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How is the EM method used in Bayesian inference?
The EM method was modified to compute maximum a posteriori (MAP) estimates for Bayesian inference in the original paper by Dempster, Laird, and Rubin. Other methods exist to find maximum likelihood estimates, such as gradient descent, conjugate gradient, or variants of the Gauss–Newton algorithm.
What’s the difference between Bayesian and non-Bayesian beliefs?
That original belief about the world is often called the “null hypothesis”. Our null hypothesis for the coin is that it is fair – heads and tails both come up 50% of the time. If that’s true, you get five heads in a row 1 in 32 times. That’s 3.125% of the time, or just 0.03125, and this sort of probability is sometimes called a “p-value”.
Which is better the alternative approach or the Bayesian approach?
Notice that even with just four flips we already have better numbers than with the alternative approach and five heads in a row. And the Bayesian approach is much more sensible in its interpretation: it gives us a probability that the coin is the fair coin.
Can an EM algorithm converge to a maximum likelihood estimator?
Although an EM iteration does increase the observed data (i.e., marginal) likelihood function, no guarantee exists that the sequence converges to a maximum likelihood estimator. For multimodal distributions, this means that an EM algorithm may converge to a local maximum of the observed data likelihood function,…
How is EM clustering of Old Faithful eruption data?
EM clustering of Old Faithful eruption data. The random initial model (which, due to the different scales of the axes, appears to be two very flat and wide spheres) is fit to the observed data. In the first iterations, the model changes substantially, but then converges to the two modes of the geyser.
Which is the maximization step in the EM iteration?
The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step.