Richard Carrier has never been broadly accepted by the academic biblical community. His status remains as that of a hyper-minimalist and, as far as I'm concerned, he is more of a troll than anything else. Carrier has significant deficiencies in his training yet pontificates on many and various issues on which he is not equipped to comment. His work seeks to justify his agenda (i.e., minimalist, atheist, etc.) and does not do due diligence to the data set available to researchers. I once interacted with him on his blog wherein he acted most caustic. In querying him on some of the most basic pieces of solid evidence for the historicity of things like King David, he exhibited his lack of ability to treat the data appropriately, dodged significant points, created straw men, etc. (He actually called the Tel Dan stele a Hebrew inscription when it is widely known to be Old Aramaic.)

Bart Ehrman has taken the 'mythicist' view of early Christian origins and the New Testament to task in his book Did Jesus Exist. Carrier responded to the book (in non-peer reviewed format--this is a point of note), before it even came out IIRC. As one example, Carrier's 'dying messiah' nonsense has been debunked in a few places, but my friend Thom Stark did a pretty decent job here, here, and here--posts which I consulted on.

There's always room for more, but here is an older thread in which Carrier is discussed and which you may find interesting as you await more responses:

http://www.reddit.com/r/AskHistorians/comments/1aqe6h/what_is_the_standard_of_evidence_to_accept_the/

This publication is very recent, so might be too early to generate a significant academic response. I'm not a historian myself, but I am an interested amateur (and a fan of Carrier, to reveal my own bias) and found a few links that might be relevant to your question:

1. Carrier is keeping a list of reviews of his two books on historicity (both positive and negative) on his blog, along with his response and further discussion. I don't know anything about the academic reputation of those responding, but he does intend to keep this list updated over time.
2. It does appear he is publishing the core of his thesis in an academic online journal: Richard Carrier, “Why We Might Have Reason for Doubt: Should We Still Be Looking for a Historical Jesus?” The Bible & Interpretation (August 2014). It may be that we see academic responses to this journal article instead of the longer work. EDIT: See below*.
3. Other scholars in the field have produced relevant recent work on the question of historicity. I have no basis to judge the quality or reputation of their work, but Carrier mentions and comments on several here:

• Notable recent books on both sides of this issue and Carrier's comments.
• More Biblical Scholars come out as mythicists or agnostic on the Jesus question. Mentioned is Thomas Brodie's new book, Beyond the Quest for the Historical Jesus.
• Analysis and criticism of Brodie's book (mostly negative).

Also worth mentioning is a recently published anthology of Carrier's peer-reviewed journal publications. This includes papers on unrelated Biblical and non-biblical historical topics, plus his recently published papers, "Thallus and the Darkness at Christ's Death" and "Origen, Eusebius, and the Accidental Interpolation in Josephus, Jewish Antiquities 20.200" which are cited in his book on historicity.

Regarding Carrier's use of Bayesian methods, that's more directly addressed by his immediately prior book, "Proving History: Bayes's Theorem and the Quest for the Historical Jesus", where he justifies his methods.

*EDIT: Looks like "The Bible and Interpretation" is an online news/commentary site, not a peer-reviewed journal. This was my mistake, not Carrier's.