46 research outputs found
On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression
In logistic regression, separation occurs when a linear combination of the
predictors can perfectly classify part or all of the observations in the
sample, and as a result, finite maximum likelihood estimates of the regression
coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy
distributions as default priors for the regression coefficients in logistic
regression, even in the case of separation, and reported posterior modes in
their analyses. As the mean does not exist for the Cauchy prior, a natural
question is whether the posterior means of the regression coefficients exist
under separation. We prove theorems that provide necessary and sufficient
conditions for the existence of posterior means under independent Cauchy priors
for the logit link and a general family of link functions, including the probit
link. We also study the existence of posterior means under multivariate Cauchy
priors. For full Bayesian inference, we develop a Gibbs sampler based on
Polya-Gamma data augmentation to sample from the posterior distribution under
independent Student-t priors including Cauchy priors, and provide a companion R
package in the supplement. We demonstrate empirically that even when the
posterior means of the regression coefficients exist under separation, the
magnitude of the posterior samples for Cauchy priors may be unusually large,
and the corresponding Gibbs sampler shows extremely slow mixing. While
alternative algorithms such as the No-U-Turn Sampler in Stan can greatly
improve mixing, in order to resolve the issue of extremely heavy tailed
posteriors for Cauchy priors under separation, one would need to consider
lighter tailed priors such as normal priors or Student-t priors with degrees of
freedom larger than one
Analysis of adiabatic transfer in cavity quantum electrodynamics
A three-level atom in a ∧ configuration trapped in an optical cavity forms a basic unit in
a number of proposed protocols for quantum information processing. This system allows for efficient
storage of cavity photons into long-lived atomic excitations, and their retrieval with high fidelity, in an
adiabatic transfer process through the ‘dark state’ by a slow variation of the control laser intensity. We
study the full quantum mechanics of this transfer process with a view to examine the non-adiabatic
effects arising from inevitable excitations of the system to states involving the upper level of ∧, which
is radiative. We find that the fidelity of storage is better, the stronger the control field and the slower
the rate of its switching off. On the contrary, unlike the adiabatic notion, retrieval is better with faster
rates of switching on of an optimal control field. Also, for retrieval, the behaviour with dissipation is
non-monotonic. These results lend themselves to experimental tests. Our exact computations, when
applied to slow variations of the control intensity for strong atom–photon couplings, are in very good
agreement with Berry’s superadiabatic transfer results without dissipation
Prepare-and-measure based QKD protocol under free-space losses
In this study, we have theoretically presented a prepare-and-measure-based
SARG04 protocol over free space. It has shown that the highest secret key rate
is possible even under free-space losses with a maximum tolerance of noise.Comment: 4 pages, 1 figur
Realistic theory of electromagnetically-induced transparency and slow light in a hot vapor of atoms undergoing collisions
We present a realistic theoretical treatment of a three-level
system in a hot atomic vapor interacting with a coupling and a probe field of
arbitrary strengths, leading to electromagnetically-induced transparency and
slow light under the two-photon resonance condition. We take into account all
the relevant decoherence processes including col5Blisions. Velocity-changing
collisions (VCCs) are modeled in the strong collision limit effectively, which
helps in achieving optical pumping by the coupling beam across the entire
Doppler profile. The steady-state expressions for the atomic density-matrix
elements are numerically evaluated to yield the experimentally measured
response characteristics. The predictions, taking into account a dynamic rate
of influx of atoms in the two lower levels of the , are in excellent
agreement with the reported experimental results for He*. The role played
by the VCC parameter is seen to be distinct from that by the transit time or
Raman coherence decay rate
Measurement and shaping of biphoton spectral wavefunctions
In this work we present a simple method to reconstruct the complex spectral
wavefunction of a biphoton, and hence gain complete information about the
spectral and temporal properties of a photon pair. The technique, which relies
on quantum interference, is applicable to biphoton states produced with a
monochromatic pump when a shift of the pump frequency produces a shift in the
relative frequencies contributing to the biphoton. We demonstrate an example of
such a situation in type-II parametric down-conversion (SPDC) allowing
arbitrary paraxial spatial pump and detection modes. Moreover, our test cases
demonstrate the possibility to shape the spectral wavefunction. This is
achieved by choosing the spatial mode of the pump and of the detection modes,
and takes advantage of spatiotemporal correlations.Comment: Supplementary information also available. Comments and feedback
appreciated. Compared to the previous version, here we have made the
following changes: -corrected a typo in the text between Eq. (11) and (12)
-corrected a typo in the references -added reference
Phase diffusion pattern in quantum nondemolition systems
We quantitatively analyze the dynamics of the quantum phase distribution
associated with the reduced density matrix of a system, as the system evolves
under the influence of its environment with an energy-preserving quantum
nondemolition (QND) type of coupling. We take the system to be either an
oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a
spin-1/2 system), and model the environment as a bath of harmonic oscillators,
initially in a general squeezed thermal state. The impact of the different
environmental parameters is explicitly brought out as the system starts out in
various initial states. The results are applicable to a variety of physical
systems now studied experimentally with QND measurements.Comment: 18 pages, REVTeX, 8 figure
Obesity and diabetes genetic variants associated with gestational weight gain
To determine whether genetic variants associated with diabetes and obesity predict gestational weight gain