org)

**solve**- On this view, in terms of learning, humans have statistical learning capabilities that allow them to problem solve. (wikipedia.org)

**limits**- Some research limits the model to teachers of third grade and above. (wikipedia.org)