[HN Gopher] An Overview of Bayesian Inference (2019)
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       An Overview of Bayesian Inference (2019)
        
       Author : luu
       Score  : 69 points
       Date   : 2020-04-01 01:33 UTC (21 hours ago)
        
 (HTM) web link (jaydaigle.net)
 (TXT) w3m dump (jaydaigle.net)
        
       | ur-whale wrote:
       | Slightly OT, but I wonder if anyone in the know could shed a
       | light on where Baye's theorem is applied (if anywhere) in quantum
       | mechanics?
       | 
       | In particular, has anyone tries to apply the bayesian framework
       | to the whole "the wave collapses upon measurement" shebang?
        
         | shoo wrote:
         | You may find this interesting:
         | 
         | Gelman, Yao - Holes in Bayesian Statistics
         | 
         | > Every philosophy has holes, and it is the responsibility of
         | proponents of a philosophy to point out these problems. Here
         | are a few holes in Bayesian data analysis: (1) the usual rules
         | of conditional probability fail in the quantum realm, (2) flat
         | or weak priors lead to terrible inferences about things we care
         | about, (3) subjective priors are incoherent, (4) Bayes factors
         | fail in the presence of flat or weak priors, (5) for Cantorian
         | reasons we need to check our models, but this destroys the
         | coherence of Bayesian inference.
         | 
         | In particular, you may appreciate the example and discussion in
         | section 2:
         | 
         | > Probability theory isn't true (quantum physics)
         | 
         | http://www.stat.columbia.edu/~gelman/research/unpublished/ba...
        
           | deepnet wrote:
           | contrarily "...we obtain that quantum mechanics is the
           | Bayesian theory in the complex numbers."
           | 
           | from Quantum mechanics: The Bayesian theory generalised to
           | the space of Hermitian matrices by Alessio Benavoli,
           | Alessandro Facchini, Marco Zaffalon
           | 
           | https://arxiv.org/abs/1605.08177
        
         | gjm11 wrote:
         | There is a thing called "Quantum Bayesianism":
         | https://en.wikipedia.org/wiki/Quantum_Bayesianism
        
         | deepnet wrote:
         | "Quantum Bayesianism, or QBism as Fuchs now calls it, solves
         | many of quantum theory's deepest mysteries. Take, for instance,
         | the infamous "collapse of the wave function," wherein the
         | quantum system inexplicably transitions from multiple
         | simultaneous states to a single actuality. According to QBism,
         | the wave function's "collapse" is simply the observer updating
         | his or her beliefs after making a measurement."
         | 
         | https://www.quantamagazine.org/quantum-bayesianism-explained...
        
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