Figure 4. Examples of statistical models for neural temporal data. (A) Time series. Each transcript is modeled separately (univariate) or as part of a group (multivariate). The model uses information from previous time points in modeling future time points, and can capture contemporaneous and lagged dependencies among transcripts. (B) Discrete Markov chain model. Each cellular stage is considered a “state” and the chain models the probabilities of moving from one “state” to another in a given time step. Depending on the type of Markov model it may or may not be possible to move both backward and forward in time, and hence for cells to differentiate as well as dedifferentiate. (C) Bayesian network model. If we consider a directed acyclic graph (DAG), then we define a joint probability distribution over cellular states. For each node or state we define a probability distribution for transcription in each state, conditional on transcription in previous states. If we consider a dynamic graphical model (DGM), then we can model each state with a graphical model, and separately model the movement from state to state across time. In this way transcripts can have contemporaneous as well as time-dependent relationships. NSC, neural stem cell; OPC1, oligodendrocyte precursor cell 1; OPC2, oligodendrocyte precursor cell 2; Olig, oligodendrocyte; GBM, glioblastoma cell. Pa₁ is the probability that a neural stem cell remains a stem cell from one time point to the next. Pa₂ is the probability that a neural stem cell transforms from the current time point to the next time point. Pb₃ is the probability that a GBM cell de-differentiates from the current time point to the prior time point. Pb₁ is the probability that a GBM cell remains a GBM cell from the current time point to the next. Pc₂ is the probability that an oligodendrocyte precursor cell (OPC) transforms from the current time point to the next. Pc₁ is the probability that an OPC remains an OPC from the current time point to the next. Pb₂ is the probability that a GBM cell de-differentiates into an OPC from the current time point to the next time point. Pc₄ is the probability that an OPC differentiates into an oligodendrocyte from the current time point to the next time point. Pc₃ is the probability that an OPC dedifferentiates into a neural stem cell from the current time point to the next. Pa₃ is the probability that a NSC differentiates into an OPC from the current time point to the next. Pd₁ is the probability that an oligodendrocyte will remain an oligodendrocyte from the current time point to the next. Pd₂ is the probability that an oligodendrocyte dedifferentiates into an OPC form the current time point to the next. Pa₁+Pa₂+Pa₃ = 1; Pb₁+Pb₂+Pb₃ = 1; Pc₁+Pc₂+Pc₃ = 1.