Table 1.

Variables of the POMDP generative model of single-agent opinion formation. The abstract name of each variable is written in the left column, its mathematical notation is in the middle column, and the right column shows how these variables correspond to different components of the opinion formation generative model. M is the total number of observation modalities and F is the number of hidden state/control factors. The observation model is a categorical likelihood distribution encoded by $\mathbf{A}$, which comprises a collection of modality-specific $A^{\left(m\right)}$ arrays. The transition model is also a likelihood, mapping each state to its successor in time, encoded by the $B^{\left(f\right)}$ arrays. The initial distribution over hidden states is encoded by the $\mathbf{D}$ vector, and the prior distribution over control factors is encoded by the $\mathcal{E}$ and $\epsilon$ distributions.

Variable Name	Notation	Meaning
		The focal agent’s tweets $o^{\mathbf{ST}}\in {\mathbb{Z}}^{1\times H}$
Observations	$\mathbf{o}=\{o^{\left(1\right)},\dots ,o^{\left(M\right)}\}$	Neighbour k’s tweets $o^{\mathbf{NT}k}\in {\mathbb{Z}}^{1\times (H+1)}$
		The sampled agent $o^{\mathbf{Who}}\in {\mathbb{Z}}^{1\times K}$
		The focal agent’s beliefs $s^{\mathbf{Idea}}\in {\mathbb{Z}}^{1\times 2}$
Hidden States	$\mathbf{s}=\{s^{\left(1\right)},\dots ,s^{\left(F\right)}\}$	Neighbour k’s beliefs $s^{\mathbf{MB}k}\in {\mathbb{Z}}^{1\times 2}$
		The Hashtag tweeted by focal agent $s^{\mathbf{T}}\in {\mathbb{Z}}^{1\times H}$
		The neighbour sampled focal agent $s^{\mathbf{Who}}\in {\mathbb{Z}}^{1\times n}$
Actions	$\mathbf{u}=\{u^{\left(1\right)},\dots ,u^{\left(F\right)}\}$	The Hashtag control state $u^{\mathbf{T}}\in {\mathbb{Z}}^{1\times H}$
		The neighbour attendance control state $u^{\mathbf{Who}}\in {\mathbb{Z}}^{1\times n}$
		Self tweet likelihood ${\mathbf{A}}^{\mathbf{ST}}\in {\left({\mathbb{R}}_{>0}\right)}^{2\times 2\times 2K\times H\times K}$
Observation model	$P(o_t^{\left(m\right)}=i|s_t^{\left(1\right)}=j,s_t^{\left(2\right)}=k,\dots )={\left[A^{\left(m\right)}\right]}_{ijk\dots }$	Neighbour tweet likelihood ${\mathbf{A}}^{\mathbf{NT}k}\in {\left({\mathbb{R}}_{>0}\right)}^{2\times 2\times 2K\times H\times K}$
		Neighbour attend likelihood ${\mathbf{A}}^{\mathbf{Who}}\in {\left({\mathbb{R}}_{>0}\right)}^{K\times 2\times 2K\times H\times K}$
		Environmental dynamics and volatility ${\mathbf{B}}^{\mathbf{Idea}}\in {\mathbb{R}}_{>0}^{2\times 2}$
Transition model	$P(s_{t+1}^{\left(f\right)}=i|s_t^{\left(f\right)}=j,u_t^{\left(f\right)}=k)={\left[B^{\left(f\right)}\right]}_{ijk}$	Meta-belief dynamics and volatility ${\mathbf{B}}^{\mathbf{MB}k}\in {\left({\mathbb{R}}_{>0}\right)}^{2\times 2}$
		Tweet control ${\mathbf{B}}^{\mathbf{T}}\in {\left({\mathbb{R}}_{>0}\right)}^{H\times H\times H}$
		Neighbour attendance control ${\mathbf{B}}^{\mathbf{Who}}\in {\left({\mathbb{R}}_{>0}\right)}^{K\times K\times K}$
Initial State	$p(s_0^{\left(f\right)}=i)={\left[D^{\left(f\right)}\right]}_i$	Initial state distribution $\mathbf{D}\in {\left({\mathbb{R}}_{>0}\right)}^{2\times 2K\times H\times K}$
Control State Prior	$P\left({\mathbf{u}}_0^{\mathbf{T}}\right|s^{\mathbf{idea}})={\mathcal{E}}^{\mathbf{T}}$	Empirical prior over Hashtag control state ${\mathcal{E}}^{\mathbf{T}}\in {\left({\mathbb{R}}_{>0}\right)}^{H\times 2}$
	$P\left(u_0^{\mathbf{Who}}\right|{\mathcal{E}}^{\mathbf{Who}})=\mathbb{E}\left[Dir\left(\epsilon \right)\right]$	Dirichlet hyperparameters over neighbour attendance control state $\epsilon \in {\left({\mathbb{R}}_{>0}\right)}^{1\times K}$