scholarly journals A software toolkit for modeling human sentence parsing: An approach using continuous-time, discrete-state stochastic dynamical systems

2021 ◽  
Author(s):  
Garrett Smith ◽  
Shravan Vasishth
Keyword(s):  
Sentence Processing ◽  
Continuous Time ◽  
Broad Class ◽  
Comprehension Question ◽  
Stochastic Dynamical Systems ◽  
Discrete State ◽  
Software Toolkit ◽  
Ambiguity Advantage ◽  
Python Package ◽  
Quantitative Evaluations

We present a new software toolkit for implementing a broad class oftheories of sentence processing. In this framework, processing a word ina sentence is viewed as a continuous-time random walk through a set ofdiscrete states that encode information about the emerging structure of thesentence so far. The state space includes one or more special absorbingstates, which, when reached, indicate the decision to move on to the nextword of the sentence. This setup allows us to ask how how long it takesto reach an absorbing state and what the probability of reaching this stateis. We summarize a number of important statistics that can be directlyrelated to human reading times and comprehension question performance.To illustrate the use of the toolkit, we model two types of garden paths,local coherence effects, and the ambiguity advantage using three qualitativelydifferent theories of sentence processing. While the modeler must still makedefensible theoretical and implementation choices, this framework representsan improvement over the descriptive, paper-pencil modeling that is thenorm in psycholinguistics by facilitating quantitative evaluations of modelperformance and laying the groundwork for Bayesian fitting of free parametersin a model. An open-source Python package is provided.

scholarly journals State Variable Effects in Graphical Event Models

2020 ◽  
Author(s):  
Debarun Bhattacharjya ◽  
Dharmashankar Subramanian ◽  
Tian Gao
Keyword(s):  
Real World ◽  
Continuous Time ◽  
Point Processes ◽  
Temporal Dynamics ◽  
Search Algorithm ◽  
State Variables ◽  
Discrete State ◽  
State Variable ◽  
Event Models ◽  
Real World Datasets

Many real-world domains involve co-evolving relationships between events, such as meals and exercise, and time-varying random variables, such as a patient's blood glucose levels. In this paper, we propose a general framework for modeling joint temporal dynamics involving continuous time transitions of discrete state variables and irregular arrivals of events over the timeline. We show how conditional Markov processes (as represented by continuous time Bayesian networks) and multivariate point processes (as represented by graphical event models) are among various processes that are covered by the framework. We introduce and compare two simple and interpretable yet practical joint models within the framework with relevant baselines on simulated and real-world datasets, using a graph search algorithm for learning. The experiments highlight the importance of jointly modeling event arrivals and state variable transitions to better fit joint temporal datasets, and the framework opens up possibilities for models involving even more complex dynamics whenever suitable.

Integer-valued branching processes with immigration

1983 ◽  
Vol 15 (04) ◽  
pp. 713-725 ◽  
Author(s):  
F. W. Steutel ◽  
W. Vervaat ◽  
S. J. Wolfe
Keyword(s):  
Difference Equation ◽  
Continuous Time ◽  
Queueing Theory ◽  
Branching Processes ◽  
Random Variables ◽  
Discrete State ◽  
Limiting Behaviour ◽  
Supercritical Branching Processes

The notion of self-decomposability for -valued random variables as introduced by Steutel and van Harn [10] and its generalization by van Harn, Steutel and Vervaat [5], are used to study the limiting behaviour of continuous-time Markov branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of random variables obeying a certain difference equation as studied by Vervaat [12] and their continuous-time counterpart considered by Wolfe [13]. An application in queueing theory is indicated. Furthermore, discrete-state analogues are given for results on stability in the processes studied by Wolfe, and for results on self-decomposability in supercritical branching processes by Yamazato [14].

scholarly journals A Limit Theorem for Discrete Galton-Watson Branching Processes with Immigration

2006 ◽  
Vol 43 (01) ◽  
pp. 289-295 ◽  
Author(s):  
Zenghu Li
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Discrete State ◽  
Simple Set ◽  
Continuous State

We provide a simple set of sufficient conditions for the weak convergence of discrete-time, discrete-state Galton-Watson branching processes with immigration to continuous-time, continuous-state branching processes with immigration.

scholarly journals Possibility of Application of the Theory of Semi-Markov Processes to Determine Reliability of Diagnosing Systems / MOŻLIWOŚĆ ZASTOSOWANIA TEORII PROCESÓW SEMI-MARKOWA DO OKREŚLENIA NIEZAWODNOŚCI SYSTEMÓW DIAGNOZUJĄCYCH

2012 ◽  
Vol 24 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Jerzy Girtler
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Continuous Time ◽  
Diagnostic Tests ◽  
The State ◽  
Actual State ◽  
Reliability Model ◽  
Discrete State ◽  
Semi Markov Process ◽  
Semi Markov Processes

Abstract The paper provides justification for the necessity to define reliability of diagnosing systems (SDG) in order to develop a diagnosis on state of any technical mechanism being a diagnosed system (SDN). It has been shown that the knowledge of SDG reliability enables defining diagnosis reliability. It has been assumed that the diagnosis reliability can be defined as a diagnosis property which specifies the degree of recognizing by a diagnosing system (SDG) the actual state of the diagnosed system (SDN) which may be any mechanism, and the conditional probability p(S*/K*) of occurrence (existence) of state S* of the mechanism (SDN) as a diagnosis measure provided that at a specified reliability of SDG, the vector K* of values of diagnostic parameters implied by the state, is observed. The probability that SDG is in the state of ability during diagnostic tests and the following diagnostic inferences leading to development of a diagnosis about the SDN state, has been accepted as a measure of SDG reliability. The theory of semi-Markov processes has been used for defining the SDG reliability, that enabled to develop a SDG reliability model in the form of a seven-state (continuous-time discrete-state) semi-Markov process of changes of SDG states.

scholarly journals Kekonvergenan MSE Penduga Kernel Seragam Fungsi Intensitas Proses Poisson Periodik dengan Tren Fungsi Pangkat

2012 ◽  
Vol 3 (1) ◽  
pp. 204
Author(s):  
Ro’fah Nur Rachmawati
Keyword(s):  
Stochastic Process ◽  
Poisson Process ◽  
Continuous Time ◽  
Kernel Estimator ◽  
Intensity Function ◽  
Rank Function ◽  
Service Center ◽  
Discrete State ◽  
Number Of Customers ◽  
Discrete State Space

The number of customers who come to a service center will be different for each particular time. However, it can be modeled by a stochastic process. One particular form of stochastic process with continuous time and discrete state space is a periodic Poisson process. The intensity function of the process is generally unknown, so we need a method to estimate it. In this paper an estimator of kernel uniform of a periodic Poisson process is formulated with a trend component in a rank function (rank coefficient 0 <b <1 is known, and the slope coefficient of the power function (trend) a> 0 is known). It is also demonstrated the convergenity of the estimators obtained. The result of this paper is a formulation of a uniform kernel estimator for the intensity function of a periodic Poisson process with rank function trends (for the case “a” is known) and the convergenity proof of the estimators obtained.

scholarly journals Bayesian model discrimination for partially-observed epidemic models

2019 ◽  
Author(s):  
James N. Walker ◽  
Andrew J. Black ◽  
Joshua V. Ross
Keyword(s):  
Model Selection ◽  
Importance Sampling ◽  
Continuous Time ◽  
Bayesian Model ◽  
Broad Class ◽  
Infectious Period ◽  
Importance Sampling Method ◽  
Markov Chain Models ◽  
Wide Range ◽  
Partially Observed

AbstractAn efficient method for Bayesian model selection is presented for a broad class of continuous-time Markov chain models and is subsequently applied to two important problems in epidemiology. The first problem is to identify the shape of the infectious period distribution; the second problem is to determine whether individuals display symptoms before, at the same time, or after they become infectious. In both cases we show that the correct model can be identified, in the majority of cases, from symptom onset data generated from multiple outbreaks in small populations. The method works by evaluating the likelihood using a particle filter that incorporates a novel importance sampling algorithm designed for partially-observed continuous-time Markov chains. This is combined with another importance sampling method to unbiasedly estimate the model evidence. These come with estimates of precision, which allow for stopping criterion to be employed. Our method is general and can be applied to a wide range of model selection problems in biological and epidemiological systems with intractable likelihood functions.

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