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Table 7 Model selection for the \(\uplambda\) RM promoter data. The columns show the maximum likelihood estimates, the loglikelihood values, and the AICs, respectively

From: Statistical inference for a quasi birth–death model of RNA transcription

   \({\varvec{q}}_{\textbf{on}}\) \({\varvec{q}}_{\textbf{off}}\) \({\boldsymbol{\uplambda}} _1\) \({\boldsymbol{\uplambda}}_2\) \({\boldsymbol{\uplambda}} _3\) \({\mathbf{log }}{{\mathcal {L}}}\) AIC
Seq-1 0.0144 − 3569.9 7141.8
Seq-2 \(\uplambda _1 \le \uplambda _2\) 0.0144 8.9245 − 3569.4 7142.7
Seq-2 \(\uplambda _2 \le \uplambda _1\) 5.8876 0.0144 − 3569.5 7143.1
Seq-3 \(\uplambda _1 \le \uplambda _2 \le \uplambda _3\) 0.0144 9.9536 9.9875 − 3569.3 7144.6
Seq-3 \(\uplambda _2 \le \uplambda _1 \le \uplambda _3\) 5.8876 0.0144 6.0453 − 3570.5 7147.0
Seq-3 \(\uplambda _2 \le \uplambda _3 \le \uplambda _1\) 5.8876 0.0144 5.7305 − 3570.7 7147.3
On/off-seq-1 0.0249 0.0608 0.0496 − 3475.2 6956.5
On/off-seq-2 \(\uplambda _1 \le \uplambda _2\) 0.0303 0.4089 0.2220 0.2221 − 3474.8 6957.6
On/off-seq-2 \(\uplambda _2 \le \uplambda _1\) 0.0254 1.2284 0.7920 0.1416 − 3468.2 6944.4
On/off-seq-3 \(\uplambda _1 \le \uplambda _2 \le \uplambda _3\) 0.0312 0.4410 0.2314 0.2314 9.9983 − 3475.6 6961.3
On/off-seq-3 \(\uplambda _2 \le \uplambda _1 \le \uplambda _3\) 0.0255 2.4371 1.5558 0.1427 3.8107 − 3466.5 6943.1
On/off-seq-3 \(\uplambda _2 \le \uplambda _3 \le \uplambda _1\) 0.0254 4.4154 2.8221 0.1423 2.6958 − 3466.9 6943.7