The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

/pdf/riemann-manifold-langevin-and-hamiltonian-monte-carlo-254effw0xm.pdf

Riemann manifold Langevin and Hamiltonian Monte Carlo methods

The International Reference Ionosphere (IRI) is the international standard for the specification of ionospheric densities and temperatures. It was developed and is being improved-updated by a joint working group of the International Union of Radio Science (URSI) and the Committee on Space Research (COSPAR). A new version of IRI is scheduled for release in the year 2000. This paper describes the most important changes compared to the current version of IRI: (1) an improved representation of the electron density in the region from the F peak down to the E peak including a better description of the F1 layer occurrence statistics and a more realistic description of the low-latitude bottomside thickness, (2) inclusion of a model for storm-time conditions, (3) inclusion of an ion drift model, (4) two new options for the electron density in the D region, and (5) an improved model for the topside electron temperatures. The outcome of the most recent IRI Workshops (Kuhlungsborn, 1997, and Nagoya, 1998) will be reviewed, and the status of several ongoing task force activities (e.g., efforts to improve the representation of electron and ion densities in the topside ionosphere and the inclusion of a plasmaspheric extension) will be discussed. A few typical IRI applications will be highlighted in section 6.

/pdf/international-reference-ionosphere-2000-zhazhxmwus.pdf

International Reference Ionosphere 2000

The Dual Auroral Radar Network (DARN) is a global-scale network of HF and VHF radars capable of sensing backscatter from ionospheric irregularities in the E and F-regions of the high-latitude ionosphere. Currently, the network consists of the STARE VHF radar system in northern Scandinavia, a northern-hemisphere, longitudinal chain of HF radars that is funded to extend from Saskatoon, Canada to central Finland, and a southern-hemisphere chain that is funded to include Halley Station, SANAE and Syowa Station in Antarctica. When all of the HF radars have been completed they will operate in pairs with common viewing areas so that the Doppler information contained in the backscattered signals may be combined to yield maps of high-latitude plasma convection and the convection electric field. In this paper, the evolution of DARN and particularly the development of its SuperDARN HF radar element is discussed. The DARN/SupperDARN network is particularly suited to studies of large-scale dynamical processes in the magnetosphere-ionosphere system, such as the evolution of the global configuration of the convection electric field under changing IMF conditions and the development and global extent of large-scale MHD waves in the magnetosphere-ionosphere cavity. A description of the HF radars within SuperDARN is given along with an overview of their existing and intended locations, intended start of operations, Principal Investigators, and sponsoring agencies. Finally, the operation of the DARN experiment within ISTP/GGS, the availability of data, and the form and availability of the Key Parameter files is discussed.

DARN/SUPERDARN : A global view of the dynamics of high-latitude convection

A numerical simulation study of the thermospheric winds produced by auroral heating during magnetic storms, and of their global dynamo effects, establishes the main features of the ionospheric disturbance dynamo. Driven by auroral heating, a Hadley cell is created with equatorward winds blowing above about 120 km at mid-latitudes. The transport of angular momentum by these winds produces a subrotation of the mid-latitude thermosphere or westward motion with respect to the earth. The westward winds in turn drive equatorward Pedersen currents which accumulate charge toward the equator, resulting in the generation of a poleward electric field, a westward E × B drift, and an eastward current. When realistic local time conductivity variations are simulated, the eastward mid-latitude current is found to close partly via lower latitudes, resulting in an ‘anti-Sq’ type of current vortex. Both electric field and current at low latitudes thus vary in opposition to their normal quiet-day behavior. This total pattern of disturbance winds, electric fields, and currents is superimposed upon the background quiet-day pattern. When the neutral winds are artificially confined on the nightside, the basic pattern of predominantly westward E × B plasma drifts still prevails on the nightside but no longer extends into the dayside. Considerable observational evidence exists, suggesting that the ionospheric disturbance dynamo has an appreciable influence on storm-time ionospheric electric fields at middle and low latitudes.

The ionospheric disturbance dynamo

The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

Ground-based studies of sensing magnetosphere/ionosphere interactions: convection and substorms.

Reply to the Comment by Lockwood and Cowley on “Ionospheric convection response to changing IMF direction”

Magnetic potential plots over the northern hemisphere for 26-28 March 1976

Global-scale Observations of the Limb and Disk (GOLD): Science Implementation

Erratum: ``Ionospheric convection response to slow, strong variations in a northward interplanetary magnetic field: A case study for January 14, 1988'' [J. Geophys. Res., 98, 19,273-19,292 (1993)

Arthur D. Richmond

Papers

Ground-based studies of sensing magnetosphere/ionosphere interactions: convection and substorms.

Reply to the Comment by Lockwood and Cowley on “Ionospheric convection response to changing IMF direction”

Magnetic potential plots over the northern hemisphere for 26-28 March 1976

Global-scale Observations of the Limb and Disk (GOLD): Science Implementation

Erratum: ``Ionospheric convection response to slow, strong variations in a northward interplanetary magnetic field: A case study for January 14, 1988'' [J. Geophys. Res., 98, 19,273-19,292 (1993)