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- Timestamp:
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Nov 11, 2010, 7:09:24 PM (14 years ago)
- Author:
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lcereceda
- Comment:
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v10
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v11
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31 | 31 | [[LatexEquation(y_{n} )]] |
32 | 32 | |
33 | | All residuals inside the same row are incorrelated normal, but resiudals in |
| 33 | All residuals inside the same row are incorrelated normal, but residuals in |
34 | 34 | the same column [[LatexEquation(j)]] are [[BR]] |
35 | 35 | |
… |
… |
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39 | 39 | same for each column.[[BR]] |
40 | 40 | |
41 | | Minka defines also the known data pair [[LatexEquation(D = left(Y,Xright))]] |
| 41 | Minka defines also the known data pair [[LatexEquation(D = \left(Y,X \right))]] |
42 | 42 | that will be used just to get more compact conditioninig expressions. |
43 | 43 | |
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50 | 50 | [[LatexEquation(\Omega = \left\{ A\in\mathbb{R}^{d\times m} \mid F\left(A\right) \le 0 \right\})]] [[BR]] |
51 | 51 | |
52 | | being [[BR]] |
| 52 | with [[BR]] |
53 | 53 | |
54 | 54 | [[LatexEquation( F\left(A\right):\mathbb{R}^{d\times m}\longrightarrow\mathbb{R}^{r} )]] [[BR]] |
55 | 55 | |
56 | | the arbitrary constraining function. [[BR]] |
| 56 | being the arbitrary constraining function. [[BR]] |
57 | 57 | |
58 | 58 | == Invariant-scale prior over coefficient matrix == |
59 | 59 | |
60 | | Although Minka not explicitly stated in any place, under the invariant prior |
| 60 | Although Minka does not explicitly state this, from the invariant prior it |
61 | 61 | follows that [[LatexEquation(X)]] must be full-rank [[LatexEquation(m <= N)]] |
62 | 62 | because [[LatexEquation(X W X ^ T)]] must be nonsingular with |
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64 | 64 | scale-invariant parameter governing the prior and estimated more |
65 | 65 | forward to maximize the evidence of the data, which depends on the assumptions |
66 | | the model. |
| 66 | of the model. |
67 | 67 | |
68 | 68 | == Inverse Wishart prior over covariance matrix == |