sigma | probabilistic model for the sequential dependencies | Machine Learning library

I just learned how to insert (a limited number of) LaTeX expressions into my plot titles with expression(). How can I generate plots containing LaTeX in their titles using a loop? For example, say I have:

I am currently having issue with the implementation of the Metropolis-Hastings algorithm.

I am trying to use the algorithm to calculate integrals of the form

In using this algorithm, we can obtain a long chain of configurations ( in this case, each configuration is just a single numbers) such that in the tail-end of the chain the probability of having a particular configuration follows (or rather tends to) a gaussian distribution.

My code seems to be messing up with obtaining the said gaussian distributions. There is a strange dependence on the transition probablity (the probablity of picking a new candidate configuration depending on the previous configuration in the chain). However, if this transition probability is symmetric, there should be no dependence on this function at all (it only affects speed at which phase space [space of potential configurations] is explored and how quickly the chain converges to the desired distribution)!

In my case I am using a normal distribution transition function (which satisfies the need to be symmetric), with width d. For each d I use I do indeed get a gaussian distribution however the standard deviation, sigma, depends on my choice of d. The resulting gaussian should have a sigma of roughly 0.701 but I find that the value I actually get depends on the parameter d, when it shouldn't.

I am not sure where the error in this code is, any help would be greatly appreciated!

I am aiming to create a progress bar for an iteration happening inside an installed module.

To create a progress bar for an iteration inside a user-defined function, I pass an tqdm.notebook.tqdm_notebook object as iterable:

While plotting with a meshgrid defined like this:

How can I make the lines for the x- and y-axes thicker in Julia Plots? Is there a simple way to achieve this?

MWE:

Suppose the random variable X ∼ N(μ,σ2) distribution

and I am given the observations x =(0.7669, 1.6709, 0.8944, 1.0321, 0.0793, 0.1033, 1.2709, 0.7798, 0.6483, 0.3256)

Given prior distribution μ ∼ N(0, (100)^2) and σ2 ∼ Inverse − Gamma(5/2, 10/2).

I am trying to give a MCMC estimation of the parameter.

Here is my sample code, I am trying to use Random Walk MCMC to do the estimation, but it seems that it does not converge:

I have a gradient exploding problem which I couldn't solve after trying for several days. I implemented a custom message passing graph neural network in TensorFlow which is used to predict a continuous value from graph data. Each graph is associated with one target value. Each node of a graph is represented by a node attribute vector, and the edges between nodes are represented by an edge attribute vector.

Within a message passing layer, node attributes are updated in a certain way (e.g., by aggregating other node/edge attributes), and these updated node attributes are returned.

Now, I managed to figure out where the gradient problem occurs in my code. I have the below snippet.

I have the following:

I am still quite new to coding but wanted to learn about modules. I am trying to build an app that will display data based on a selected date range. I tried to do this with different modules for selecting the dates and other modules to handle data and eventually create plots. The goal is to reuse some of these modules in different parts of the app. I seem to have become stuck following the article here. I realise that the article describes the callModule method of using modules.

Here is a sample of the app and modules: