Quantifying Individuals’ Theory-Based Knowledge Using Probabilistic Causal Graphs: A Bayesian Hierarchical Approach

2020 ◽  
Author(s):  
Atharva Hans ◽  
Ashish M. Chaudhari ◽  
Ilias Bilionis ◽  
Jitesh H. Panchal
Keyword(s):  
Engineering Students ◽  
Likelihood Function ◽  
Computational Design ◽  
Directed Acyclic Graphs ◽  
Causal Knowledge ◽  
Bayesian Hierarchical ◽  
Proposed Model ◽  
Significant Research ◽  
Ability Parameter ◽  
3Pl Model

Abstract Extracting an individual’s knowledge structure is a challenging task as it requires formalization of many concepts and their interrelationships. While there has been significant research on how to represent knowledge to support computational design tasks, there is limited understanding of the knowledge structures of human designers. This understanding is necessary for comprehension of cognitive tasks such as decision making and reasoning, and for improving educational programs. In this paper, we focus on quantifying theory-based causal knowledge, which is a specific type of knowledge held by human designers. We develop a probabilistic graph-based model for representing individuals’ concept-specific causal knowledge for a given theory. We propose a methodology based on probabilistic directed acyclic graphs (DAGs) that uses logistic likelihood function for calculating the probability of a correct response. The approach involves a set of questions for gathering responses from 205 engineering students, and a hierarchical Bayesian approach for inferring individuals’ DAGs from the observed responses. We compare the proposed model to a baseline three-parameter logistic (3PL) model from the item response theory. The results suggest that the graph-based logistic model can estimate individual students’ knowledge graphs. Comparisons with the 3PL model indicate that knowledge assessment is more accurate when quantifying knowledge at the level of causal relations than quantifying it using a scalar ability parameter. The proposed model allows identification of parts of the curriculum that a student struggles with and parts they have already mastered which is essential for remediation.

scholarly journals Bayesian Derivative Order Estimation for a Fractional Logistic Model

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 109
Author(s):  
Francisco J. Ariza-Hernandez ◽  
Martin P. Arciga-Alejandre ◽  
Jorge Sanchez-Ortiz ◽  
Alberto Fleitas-Imbert
Keyword(s):  
Inverse Problem ◽  
Logistic Model ◽  
Likelihood Function ◽  
Synthetic Data ◽  
Real Data ◽  
Posterior Distributions ◽  
Rate Parameter ◽  
Order Estimation ◽  
Proposed Model ◽  
Derivative Order

In this paper, we consider the inverse problem of derivative order estimation in a fractional logistic model. In order to solve the direct problem, we use the Grünwald-Letnikov fractional derivative, then the inverse problem is tackled within a Bayesian perspective. To construct the likelihood function, we propose an explicit numerical scheme based on the truncated series of the derivative definition. By MCMC samples of the marginal posterior distributions, we estimate the order of the derivative and the growth rate parameter in the dynamic model, as well as the noise in the observations. To evaluate the methodology, a simulation was performed using synthetic data, where the bias and mean square error are calculated, the results give evidence of the effectiveness for the method and the suitable performance of the proposed model. Moreover, an example with real data is presented as evidence of the relevance of using a fractional model.

Maximum likelihood function for fuzzy count data models (using heaped data as fuzzy)

2020 ◽  
Vol 39 (5) ◽  
pp. 6891-6901
Author(s):  
Godrick Oketch ◽  
Filiz Karaman
Keyword(s):  
Count Data ◽  
Likelihood Function ◽  
Real Data ◽  
Study Data ◽  
Data Models ◽  
Count Data Models ◽  
Proposed Model ◽  
Data Points ◽  
Heaped Data ◽  
Entire Dataset

Count data models are based on definite counts of events as dependent variables. But there are practical situations in which these counts may fail to be specific and are seen as imprecise. In this paper, an assumption that heaped data points are fuzzy is used as a way of identifying counts that are not definite since heaping can result from imprecisely reported counts. Because it is practically unlikely to report all counts in an entire dataset as imprecise, this paper proposes a likelihood function that not only considers both precise and imprecisely reported counts but also incorporates α - cuts of fuzzy numbers with the aim of varying impreciseness of fuzzy reported counts. The proposed model is then illustrated through a smoking cessation study data that attempts to identify factors associated with the number of cigarettes smoked in a month. Through the real data illustration and a simulation study, it is shown that the proposed model performs better in predicting the outcome counts especially when the imprecision of the fuzzy points in a dataset are increased. The results also show that inclusion of α - cuts makes it possible to identify better models, a feature that was not previously possible.

Two-Dimensional Stability Analysis of Interrupted High-Speed Milling

2010 ◽  
Vol 43 ◽  
pp. 492-498
Author(s):  
Zi Xiong Lin ◽  
Xiang Huang ◽  
Muhammad Masud Akhtar
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Research Work ◽  
Stable Region ◽  
Dimensional Model ◽  
Analysis Model ◽  
Milling Operations ◽  
Proposed Model ◽  
Significant Research ◽  
Made In

Significant research has been made regarding chatter stability of milling operations. This paper presents a 2 degree of freedom stability analysis model (2 DOF model) for interrupted cutting. The cutting process is divided into two parts namely “free vibration” and “forced vibration” considering the flexibility in x and y directions. Calculating the solutions of the two parts, a four-dimensional-single-variation discretization map is established and the eigenvalues of the Jacques Matrix are checked at the fixed point on the Floquet unit circle. The two Neimark-Sacker and flip bifurcations are evaluated. The research work shows that the up milling is more stable than the down milling under the same operating parameters. The comprison of the proposed 2 DOF model with Davies one degree of dimensional model (1 DOF Davieas model) has been made in the paper which shows that the area of stable region in the proposed model is greater than the stable region in the 1 DOF Davies model. In the last the results of the experiments support the proposed model has been verified by experimentation.

scholarly journals Bayesian modelling of compositional heterogeneity in molecular phylogenetics

2014 ◽  
Vol 13 (5) ◽  
Author(s):  
Sarah E. Heaps ◽  
Tom M.W. Nye ◽  
Richard J. Boys ◽  
Tom A. Williams ◽  
T. Martin Embley
Keyword(s):  
Molecular Phylogenetics ◽  
Data Augmentation ◽  
Likelihood Function ◽  
Sequence Evolution ◽  
Compositional Heterogeneity ◽  
Sequence Composition ◽  
Posterior Inference ◽  
Proposed Model ◽  
Root Position ◽  
Biological Interpretation

AbstractIn molecular phylogenetics, standard models of sequence evolution generally assume that sequence composition remains constant over evolutionary time. However, this assumption is violated in many datasets which show substantial heterogeneity in sequence composition across taxa. We propose a model which allows compositional heterogeneity across branches, and formulate the model in a Bayesian framework. Specifically, the root and each branch of the tree is associated with its own composition vector whilst a global matrix of exchangeability parameters applies everywhere on the tree. We encourage borrowing of strength between branches by developing two possible priors for the composition vectors: one in which information can be exchanged equally amongst all branches of the tree and another in which more information is exchanged between neighbouring branches than between distant branches. We also propose a Markov chain Monte Carlo (MCMC) algorithm for posterior inference which uses data augmentation of substitutional histories to yield a simple complete data likelihood function that factorises over branches and allows Gibbs updates for most parameters. Standard phylogenetic models are not informative about the root position. Therefore a significant advantage of the proposed model is that it allows inference about rooted trees. The position of the root is fundamental to the biological interpretation of trees, both for polarising trait evolution and for establishing the order of divergence among lineages. Furthermore, unlike some other related models from the literature, inference in the model we propose can be carried out through a simple MCMC scheme which does not require problematic dimension-changing moves. We investigate the performance of the model and priors in analyses of two alignments for which there is strong biological opinion about the tree topology and root position.

scholarly journals A Spatiotemporal Prediction Model for Regional Scheduling of Shared Bicycles Based on the INLA Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhuoran Yu ◽  
Yimeng Duan ◽  
Shen Zhang ◽  
Xin Liu ◽  
Kui Li
Keyword(s):  
Prediction Models ◽  
Bayesian Hierarchical ◽  
Demand Prediction ◽  
Point Of Interest ◽  
Modeling Process ◽  
Proposed Model ◽  
Bayesian Hierarchical Method ◽  
Spatial Entities ◽  
Operation Results ◽  
The Impact

Dock-less bicycle-sharing programs have been widely accepted as an efficient mode to benefit health and reduce congestions. And modeling and prediction has always been a core proposition in the field of transportation. Most of the existing demand prediction models for shared bikes take regions as research objects; therefore, a POI-based method can be a beneficial complement to existing research, including zone-level, OD-level, and station-level techniques. Point of interest (POI) is the location description of spatial entities, which can reflect the cycling route characteristics for both commuting and noncommuting trips to a certain extent, and is also the main generating point and attraction point of shared-bike travel flow. In this study, we make an effort to model a POI-level cycling demand with a Bayesian hierarchical method. The proposed model combines the integrated nested Laplace approximation (INLA) and random partial differential equation (SPDE) to cope with the huge computation in the modeling process. In particular, we have adopted the dock-less bicycle-sharing rental records of Mobike as a case study to validate our method; the study area was one of the fastest growing urban districts in Shanghai in August 2016. The operation results show that the method can help better understand, measure, and characterize spatiotemporal patterns of bike-share ridership at the POI level and quantify the impact of the spatiotemporal effect on bicycle-sharing use.

A Pedagogical Model to Integrate Computational Thinking Logic to First Year Design Studio

2021 ◽  
pp. 94-117
Author(s):  
Orkan Zeynel Güzelci ◽  
Meltem Çetinel
Keyword(s):  
Interior Design ◽  
Computational Thinking ◽  
Computational Design ◽  
Design Studio ◽  
First Year ◽  
Pedagogical Model ◽  
First Year Students ◽  
Analog Computing ◽  
Proposed Model ◽  
Almost All

Today, computational thinking and computational design approaches transform almost all stages of architectural practice and education. In this context, since students are most likely to encounter computers, in this study, the approach of teaching students computational design logic is adopted instead of teaching how to use computers only as a drafting or representation tool. This study focuses on developing a pedagogical model that aims to teach computational thinking logic and analog computing through a design process. The proposed model consists of four modules as follows: abstraction of music and text (Module 1), decomposition of buildings (Module 2), analysis of body-space (Module 3), design of a space by the help of spatial patterns (Module 4). The proposed model is applied to first-year students in Interior Design Studio in the 2019-2020 fall semester. As a result of Module 4, students designed both anticipated and unanticipated spaces in an algorithmic way.

A Pedagogical Model to Integrate Computational Thinking Logic to First Year Design Studio

2022 ◽  
pp. 368-391
Author(s):  
Orkan Zeynel Güzelci ◽  
Meltem Çetinel
Keyword(s):  
Interior Design ◽  
Computational Thinking ◽  
Computational Design ◽  
Design Studio ◽  
First Year ◽  
Pedagogical Model ◽  
First Year Students ◽  
Analog Computing ◽  
Proposed Model ◽  
Almost All

Today, computational thinking and computational design approaches transform almost all stages of architectural practice and education. In this context, since students are most likely to encounter computers, in this study, the approach of teaching students computational design logic is adopted instead of teaching how to use computers only as a drafting or representation tool. This study focuses on developing a pedagogical model that aims to teach computational thinking logic and analog computing through a design process. The proposed model consists of four modules as follows: abstraction of music and text (Module 1), decomposition of buildings (Module 2), analysis of body-space (Module 3), design of a space by the help of spatial patterns (Module 4). The proposed model is applied to first-year students in Interior Design Studio in the 2019-2020 fall semester. As a result of Module 4, students designed both anticipated and unanticipated spaces in an algorithmic way.

scholarly journals Correlating Synthesis Parameters to Morphological Entities: Predictive Modeling of Biopolymer Aerogels

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1670 ◽  
Author(s):  
Ameya Rege ◽  
Imke Preibisch ◽  
Maria Schestakow ◽  
Kathirvel Ganesan ◽  
Pavel Gurikov ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Clear Correlation ◽  
Model Parameters ◽  
Pore Collapse ◽  
Research Attention ◽  
Nonlinear Constitutive Model ◽  
Synthesis Parameters ◽  
Proposed Model ◽  
Significant Research ◽  
Nitrogen Desorption

In the past decade, biopolymer aerogels have gained significant research attention due to their typical properties, such as low density and thermal insulation, which are reinforced with excellent biocompatibility, biodegradability, and ease of functionalization. Mechanical properties of these aerogels play an important role in several applications and should be evaluated based on synthesis parameters. To this end, preparation and characterization of polysaccharide-based aerogels, such as pectin, cellulose and k-carrageenan, is first discussed. An interrelationship between their synthesis parameters and morphological entities is established. Such aerogels are usually characterized by a cellular morphology, and under compression undergo large deformations. Therefore, a nonlinear constitutive model is proposed based on large deflections in microcell walls of the aerogel network. Different sizes of the microcells within the network are identified via nitrogen desorption isotherms. Damage is initiated upon pore collapse, which is shown to result from the failure of the microcell wall fibrils. Finally, the model predictions are validated against experimental data of pectin, cellulose, and k-carrageenan aerogels. Given the micromechanical nature of the model, a clear correlation—qualitative and quantitative—between synthesis parameters and the model parameters is also substantiated. The proposed model is shown to be useful in tailoring the mechanical properties of biopolymer aerogels subject to changes in synthesis parameters.

scholarly journals A regression model for pooled data in a two-stage survey under informative sampling with application for detecting and estimating the presence of transgenic corn

2016 ◽  
Vol 26 (2) ◽  
pp. 182-197
Author(s):  
Osval A. Montesinos-López ◽  
Kent Eskridge ◽  
Abelardo Montesinos-López ◽  
José Crossa ◽  
Moises Cortés-Cruz ◽  
...  
Keyword(s):  
Likelihood Function ◽  
Group Testing ◽  
Transgenic Corn ◽  
Sampling Weights ◽  
Two Stage ◽  
Binary Responses ◽  
Regression Methods ◽  
Proposed Model ◽  
Informative Sampling ◽  
Selection Probabilities

AbstractGroup-testing regression methods are effective for estimating and classifying binary responses and can substantially reduce the number of required diagnostic tests. However, there is no appropriate methodology when the sampling process is complex and informative. In these cases, researchers often ignore stratification and weights that can severely bias the estimates of the population parameters. In this paper, we develop group-testing regression models for analysing two-stage surveys with unequal selection probabilities and informative sampling. Weights are incorporated into the likelihood function using the pseudo-likelihood approach. A simulation study demonstrates that the proposed model reduces the bias in estimation considerably compared to other methods that ignore the weights. Finally, we apply the model for estimating the presence of transgenic corn in Mexico and we give the SAS code used for the analysis.

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