Statistical inference vs Machine Learning inference: Bayesian vs frequentist perspectives

Thanks for your feedback on my previous post. The biggest misconception in learning the mathematical foundations of data science which no one tells you is.??

One qs is:

How does the discussion on Statistical inference vs Machine Learning inference co-relate to Bayesian vs Frequentist.?

Here are my thoughts?

Both Bayesian and frequentist statistics use sampling since both are statistical approaches.?

Frequentist inference interprets probability as the long-run frequency of events. It does not assign probabilities to hypotheses or parameters but instead focuses on the likelihood of observing data given the parameters. It relies on methods like hypothesis testing, confidence intervals, and p-values to make inferences about population parameters based on sample data.?

The emphasis is on estimating parameters without prior information about their possible values. Frequentist statistics assumes that the parameters are fixed but unknown.?

Bayesian inference interprets probability more subjectively as a degree of belief or certainty about a statement. This approach allows for the direct probability assignment to hypotheses and parameters. Bayesian inference uses Bayes' theorem to update the probability of a hypothesis as more evidence or data becomes available. Bayesian inference involves specifying prior probabilities (which express what is known about parameters before observing the data) and likelihoods (how probable the observed data is given different parameter values) to compute posterior probabilities (updated beliefs after considering the data).

In Bayesian inference, parameters are considered random variables because their values are uncertain.?

The main difference is:? In frequentist approaches, parameters are considered fixed and unknown constants that can be estimated from the data. In contrast, Bayesian approaches treat parameters as random variables with their own distributions, reflecting uncertainty about their values. This allows for the incorporation of prior knowledge or beliefs about parameters in the Bayesian approach, which get updated with new data through Bayes' theorem, leading to a posterior distribution that expresses updated beliefs about the parameters' values.

However, from our perspective, in both these cases, we try to understand the behaviour of a larger population from a smaller sample.

In frequentist statistics, samples are used to estimate population parameters. Bayesian inference uses samples to update prior beliefs or knowledge about parameters in light of new evidence.?

Contrast this with machine learning where we split the entire data intro? test and train sets.?

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