Studies in dialogue and discourse; an exponential law of successive questioning

1975 ◽  
Vol 4 (1) ◽  
pp. 31-51 ◽  
Author(s):  
Elliot G. Mishler
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Exponential Function ◽  
First Grade ◽  
Finite Markov Chain ◽  
Constant Ratio ◽  
Conversational Analysis ◽  
Exponential Law ◽  
Simple Exponential Function ◽  
Temporal Location

ABSTRACTThe structure of natural conversations in first-grade classrooms is the focus of this inquiry. Analyses of a particular type of discourse, namely, connected conversations initiated and sustained by questioning, suggest that the probability that a conversation will be continued may be expressed as a simple exponential function. The formula, pi = ari−1, generates a curve of theoretically-expected rates of successive questions in a series that closely matches observed rates. The formula is based on the application of a constant ratio, that is, the ratio of rates within each pair of adjacent questions is the same throughout the series: p2:p1=p3:p2 = p4:p3. … Thus, it appears that the probability of a ‘next’ question following an exchange that contains a previous question remains constant through the length of the discourse series. In other words, the probability of a question is independent of the temporal location of an utterance in this type of connected conversation. The analyses suggest further that the model of a finite Markov chain, that is, of a particular type of stochastic process, may be applicable to certain features of a discourse. (Conversational analysis, sequencing in exchanges, U.S. English in first-grade classrooms.)

scholarly journals Chain-referral sampling on stochastic block models

2020 ◽  
Vol 24 ◽  
pp. 718-738
Author(s):  
Thi Phuong Thuy Vo
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Social Network ◽  
Discrete Time ◽  
Precise Description ◽  
Stochastic Block Model ◽  
Hidden Population ◽  
The People ◽  
A Chain ◽  
Block Models

The discovery of the “hidden population”, whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling (CRS) method, where participants recommend the people they know. This leads to the study of a Markov chain on a random graph where vertices represent individuals and edges connecting any two nodes describe the relationships between corresponding people. We are interested in the study of CRS process on the stochastic block model (SBM), which extends the well-known Erdös-Rényi graphs to populations partitioned into communities. The SBM considered here is characterized by a number of vertices N, a number of communities (blocks) m, proportion of each community π = (π1, …, πm) and a pattern for connection between blocks P = (λkl∕N)(k,l)∈{1,…,m}2. In this paper, we give a precise description of the dynamic of CRS process in discrete time on an SBM. The difficulty lies in handling the heterogeneity of the graph. We prove that when the population’s size is large, the normalized stochastic process of the referral chain behaves like a deterministic curve which is the unique solution of a system of ODEs.

STATE ESTIMATION OF A DISCRETE INHOMOGENEOUS MARKOV CHAIN

2021 ◽  
Author(s):  
E. A. Perepelkin ◽  
Keyword(s):  
Markov Chain ◽  
State Estimation ◽  
Finite Markov Chain ◽  
Luenberger Observer ◽  
Inhomogeneous Markov Chain

The problem of constructing a state estimation of inhomogeneous finite Markov chain based on a Luenberger observer is solved. The conditions of existence of the observer are defined. An algorithm for synthesizing the observer is described.

Perturbation bounds for the stationary probabilities of a finite Markov chain

1984 ◽  
Vol 16 (04) ◽  
pp. 804-818 ◽  
Author(s):  
Moshe Haviv ◽  
Ludo Van Der Heyden
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Finite Markov Chain ◽  
Perturbation Bounds ◽  
Aggregation Technique ◽  
Stationary Probabilities

This paper discusses perturbation bounds for the stationary distribution of a finite indecomposable Markov chain. Existing bounds are reviewed. New bounds are presented which more completely exploit the stochastic features of the perturbation and which also are easily computable. Examples illustrate the tightness of the bounds and their application to bounding the error in the Simon–Ando aggregation technique for approximating the stationary distribution of a nearly completely decomposable Markov chain.

Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol

1987 ◽  
Vol 24 (02) ◽  
pp. 347-354 ◽  
Author(s):  
Guy Fayolle ◽  
Rudolph Iasnogorodski
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Stochastic Processes ◽  
State Space ◽  
Discrete Time ◽  
Random Variables ◽  
Countable State Space ◽  
Countable State ◽  
New Criteria

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn ), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn ) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.

scholarly journals Approximations: replacing random variables with their means

2014 ◽  
Vol 51 (A) ◽  
pp. 57-62
Author(s):  
Joe Gani
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Continuous Time ◽  
Random Variables ◽  
Original Form ◽  
Continuous Time Markov Chain ◽  
Standard Methods ◽  
Sis Epidemics

One of the standard methods for approximating a bivariate continuous-time Markov chain {X(t), Y(t): t ≥ 0}, which proves too difficult to solve in its original form, is to replace one of its variables by its mean, This leads to a simplified stochastic process for the remaining variable which can usually be solved, although the technique is not always optimal. In this note we consider two cases where the method is successful for carrier infections and mutating bacteria, and one case where it is somewhat less so for the SIS epidemics.

Measurement of Extracellular Fluid Volume of Nephrectomized Dogs With Mannitol, Sucrose, Thiosulfate and Radiosulfate

1956 ◽  
Vol 185 (1) ◽  
pp. 179-184 ◽  
Author(s):  
Patrick J. Mulrow ◽  
Herbert M. Oestreich ◽  
Roy C. Swan
Keyword(s):  
Exponential Function ◽  
Extracellular Fluid ◽  
Volume Of Distribution ◽  
Fluid Volume ◽  
Extracellular Fluid Volume ◽  
Simple Exponential Function ◽  
Volumes Of Distribution

Volumes of distribution of mannitol, sucrose, thiosulfate and radiosulfate have been measured simultaneously in nephrectomized dogs. The volume of distribution of each substance is reproducible when the substance is reinfused 6 hours later. There appears to be no increase in the extracellular fluid volume during this interval as a result of the nephrectomy. The logarithm of the concentration of mannitol, sucrose and radiosulfate continues as a simple exponential function of time from the 3rd to 30th hour after their infusion. The volumes of distribution of mannitol and radiosulfate reflect increments in extracellular fluid with fair accuracy, while the sucrose distribution measures only 72% of a 1-liter expansion of extracellular fluid. There are serious limitations in the application of thiosulfate distribution to such measurements.

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