04.3 Which settings better explain observations

Content and key concepts

On the previous page, the new certificate changes the evaluation.
Data are already available, and we're now comparing how different parameter values are consistent with these data.
We've already seen three successes and one failure, assuming a probability of success 0.75.
Для изменения рисунка включитеJavaScript; расчёт и теория доступны далее.
What kind of settings better explain surveillance?
The parameters in the probability question are fixed, the results vary. The data are already observed, and we're comparing the parameters. For four independent Bernoulli figures, the probability of success of theta and the particular sequence[1,1.0]:
L
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L(\theta)=\theta^3(1-\theta),\quad
\ell(\theta)=3\ln\theta+\ln(1-\theta).
L
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Here L is not the loss of other chapters, but the likelihood; the negative log-likelihood is used to minimize. There is no regulation. For posterior p(
===5 lykelihood===0625;=75 = 10546875. The production logL is equal to 3-1/(1-__). At the ratio of 0 to 3(1 to) = , the second derivative is negative within(0.1), means a fixed point maximum. The zero probability of any actual result is defrosting lykelihood.
Experiment.
Lead from 0.01 to 99 and observe the curve. The best explanation for these four data does not mean that "the true probability is exactly 75": the sample is small. This is an estimate in a selected model family, not a guarantee of generalization.
Debug.
The probability of an event "level 3 out of 4 without counting order" includes a factor.
theta = .75
likelihood = theta**3 * (1-theta)
assert likelihood == .10546875
The code repeats the operations just taken care of.
Completely checked Python-example Chapter
Available with a separate file; the short piece shown does not replace its implementation.
The observations are fixed; the tested settings are changing. Plausibility is not the probability of the parameter itself.
How much uncertainty remains, how does this question go on with the result?
Python examples of Chapter 04
Academic base