### Table 4. Priors by Country

2007

"... In PAGE 38: ... Table4 . Priors by Country (Cont.... In PAGE 39: ... Table4 . Priors by Country (Cont.... ..."

### Table 8: Combining priors

2002

"... In PAGE 6: ...6%) 1557719 (92%) Table 7: Distribution entry pages and WT10g over different document types statistics we computed a combined inlink-URL prior, using: Pinlink URL(EPjdt(D) = ti) = c(EP; ti) c(ti) ; (10) where dt(D) is the document type of D and c(:) is as defined in equation 9. Table8 summarises results for the combination experiments. In addition to the already tabulated single prior results, it shows the result for a run where the inlink prior was estimated on the training data instead of being modeled by Formula (2).... ..."

Cited by 85

### Table 8: Combining priors

2002

"... In PAGE 6: ...6%) 1557719 (92%) Table 7: Distribution entry pages and WT10g over different document types statistics we computed a combined inlink-URL prior, using: a6 a26 a25 a51 a26 a25 a75 a131 a116a111a118a76a119 a7a56a121a12a6 a9 a58 a104 a7 a4a15a11a54a13a125a104a37a26a126a11a69a13 a61 a7a56a121a122a6 a19 a104 a26 a11 a61 a7 a104 a26 a11 a19 (10) where a58 a104 a7 a4a15a11 is the document type of a4 and a61 a7 a71 a11 is as defined in equation 9. Table8 summarises results for the combination experiments. In addition to the already tabulated single prior results, it shows the result for a run where the inlink prior was estimated on the training data instead of being modeled by Formula (2).... ..."

Cited by 85

### Table 8: Combining priors

2002

"... In PAGE 6: ...6%) 1557719 (92%) Table 7: Distribution entry pages and WT10g over different document types statistics we computed a combined inlink-URL prior, using: a7 a27 a26 a52 a27 a26 a75 a133 a119a105a120a76a121 a8a57a123a13a7 a10 a59 a104 a8 a5a16a12a55a14a127a104a38a27a128a12a69a14 a62 a8a57a123a124a7 a20 a104 a27 a12 a62 a8 a104 a27 a12 a20 (10) where a59 a104 a8 a5a16a12 is the document type of a5 and a62 a8 a71 a12 is as defined in equation 9. Table8 summarises results for the combination experiments. In addition to the already tabulated single prior results, it shows the result for a run where the inlink prior was estimated on the training data instead of being modeled by Formula (2).... ..."

Cited by 85

### TABLE 3. DESCRIPTION OF PRIORS

2008

### TABLE 4 Prior Parameters

2005

### Table 3: Distributions and their conjugate priors

1994

"... In PAGE 25: ... Once the posterior distribution is found, and assuming it is one of the standard distributions, the property can easily be established. Table3 in Appendix B gives some standard conjugate prior distri- butions for those in Table 2, and Table 4 gives their matching posteriors. More extensive summaries of this are given by DeGroot (1970) and Bernardo and Smith (1994).... In PAGE 41: ... The evidence for some common exponential family distributions is given in Appendix B in Table 5 For instance, consider the learning problem given in Figure 24. Assume that the variables var1 and var2 are both binary (0 or 1) and that the parameters 1 and 2 are interpreted as follows: p(var1 = 0j 1) = 1 ; p(var2 = 0jvar1 = 0; 2) = 2;0j0 ; p(var2 = 0jvar1 = 1; 2) = 2;0j1 : If we use Dirichlet priors for these parameters, as shown in Table3 , then the priors are: ( 1; 1 ? 1) Dirichlet( 1;0; 1;1) ; ( 2;0jj; 1 ? 2;0jj) Dirichlet( 2;0jj; 2;1jj) for j = 0; 1 ; where 2;0j0 is a priori independent of 2;0j1. The choice of priors for these distributions is discussed in (Box amp; Tiao, 1973; Bernardo amp; Smith, 1994).... In PAGE 42: ...statistics, and contribution to the evidence. Conjugate priors from Table3 in Appendix B (using yjx Gaussian) are indexed accordingly as: ijjj ijj Gaussian( 0;ijj; 0;ijj 2 ijj ) for i = 1; 2 and j = 0; 1 ; ?2 ijj Gamma( 0;ijj=2; 0;ijj) for i = 1; 2 and j = 0; 1 : Notice that 0;ijj is one-dimensional when i = 0 and two-dimensional when i = 2. Suitable su cient statistics for this situation are read from Table 4 by looking at the data summaries used there.... In PAGE 58: ... Further details and more extensive tables can be found in most Bayesian textbooks on probability distributions (DeGroot, 1970; Bernardo amp; Smith, 1994). Table3 gives some standard conjugate prior distributions for those in Table 2, and Table 4 gives their matching posteriors (DeGroot, 1970; Bernardo amp; Smith,... In PAGE 60: ...Distribution Evidence j C-dim multinomial Beta(n1 + 1; : : :; nC + C)=Beta( 1; : : :; C) yjx Gaussian det1=2 0 N=2 det1=2 ?(( 0+N)=2) ( 0+N)=2 ?( 0=2) 0=2 0 x Gamma 0 0 ?(N + 0) ?( 0)?PN i=1 xi+ 0 N + 0 for xed x d-dim Gaussian det 0=2 S0 ( )dN=2 det( 0+N)=2(S+S0) Nd 0 (N+N0)d Qd i=1 ?(( 0+N?1?i)=2) ?(( 0?1?i)=2) Table 5: Distributions and their evidence 1994). For the distributions in Table 2 with priors in Table3 , Table 5 gives their matching evidence derived using Lemma 6.4 and cancelling a few common terms.... ..."

Cited by 189

### Table 2: Distributions and their conjugate priors

1994

"... In PAGE 40: ...stablish properties of it. In Sections 5.3.2 and 5.3.3 it is shown how this property forms the basis of several fast Bayesian learning algorithms looking at multiple models, including decision trees [Bun91b], and Bayesian networks [SL90, SDLC93, Bun91d]. Table2... In PAGE 44: ...2.3 Recognizing and using the exponential family As a nal note, how can we apply these operations automatically to a graphical model? Which distributions are exponential family and which have conjugate distributions with normalizing con- stants in closed form? Table2 gives a selection of distributions, and their conjugate distribution. Further details can be found in most textbooks on probability distributions.... In PAGE 54: ...emma 5.8 Consider the context of Lemma 5.1. Then the model likelihood or evidence, given by evidence(M) = p(x1; : : :; xNjy1; : : :; yN; M), can be computed as: evidence(M) = p( j ) QN j=1 p(xjjyj; ) p( j 0) = Z ( 0) Z ( )ZN 2 : For the distributions in Table 1 with priors in Table2 , Table 4 gives their matching evidence derived using Lemma 5.8 and cancelling a few common terms.... In PAGE 55: ...Learning with Graphical Models 55 p(var2 = 1jvar1 = 0; 2) = 2;0j0 ; p(var2 = 1jvar1 = 1; 2) = 2;0j1 : If we use Dirichlet priors for these parameters, as shown in Table2 , then the priors are: ( 1; 1 ? 1) Dirichlet( 1;0; 1;1) ; ( 2;0jj; 1 ? 2;0jj) Dirichlet( 2;0jj; 2;1jj) for j = 0; 1 ; where 2;0j0 is aprior independent of 2;0j1. Arguments for choosing the values of these parameters are given later in Section 6.... In PAGE 55: ... Each get their own parameters, su cient statistics, and contribution to the evidence. Conjugate priors from Table2 (using xjy Gaussian) are indexed accordingly as: ijjj ijj Gaussian( 0;ijj; 0;ijj 2 ijj ) for i = 1; 2 and j = 0; 1 ; ?2 ijj Gamma( 0;ijj=2; 0;ijj) for i = 1; 2 and j = 0; 1 ; Notice that 0;ijj is one dimensional when i = 0 and two dimensional when i = 2. Suitable su cient statistics for this situation are read from Table 3 by looking at the data summaries used there.... ..."

Cited by 189

### Table 4: Results for different priors

2002

"... In PAGE 6: ... stop terms 5. stem terms using the Porter algorithm Table4 shows the mean reciprocal rank (MRR) for runs on both the web page and the anchor text collection in combination with different priors. Both inlinks and URL form help to increase search effectiveness, especially the URL prior is highly effective.... In PAGE 6: ...2 Combining Priors In section 4 we saw that both the number of inlinks and the URL can give important information about whether a page is an entry a141 The experiments in this paper are based on the CSIRO anchor col- lection [6, 7], whereas the experiments reported in [38] are based on an anchor collection we built ourselves page or not. The results in Table4 confirm this. A combination of these two sources of information might also be useful.... ..."

Cited by 85

### Table 4: Results for different priors

2002

"... In PAGE 6: ... stop terms 5. stem terms using the Porter algorithm Table4 shows the mean reciprocal rank (MRR) for runs on both the web page and the anchor text collection in combination with different priors. Both inlinks and URL form help to increase search effectiveness, especially the URL prior is highly effective.... In PAGE 6: ...2 Combining Priors In section 4 we saw that both the number of inlinks and the URL can give important information about whether a page is an entry a143 The experiments in this paper are based on the CSIRO anchor col- lection [6, 7], whereas the experiments reported in [38] are based on an anchor collection we built ourselves page or not. The results in Table4 confirm this. A combination of these two sources of information might also be useful.... ..."

Cited by 85