calc_multinom_probs

Calculate multinomial probabilities

We consider the problem where we observe k vectors (possibly of different lengths), each representing an independent multinomial random vector. For a given function that takes in the concatenated vector of multinomial probabilities and outputs a real number, this is a Monte Carlo estimation procedure of an exact p-value and confidence interval. The resulting inference is valid even in small samples, when the parameter is on the boundary, and when the function is not differentiable at the parameter value, all situations where asymptotic methods and the bootstrap would fail. For more details see Sachs, Fay, and Gabriel (2025) <doi:10.48550/arXiv.2406.19141>.

Michael Sachs

xactonomial

Inference for Functions of Multinomial Parameters

Michael C Sachs

Michael P Fay

Erin E Gabriel

David B Dahl

calc_multinom_probs function

<dl><dt>sar</dt>
<dd>The unrolled matrix containing the portion of the sample space to sum over</dd>
<dt>logt</dt>
<dd>The vector of candidate theta values, as sampled from the null space</dd>
<dt>logc</dt>
<dd>The vector of log multinomial coefficients see log_multinom_coef</dd>
<dt>d</dt>
<dd>The total dimension, sum(d_j)</dd>
<dt>n</dt>
<dd>The sample size</dd>
<dt>nt</dt>
<dd>The number of candidate theta values</dd></dl>

Arguments

Calculate multinomial probabilities — calc_multinom_probs

<dl>

<dt>sar</dt>
<dd>The unrolled matrix containing the portion of the sample space to sum over</dd>


<dt>logt</dt>
<dd>The vector of candidate theta values, as sampled from the null space</dd>


<dt>logc</dt>
<dd>The vector of log multinomial coefficients see log_multinom_coef</dd>


<dt>d</dt>
<dd>The total dimension, sum(d_j)</dd>


<dt>n</dt>
<dd>The sample size</dd>


<dt>nt</dt>
<dd>The number of candidate theta values</dd>

</dl>

calc_multinom_probs: Calculate multinomial probabilities

Description

Usage

Value

Arguments

Examples