7 votes
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The Likelihood Approach a.k.a. the 'third way' versus Bayesian

How is the 'Likelihood Approach' different from the Bayesian approach? It's very different. Bayesians interpret probabilities in subjectivist terms as the measure of belief. They also use priors, so ...
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2 votes
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Bayesian inference on sequential data

Here is a framework that might be applicable. There are two related entities. There are $T_i$ observations for entity: $Y_i = (y_{i1}, \ldots, y_{iT_i})$ for $i \in \{1,2\}$. Each of the two entities ...
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2 votes

good intermediate-level textbook for undergraduate applied statistics in data science?

I challenge the notion of not covering the theory just because the students don't care. As our moderator, WHuber, writes in his profile, "The mathematics are not there for the joy of the analyst ...
2 votes
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How do find the best arm in a multi-armed bandit when exploitation is unimportant?

This answer is relevant to your question. If you are interested in minimizing the number of pulls to identify the best arm the setting you want to use is Best Arm Identification. In this setting, you ...
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1 vote

How to find the marginal prior distribution?

If we further assume that $\beta \ \bot \ \eta | \zeta$ you have the conditional density $p(\beta|\zeta,\eta) = p(\beta|\zeta) = f(\beta,\zeta)$, which then lets you expand the joint density as: $$\...
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1 vote

Is it possible to estimate the parameters of a superposition of Poisson processes through Bayesian inference from a binarized sequence?

I'd pick the prior that best represents my understanding of the underlying mechanisms of the problem. There is a lot you haven't told us, so it is next to impossible for me to guess a meaningful prior....
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1 vote

Understanding the Evidence Lower Bound (ELBO)

Don’t forget that log probabilities are non-positive, too. They’re the logs of values that cannot exceed 1. With that in mind, the ELBO can be a meaningful lower bound on the log-likelihood: both are ...
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1 vote
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Bayesian model averaging

If you have two candidate likelihoods $P_1(\text{data}=\{x_1\dots x_n\}|\theta_1)$ and $P_2(\text{data}=\{x_1\dots x_n\}|\theta_2)$ with two different parametrizations $\theta_1$ and $\theta_2$, the ...
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