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fix some typos
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gavinsimpson committed Nov 24, 2023
1 parent ac92585 commit db120bd
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4 changes: 2 additions & 2 deletions day-5/index.Rmd
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Expand Up @@ -350,7 +350,7 @@ For the Gaussian distribution

* $\vartheta_{1}(\boldsymbol{x}_i) = \mu(\boldsymbol{x}_i)$

* $\vartheta_{1}(\boldsymbol{x}_i) = \sigma(\boldsymbol{x}_i)$
* $\vartheta_{2}(\boldsymbol{x}_i) = \sigma(\boldsymbol{x}_i)$

???

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$$\mathcal{L}_{p}(\boldsymbol{\beta}, \boldsymbol{\lambda}) = \mathcal{L}(\boldsymbol{\beta})\exp(-\boldsymbol{\beta}^{\mathsf{T}}\boldsymbol{S}_{\boldsymbol{\lambda}}\boldsymbol{\beta})$$

The exponential term is porportional to a mean zero MVN with prior precision matrix $\boldsymbol{S}_{\boldsymbol{\lambda}}$
The exponential term is proportional to a mean zero MVN with prior precision matrix $\boldsymbol{S}_{\boldsymbol{\lambda}}$

This implies

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4 changes: 2 additions & 2 deletions day-5/index.html
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Expand Up @@ -306,7 +306,7 @@

* `\(\vartheta_{1}(\boldsymbol{x}_i) = \mu(\boldsymbol{x}_i)\)`

* `\(\vartheta_{1}(\boldsymbol{x}_i) = \sigma(\boldsymbol{x}_i)\)`
* `\(\vartheta_{2}(\boldsymbol{x}_i) = \sigma(\boldsymbol{x}_i)\)`

???

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`$$\mathcal{L}_{p}(\boldsymbol{\beta}, \boldsymbol{\lambda}) = \mathcal{L}(\boldsymbol{\beta})\exp(-\boldsymbol{\beta}^{\mathsf{T}}\boldsymbol{S}_{\boldsymbol{\lambda}}\boldsymbol{\beta})$$`

The exponential term is porportional to a mean zero MVN with prior precision matrix `\(\boldsymbol{S}_{\boldsymbol{\lambda}}\)`
The exponential term is proportional to a mean zero MVN with prior precision matrix `\(\boldsymbol{S}_{\boldsymbol{\lambda}}\)`

This implies

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