statistics-r | Controls the R interpreter through Perl

I am doing some statistics-related optimization. I am trying to use scipy's minimize. However, the solution that it gives me is not feasible. My code is

I am trying to solve a statistics-related real world problem with Python and am looking for inputs on my ideas: I have N random vectors from a m-dimensional normal distribution. I have no information about the means and the covariance matrix of the underlying distribution, in fact also that it is a normal distribution is only an assumption, a very plausible one though. I want to compute an approximation of the mean vector and covariance matrix of the distribution. The number of random vectors is in the order of magnitude of 100 to 300, the dimensionality of the normal distribution is somewhere between 2 and 5. The time for the calculation should ideally not exceed 1 minute on a standard home computer.

I am currently thinking about three approaches and am happy about all suggestions for other approaches or preferences between those three:

1. Fitting: Make a multi dimensional histogram of all random vectors and fit a multi dimensional normal distribution to the histogram. Problem about that approach: The covariance matrix has many entries, this could possibly be a problem for the fitting process?

2. Invert cumulative distribution function: Make a multi dimensional histogram as approximation of the density function of the random vectors. Then integrate this to get a multi dimensional cumulative distribution function. For one dimension, this is invertible and one could use the cum-dist function to distribute random numbers like in the original distribution. Problem: For the multi-dimensional case the cum-dist function is not invertible(?) and I don't know if this approach still works then?

3. Bayesian: Use Bayesian Statistics with some normal distribution as prior and update for every observation. The result should always be again a normal distribution. Problem: I think this is computationally expensive? Also, I don't want the later updates have more impact on the resulting distribution than the earlier ones.

Also, maybe there is some library which has this task already implemented? I did not find exactly this in Numpy or Scipy, maybe someone has an idea where else to look?

This term came up a few times in the Tensorflow Dev Summit, and it shows up in the Tensorflow Extended documentation, but without any sort of definition. After a fair amount of googling, I don't see reference to it in any Statistics-related setting. Searching the Tensorflow repositories produces a few hits, but they're similarly unhelpful. The term does seem to be used in Chemistry, Psychology, and Linguistics, but those definitions appear to be unrelated.

I'm trying to understand the JMX data for the caches in SOLR -

From my understanding, the 'size' attribute indicates the size of the cache in KB [referencing this document - https://lucene.apache.org/solr/guide/7_0/performance-statistics-reference.html#statistics-for-caches ] .

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