How to normalize log-likelihoods?

by Adrian   Last Updated January 15, 2018 07:19 AM

I have referred to this post here. However, the approach in the top answer did not work out for me. Below are n = 100 of my log-likelihoods.

ll <- > dput(Lik2)
c(-35480.7118796417, -2739.42871153509, -8362.32845821982, -8365.34260282213, 
-9094.89673916007, -21270.2045379339, -12580.518821136, -13783.8037118782, 
-42712.3278071616, -423837.36571571, -1805.78632985328, -2002.85063426255, 
-3762.76492409086, -6849.63087008593, -11956.7406803718, -20976.5170841893, 
-135949.201113163, -31498.4171087018, -15446.7854298957, -5120.27102265426, 
-27618.8855708366, -1181406.765207, -80867.7262649035, -816098.492721317, 
-10945.0893400045, -1628417.58006139, -16482.9909028172, -65197.3708076204, 
-67871.4208617162, -77627.4857483449, -17479.5870536702, -93579.8562141009, 
-5281.94699357017, -5554.87325489942, -15628.8543639877, -10632.6082887688, 
-6489.97791129332, -11988.4625382098, -9170.39131516501, -9339.36646353115, 
-113156.200514024, -2567.90247055723, -14467.0183704268, -48650.137758317, 
-10495.0548182032, -2889.13562818923, -115485.747589673, -80143.5433253561, 
-5428.78386244051, -15449.3451561719, -25609.2870701355, -3832.78432518107, 
-24152.3367051411, -2272.05842004831, -3184.3778786079, -2727.35587110321, 
-2416.5798834696, -31118.8156319793, -51467.1989404669, -1847.91304055039, 
-75179.9905124732, -55387.6390729858, -6217.46116602578, -80167.2789661716, 
-2262.83239548126, -7967.86416890192, -203981.847720651, -5348.68097367683, 
-35539.3623924968, -29740.7965097703, -145107.587483733, -16038.5130132878, 
-30534.4376362393, -164907.15448187, -18269.9830224852, -10168.7453829144, 
-86431.7638673747, -30391.9503748769, -2836.02770007675, -5544.75647729347, 
-4392.30776454182, -215937.960800752, -28141.7740166936, -7439.99455094574, 
-13708.5567616969, -9908.51651663084, -46267.2625988753, -5158.62658552135, 
-5521.97889928275, -1485.65777356592, -464662.123874468, -30866.4651125434, 
-14037.8604686386, -4754.14972171724, -13552.1743710923, -4674.74137872854, 
-6890.68419568385, -12060.9906749138, -5763.51938836069, -3472.01636104686
)

#Subtract everything by maximum of the log likelihoods
ll2 <- ll - max(ll)
#Throw away anything that is < log(10e-16/n)
ll3 <- subset(ll2, ll2 > log(10e-16/100))
> exp(ll3) 
> 1

When I'm calculating ll3, I threw away my entire vector of log-likelihoods, which is problematic. Even when I was subtracting ll by its maximum, the resulting ll2 still contains values that are extremely small. So if I were to exponentiate them, I would get 0.



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