We input the z-scores into a matrix, and express hypotheses about their values via Dirichlet priors - matrices of transition probabilities between each possible state (in our case - language edition).
Analyses of these sequences of behaviour patterns, transcribed from the video tapes of mouse behaviour, enabled us to calculate the transition matrices, matrices of transition probabilities and transition rates described in [ 15].
Table 2 gives the approximate matrix of transition probabilities P for the video sequence at the quantization level 34.
The matrix of transition probabilities can be related to the breakage rate function and the breakage distribution function of the elementary breakage event.
The above process could be denoted as xt + 1 = Px t, where P represents the matrix of transition probability, which is column-normalized matrix of weighted adjacency matrix of network graph G.
Emphasis is on the matrix of rates rather than on the matrix of transition probabilities, as the rates are independent of each other and directly reflect behavior, i.e., a movement from one state to another.
The resulting K × K matrix of transition probabilities, denoted by P, can be translated into a corresponding infinitesimal generating matrix in a continuous-time domain, denoted by M, as follows M = g ( P - I ) (5).
The rate of change for p t), where p t) is a square matrix of transition probabilities, can be written in the form of the following differential equation: The rate of change for p t), where p t) is a square matrix of transition probabilities, can be written in the form of the following differential equation: d d t p ( t ) = p ( t ) R, (5 where R is a square matrix of the transfer rates.
At the heart of a Markov-chain model, there is a "matrix of transition probabilities" (Fig. 4a) that determines the instantaneous rate of change from one state to another.
The matrix of transition probabilities between price levels is M = [p(m'|m)] where p(m'|m) is the probability that next year's price level is m' given the current price level m.
Each state has a diagonal covariance matrix, with Q 1=0.5·I 7,Q 2=Q 3=0.1·I 7, where Q i is the covariance matrix of the ith state, and I D is the identity matrix of dimension D. The matrix of transition probabilities, P, is left(begin{array}{ccc} 0.4 & 0.3 & 0.3 0.3 & 0.55 & 0.15 0.35 & 0.25 & 0.4 end{array} right) and the initial probabilities are p 1=0.3,p 2=0.2,p 3=0.5.
