Sigma_star

Calculates parameter \(\Sigma^*\) of \(q^*(\beta)\) to optimize the
evidence based lower bound (ELBO) in <code>survregVB.fit</code>.

Implements Bayesian inference in accelerated failure time (AFT) models for
right-censored survival times assuming a log-logistic distribution. Details of the
variational Bayes algorithms, with and without shared frailty, are described in
Xian et al. (2024) <doi:10.1007/s11222-023-10365-6> and
Xian et al. (2024) <doi:10.48550/arXiv.2408.00177>, respectively.

Alison Zhang

survregVB

Variational Bayesian Analysis of Survival Data

Chengqian Xian

Sigma_star function

<dl><dt>y</dt>
<dd>A vector of observed log-transformed survival times.</dd>
<dt>X</dt>
<dd>A design matrix including covariates with first column of ones
to represent the intercept.</dd>
<dt>delta</dt>
<dd>A binary vector indicating right censoring.</dd>
<dt>v_0</dt>
<dd>The precision (inverse variance) hyperparameter \(v_0\),
of the prior distribution of the vector of coefficients, \(\beta\).</dd>
<dt>alpha</dt>
<dd>The shape parameter \(\alpha^*\) of \(q^*(b)\).</dd>
<dt>omega</dt>
<dd>The scale parameter \(\omega^*\) of \(q^*(b)\).</dd>
<dt>mu</dt>
<dd>Parameter \(\mu^*\) of \(q^*(\beta)\), a vector of means.</dd>
<dt>expectation_b</dt>
<dd>The expected value of b.</dd></dl>

Arguments

Calculates parameter \(\Sigma^*\) of \(q^*(\beta)\) to optimize the
evidence based lower bound (ELBO) in survregVB.fit. — Sigma_star

<dl>

<dt>y</dt>
<dd>A vector of observed log-transformed survival times.</dd>


<dt>X</dt>
<dd>A design matrix including covariates with first column of ones
to represent the intercept.</dd>


<dt>delta</dt>
<dd>A binary vector indicating right censoring.</dd>


<dt>v_0</dt>
<dd>The precision (inverse variance) hyperparameter \(v_0\),
of the prior distribution of the vector of coefficients, \(\beta\).</dd>


<dt>alpha</dt>
<dd>The shape parameter \(\alpha^*\) of \(q^*(b)\).</dd>


<dt>omega</dt>
<dd>The scale parameter \(\omega^*\) of \(q^*(b)\).</dd>


<dt>mu</dt>
<dd>Parameter \(\mu^*\) of \(q^*(\beta)\), a vector of means.</dd>


<dt>expectation_b</dt>
<dd>The expected value of b.</dd>

</dl>

Sigma_star: Calculates parameter \(\Sigma^\) of \(q^(\beta)\) to optimize the evidence based lower bound (ELBO) in `survregVB.fit`.

Description

Usage

Value

Arguments

See Also