Date: Mon, 25 May 2020 04:53:49 +0000 (GMT) Message-ID: <118491962.6601.1590382429098@c4e8295e3740> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_6600_1912018931.1590382429097" ------=_Part_6600_1912018931.1590382429097 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Means and Values of Nodes

# Question

How does BayesiaLab calculate the Means and Values in the Monito= rs? What is the difference?

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For each node that has values associated with its states, an Expected= Value $v$ is computed by using the associated values and the marginal prob= ability distribution of the node $$v =3D \sum_{s \in S} p_s \times V_s$$ wh= ere $p_s$ is the marginal probability of state $s$ and $V_s$ is its associa= ted value.
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This Expected Value is displayed in the monitor.

Example
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Ca= tegorical Variable

Let's take a discrete node Age with three categorical states:

• Senior

The Node Editor allows associating numerical values wit= h these states.  =20
$$v =3D 0.23 \times 25 + 0.415 \times 45 + 0.355 \times 80 =3D 52.825=$$
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Di= screte Numerical Variable

Let's suppose now that the variable Age has three numerical sta= tes. As it's a numerical node, its monitor will have a Mean value, a= Standard Deviation and an Expected Value. =20
When the states do not have any associated values, $V_s$ is automatic= ally set to the numerical value of the state.
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Otherwise, the state values defined by the user are used:  =20
The Mean value $m$ is computed with the following equation: $$m =3D \= sum_{s \in S} p_s \times c_s$$ where $c_s$ is the numerical value of the st= ate.
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Co= ntinuous Numerical Variable

Let's consider now a continuous variable Age defined on t= he domain [15 ; 99],  discretized into three states:

• Young Adult: [15 ; 30]
• Senior: ]60 ; 99] Since it's a numerical node, its monitor has a Mean value, a Standard Deviation and an Expected Value as well. =20
The Mean value $m$ is computed with the following equation: $$m =3D \= sum_{s \in S} p_s \times c_s$$ where $c_s$ is the central tendency of the s= tate defined as:
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• the mid-range of the state when no data is= associated,
• the arithmetic mean of the data points tha= t are associated with the state.
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When the states do not have any associated values, $V_s$ is automatic= ally set to the central tendency of the state.
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When a dataset is associated with a continuous variable, clicking on = the Generate Values buttons sets the values $V_s$ to the current arithmetic= means.
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When new pieces of evidence are set, a the delta value is displayed in t= he monitor: This delta is the difference between the current Expected Value v

and:

• the previous one,
• the one corresponding to the reference probability distribution set wit= h in the toolbar.
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When only some states have an associated value, the Expected Value is= computed on the states $S^*$ that have associated values $$v =3D \sum_{s \= in S^*} \frac{p_s}{P^*} \times V_s$$ where $S^*$ is only made of one state,= the node is considered as not having any associated values.
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