reviews: 
Comments: This paper proposes a clustered FL method based on a bayesian framework which assigns clients to clusters, and provides three different variations of the proposed bayesian clustered FL framework to address practical considerations, namely approximate BCFL, greedy BCFL, and consensus BCFL. Specifically, for $K$ clusters and $C$ clients, BCFL assigns each client to its optimal cluster based on a target posterior characterization. The work performs preliminary experiments to validate the BCFL's performance on CIFAR10 and FMNIST.
Strengths: - The work proposes many different variants of BCFL that considers practicality.
- The work investigates clustering in FL dependent on the different data distributions of the clients which is a relevant topic in FL where data heterogeneity can be particularly severe. 
- The work includes details of their experimental results including graphs that show the relationship across clients and their relatedness with the results.
Weaknesses: - A major concern I have is regarding the efficacy and practicality of the proposed framework. Although the authors have proposed the three variants of the proposed BCFL framework, they still require the downloading of the models and weights under past associations, and then again uploading the associations of the weights to get the association decisions again from the server. Then finally the clients upload the local models based on the conditional associations. This requires at least 2 times the communication rounds compared to the conventional FL framework as well as more computation imposed to the clients. I became more skeptical after looking at the experimental results which only include 10 clients in total or 8 clients in total for more cross-device like datasets such as digits-dive or amazon review. Another concern regarding this approach of BCFL is the sensitivity of the number of clusters $K$ to the performance. It will be difficult to know this value in advance in practice. How does the authors address this problem as well? Overall due to these issues I am skeptical of the efficacy and practicality of the proposed framework for realistic FL settings. 

- Another concern I had regarding the practical variant approximate BCFL, the authors assume that there is no overlap in the distribution across different client partitions. This is quite a strong assumption which does not hold in most of the cases in FL. Can the authors comment on this assumption and how realistic it is?

- The writing of the paper can be improved. for instance in pg1 when the authors address problem 1 and problem 2 in bold, there seems to be a typo/error. Ex: Problems2: The is a lack of a united theory. Moreover, optimality is used throughout the paper from the beginning without a proper explanation on what the authors exactly mean by this. It can mean differently for different readers. In addition, the presentation of Figure 3 can be improved, It is quite hard to see the differences across the curves.

Due to these concerns, I am leaning towards rejection for the work.
Recommendation: 5: marginally below the acceptance threshold
Reviewer confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 2 fair
Clarity: 2 fair