Lab · c13.s03.L1

Likelihood explorer

The parameter that makes the observed data most likely sits at the top of the likelihood curve.

Question: Which parameter makes the data most likely?

Re-simulated Re-simulated: the curve is computed by data/scripts/c13.s03.L1.py for 13 coin flips with 9 heads and 4 tails, the example of the seed chapter. No random draw is involved; the counts are fixed and the likelihood is evaluated exactly. The frames walk the candidate heads probability from 0.50 to the peak at 0.6923 and show the peak moving to 4/13, then to the boundary for 0 and 13 heads; the curve is scaled to its own peak and the peak likelihood is printed on each frame.

Lab controls

Heads in 13 flips9 heads

Left/Down one fewer, Right/Up one more; Page Down five fewer, Page Up five more, clamped to 0 and 13; Home 0, End 13

Candidate θ (heads probability)0.5

Left/Down 0.01 less, Right/Up 0.01 more; Page Down 0.10 less, Page Up 0.10 more, clamped to 0.00 and 1.00; Home 0.00, End 1.00

Frame 1 of 11: The observed dataThirteen flips produced nine heads and four tails, and those counts stay fixed. At the candidate 0.50 the likelihood of exactly this data is 0.000122; the dashed line marks where it is highest.

Keyboard: Space plays or pauses, Left and Right step, Home goes to the first frame, End goes to the last frame.

Text description of this lab

Thirteen coin flips, nine heads and four tails, sit above a likelihood curve. The horizontal axis is the candidate heads probability from 0.00 to 1.00; the vertical axis is the likelihood, scaled to this curve's peak. A gold marker shows the current candidate. The curve peaks at 9/13, about 0.6923, where the likelihood is 0.000327, and falls on either side. Changing the heads count moves the peak to that new fraction, at the edge for 0 or 13 heads.

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Caption status: re-simulated. Every lab declares one of published, re-simulated, schematic, synthetic or interpolated.