calc_prob_null

Given a set of candidate parameter vectors, the enumerated sample space, and a
logical vector with the same number of elements of the sample space, compute
the probability for each element of the sample space and take the sum.

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_prob_null function

<dl><dt>theta_cands</dt>
<dd>A matrix with samples in the rows and the parameters in
the columns</dd>
<dt>SSpacearr</dt>
<dd>A matrix with the sample space for the given size of the
problem</dd>
<dt>logC</dt>
<dd>log multinomial coefficient for each element of the sample space</dd>
<dt>II</dt>
<dd>logical vector of sample space psi being more extreme than the
observed psi</dd></dl>

Arguments

Calculate probability for given parameters — calc_prob_null

<dl>

<dt>theta_cands</dt>
<dd>A matrix with samples in the rows and the parameters in
the columns</dd>


<dt>SSpacearr</dt>
<dd>A matrix with the sample space for the given size of the
problem</dd>


<dt>logC</dt>
<dd>log multinomial coefficient for each element of the sample space</dd>


<dt>II</dt>
<dd>logical vector of sample space psi being more extreme than the
observed psi</dd>

</dl>

calc_prob_null: Calculate probability for given parameters

Description

Usage

Value

Arguments

Examples