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Fix log_mix signature #832

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merged 3 commits into from
Nov 15, 2024
Merged

Fix log_mix signature #832

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2a9da9e
Fix log_mix signature
WardBrian Nov 14, 2024
48d6b88
Example
WardBrian Nov 14, 2024
dbf2884
Update prose for log_mix
WardBrian Nov 15, 2024
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18 changes: 13 additions & 5 deletions src/functions-reference/real-valued_basic_functions.qmd
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Original file line number Diff line number Diff line change
Expand Up @@ -1601,7 +1601,7 @@ The logarithm of one minus the natural exponentiation of x
Return the natural logarithm of the difference of the natural
exponentiation of x and the natural exponentiation of y. \begin{equation*}
\mathrm{log\_diff\_exp}(x,y) = \begin{cases} \log(\exp(x)-\exp(y)) &
\text{if } +\infty > x \ge y \\[6pt]
\text{if } +\infty > x \ge y \\[6pt]
\textrm{NaN} & \text{otherwise} \end{cases}
\end{equation*}

Expand All @@ -1628,11 +1628,19 @@ proportion theta, defined by \begin{eqnarray*}
\lambda_1, \ \log(1 - \theta) + \lambda_2\right). \end{eqnarray*}
{{< since 2.6 >}}

<!-- R; log_mix; (T1 theta, T2 lp1, T3 lp2); -->
\index{{\tt \bfseries log\_mix }!{\tt (T1 theta, T2 lp1, T3 lp2): real}|hyperpage}
<!-- R; log_mix; (T1 thetas, T2 lps); -->
\index{{\tt \bfseries log\_mix }!{\tt (T1 thetas, T2 lps): real}|hyperpage}

`R` **`log_mix`**`(T1 thetas, T2 lps)`<br>\newline

Extension of the two-mixture case above to more densities.
Return the log mixture of the log densities stored in `lps`,
where each log density has the mixing proportion given by
the same index in `thetas`.
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  1. thetas is presumably required to be a simplex, so that should be mentioned.
  2. thetas and lps have to be the same length, so that should be mentioned.
  3. The result should be given explicitly in math, e.g., log(SUM_n thetas[n] * exp(lps[n])) or the more efficient but also more opaque log_sum_exp(log(thetas) + lps) (it'd be OK to include both if you think just one would be confusing).

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Oddly enough, it doesn't seem that the math library is checking that thetas is a simplex, just that it is bounded between 0 and 1. Possibly worthy of a math issue?

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Extension of the two-mixture case above to more densities. Return the log mixture of the log densities stored in lps, where each log density has the mixing proportion given by the same index in thetas.

I would prefer this to say something about how this is intended to be looped across each density observation but is generalized to more than two densities. This connects the warning in the mixture modeling section about why we need to loop.


In other words, `log_mix(a,b,c)` could be equivalent written
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to use this signature by writing `log_mix({a, 1-a}, {b, c})`.

`R` **`log_mix`**`(T1 theta, T2 lp1, T3 lp2)`<br>\newline
Vectorized implementation of the `log_mix` function
{{< since 2.26 >}}

<!-- R; log_sum_exp; (T1 x, T2 y); -->
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