This article	Friston et al. (2016b)	Note
$e_t\in \mathcal{E}$		Actual environment states
${\widehat{e}}_t\in \widehat{\mathcal{E}}$	st ∈ S	Estimated/modeled environment states
$s_t\in \mathcal{S}$	ot ∈ Ω	Actual/observed sensor or outcome values
${\widehat{s}}_t\in \widehat{\mathcal{S}}=\mathcal{S}$	ot ∈ Ω	Estimated/modeled (usually future) sensor or outcome values. Note that the index τ instead of t often indicates an estimated future sensor value in Friston et al. (2015).
$a_t\in \mathcal{A}$	ut ∈ A	Actions
${\widehat{a}}_t\in \widehat{\mathcal{A}}=\mathcal{A}$	ut ∈ Υ	Contemplated (usually future) actions
$m_t\in \mathcal{M}$		Agent memory state
${\widehat{a}}_{0:\widehat{T}}$	π,	action sequences
θ	θ	Generative model parameters
θ1	A	Sensor dynamics param.
θ2	B	Environment dynamics param.
θ3	D	Initial environment state param.
ξ	η	Generative model hyperparam. or model parameter that subsumes all hyperparameters
ξ1	a	sensor dynamics hyperparam.
ξ2	b	Environment dynamics hyperparam.
ξ3	d	Initial environment state hyperparam.
ξΓ	β	Precision hyperparam.
(ϕ, ϕΓ)	η	Variational param.
${\varphi }^{E_{0:\widehat{T}}}$	s0:T	Environment states variational param.
$q({\widehat{e}}_{\tau }|{\widehat{a}}_{t:\widehat{T}},a_{0:t-1},{\varphi }^{E_{\tau }})$	${({\mathbf{\text{s}}}_{\tau }^{\pi })}_{{\widehat{e}}_{\tau }}$	For each sequence of actions and for each timestep there is a parameter ${\mathbf{\text{s}}}_{\tau }^{\pi }$. Since a categorical distribution is used, the parameter is a vector of probabilities whose entry êτ is equal to the probability of êτ if we set $\widehat{\mathcal{E}}=\left\{1,\dots ,\left|\widehat{\mathcal{E}}\right|\right\}$
ϕ1	a	Sensor dynamics variational param.
ϕ2	b	Environment dynamics variational param.
ϕ3	d	Initial environment state variational param.
π	π	Future action sequence variational param.
ϕΓ	β	Precision variational param.
$\widehat{Q}({\widehat{a}}_{t:\widehat{T}},\varphi )$	−G(π)	Variational action-value function. The dependence of G(π) on ${\mathbf{\text{s}}}_{0:T}^{\pi }$ is omitted
p(s≼t, e≼t, a≺t)	$R(õ,\tilde{s},ã)$	Our physical environment corresponds to the generative process
$q({\widehat{s}}_{\preccurlyeq t},{\widehat{e}}_{0:\widehat{T}},{\widehat{a}}_{0:\widehat{T}},\gamma ,\theta ,\xi )$	$P(õ,\tilde{s},\pi ,\gamma ,\mathbf{\text{A}},\text{B},\mathbf{\text{D}}|a,b,d,\beta )$	The generative model for active inference
$r({\widehat{e}}_{0:\widehat{T}},{\widehat{a}}_{0:\widehat{T}},\gamma ,\theta |\pi ,{\varphi }^{\Gamma },\varphi )$	$Q(\tilde{s},\pi ,\mathbf{\text{A}},\text{B},\mathbf{\text{D}},\gamma |{\mathbf{\text{s}}}_{0:\widehat{T}}^{\pi },\pi ,\mathbf{\text{a}},\text{b},\mathbf{\text{d}},\beta )$	Approximate complete posterior for active inference
$p^d({\widehat{s}}_{\tau })$	P(oτ) = σ(Uτ)	Prior over future outcomes.