Merge branch 'StatProofBook:master' into master

Author: JoramSoch

D/beta-data.md

@@ -21,7 +21,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Beta-distributed data are defined as a set of proportions $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ with $y_i \in [0,1], \; i = 1,\ldots,n$, independent and identically distributed according to a [Beta distribution](/D/beta) with shapes $\alpha$ and $\beta$:
+**Definition:** Beta-distributed data are defined as a set of proportions $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ with $y_i \in [0,1], \; i = 1,\ldots,n$, independent and identically distributed according to a [beta distribution](/D/beta) with shapes $\alpha$ and $\beta$:
 
 $$ \label{eq:beta-data}
 y_i \sim \mathrm{Bet}(\alpha,\beta), \quad i = 1, \ldots, n \; .

D/cvlme.md

@@ -10,7 +10,7 @@ date: 2020-11-19 04:55:00
 title: "Cross-validated log model evidence"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log model evidence"
+topic: "Model evidence"
 definition: "Cross-validated log model evidence"
 
 sources:

D/eblme.md

@@ -10,7 +10,7 @@ date: 2020-11-25 07:43:00
 title: "Empirical Bayesian log model evidence"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log model evidence"
+topic: "Model evidence"
 definition: "Empirical Bayesian log model evidence"
 
 sources:

D/fe.md

@@ -34,7 +34,7 @@ $$ \label{eq:fam}
 f \Leftrightarrow m_1 \vee \ldots \vee m_M \; .
 $$
 
-Then, the family evidence (FE) of $f$ is defined as the [marginal probability](/D/prob-marg) relative to the [model evidences](/D/me) $p(y \vert m_i), conditional only on $f$:
+Then, the family evidence (FE) of $f$ is defined as the [marginal probability](/D/prob-marg) relative to the [model evidences](/D/me) $p(y \vert m_i)$, conditional only on $f$:
 
 $$ \label{eq:fe}
 \mathrm{FE}(f) = p(y|f) \; .

D/lbf.md

@@ -10,8 +10,8 @@ date: 2020-07-22 07:02:00
 title: "Log Bayes factor"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log Bayes factor"
-definition: "Definition"
+topic: "Bayes factor"
+definition: "Log Bayes factor"
 
 sources:
   - authors: "Soch J, Allefeld C"

D/lfe.md

@@ -10,8 +10,8 @@ date: 2020-07-13 22:31:00
 title: "Log family evidence"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log family evidence"
-definition: "Definition"
+topic: "Family evidence"
+definition: "Log family evidence"
 
 sources:
   - authors: "Soch J, Allefeld C"
@@ -34,13 +34,7 @@ $$ \label{eq:fam}
 f \Leftrightarrow m_1 \vee \ldots \vee m_M \; .
 $$
 
-Then, the family evidence of $f$ is the weighted average of the [model evidences](/D/ml) of $m_1, \ldots, m_M$ where the weights are the within-family [prior model probabilities](/D/prior)
-
-$$ \label{eq:fe}
-p(y|f) = \sum_{i=1}^M p(y|m_i) \, p(m_i|f) \; .
-$$
-
-The log family evidence is given by the logarithm of the family evidence:
+Then, the log family evidence is given by the logarithm of the [family evidence](/D/fe):
 
 $$ \label{eq:lfe}
 \mathrm{LFE}(f) = \log p(y|f) = \log \sum_{i=1}^M p(y|m_i) \, p(m_i|f) \; .

D/lme.md

@@ -10,8 +10,8 @@ date: 2020-02-25 12:56:00
 title: "Log model evidence"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log model evidence"
-definition: "Definition"
+topic: "Model evidence"
+definition: "Log model evidence"
 
 sources:
   - authors: "Soch J, Allefeld C"
@@ -28,7 +28,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $m$ be a [full probability model](/D/fpm) with [likelihood function](/D/lf) $p(y \vert \theta, m)$ and [prior distribution](/D/prior) $p(\theta \vert m)$. Then, the log model evidence (LME) of this model is defined as the logarithm of the [marginal likelihood](/D/ml):
+**Definition:** Let $m$ be a [full probability model](/D/fpm) with [likelihood function](/D/lf) $p(y \vert \theta, m)$ and [prior distribution](/D/prior) $p(\theta \vert m)$. Then, the log model evidence (LME) of $m$ is defined as the logarithm of the [marginal likelihood](/D/ml) of this model:
 
 $$ \label{eq:LME}
 \mathrm{LME}(m) = \log p(y|m) \; .

D/uplme.md

@@ -10,7 +10,7 @@ date: 2020-11-25 07:28:00
 title: "Uniform-prior log model evidence"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log model evidence"
+topic: "Model evidence"
 definition: "Uniform-prior log model evidence"
 
 sources:

D/vblme.md

@@ -10,7 +10,7 @@ date: 2020-11-25 08:10:00
 title: "Variational Bayesian log model evidence"
 chapter: "Model Selection"
 section: "Bayesian model selection"
-topic: "Log model evidence"
+topic: "Model evidence"
 definition: "Variational Bayesian log model evidence"
 
 sources:

I/DbA.md

@@ -8,14 +8,16 @@ title: "Definition by Author"
 
 - [Sample covariance](/D/cov-samp)
 
-### JoramSoch (170 definitions)
+### JoramSoch (174 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
 - [Bayesian information criterion](/D/bic)
 - [Bayesian model averaging](/D/bma)
 - [Bernoulli distribution](/D/bern)
 - [Beta distribution](/D/beta)
+- [Beta-binomial data](/D/betabin-data)
+- [Beta-binomial distribution](/D/betabin)
 - [Beta-distributed data](/D/beta-data)
 - [Binomial distribution](/D/bin)
 - [Binomial observations](/D/bin-data)
@@ -64,6 +66,7 @@ title: "Definition by Author"
 - [Explained sum of squares](/D/ess)
 - [Exponential distribution](/D/exp)
 - [F-distribution](/D/f)
+- [Family evidence](/D/fe)
 - [Flat, hard and soft prior distribution](/D/prior-flat)
 - [Full probability model](/D/fpm)
 - [Full width at half maximum](/D/fwhm)
@@ -100,6 +103,7 @@ title: "Definition by Author"
 - [Method-of-moments estimation](/D/mome)
 - [Minimum](/D/min)
 - [Mode](/D/mode)
+- [Model evidence](/D/me)
 - [Moment](/D/mom)
 - [Moment-generating function](/D/mgf)
 - [Multinomial distribution](/D/mult)