Statistical Inference for Partially Observed Markov Processes via the R Package pomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this paper is provided at the pomp package website: http://kingaa.github.io/pom

Interview with Ed King by Brien Williams

Biographical NoteEdward L. “Ed” King was born November 7, 1928, in Fort Worth, Texas, to Edgar L. and Zula Mae (Birch) King. He served in the Army during World War II and the Korean War and was a career officer from 1945 to 1969. He became executive director of the Coalition for National Defense and Military Policy and testified often before the U.S. House and Senate. He was hired by Senator Mike Mansfield, and in 1975 he became Maine Senator Bill Hathaway’s administrative assistant. He also worked for Senators Tsongas, Byrd, and Mitchell, focusing most specifically on Central America issues. He also worked for Mitchell on the Democratic Policy Committee and on foreign policy issues, staying on with Senator Majority Leader Tom Daschle after Mitchell’s retirement and himself retiring in early 1997. King is the author of The Death of the Army: A Pre-Mortem (1972). SummaryInterview includes discussion of: family and educational background; military career; knowledge of foreign policy issues, especially in Central America; working with several senators: Mansfield, Byrd, Tsongas, Mitchell, Hathaway; Iran-Contra and Oliver North; Democratic Policy Committee; traveling with Senator Mitchell: Mexico; issues in Haiti, Spain, Russia, China and MFN (Most Favored Nation); description of staff working relationships with Senator Mitchell and how the offices functioned; Mitchell’s memory and ability at extemporaneous speech; trademark issue; White House visits with Mitchell during Bush I and Clinton presidencies; Mitchell’s personal attributes and effective negotiating; and the relationship between Senators Dole and Mitchell

The Fundamental Plane of Black Hole Accretion and its Use as a Black Hole-Mass Estimator

We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole ($M$), its 5 GHz radio continuum luminosity ($\nu L_{\nu}$), and its 2-10 keV X-ray power-law continuum luminosity ($L_X$). We compile a sample of black holes with primary, direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a mass-predictor function of the form $\log(M/10^{8}\,M_{\scriptscriptstyle \odot}) = \mu_0 + \xi_{\mu R} \log(L_R / 10^{38}\,\mathrm{erg\,s^{-1}}) + \xi_{\mu X} \log(L_X / 10^{40}\,\mathrm{erg\,s^{-1}})$. Our best-fit results are $\mu_0 = 0.55 \pm 0.22$, $\xi_{\mu R} = 1.09 \pm 0.10$, and $\xi_{\mu X} = -0.59^{+0.16}_{-0.15}$ with the natural logarithm of the Gaussian intrinsic scatter in the log-mass direction $\ln\epsilon_\mu = -0.04^{+0.14}_{-0.13}$. This result is a significant improvement over our earlier mass scaling result because of the increase in active galactic nuclei sample size (from 18 to 30), improvement in our X-ray binary sample selection, better identification of Seyferts, and improvements in our analysis that takes into account systematic uncertainties and correlated uncertainties. Because of these significant improvements, we are able to consider potential influences on our sample by including all sources with compact radio and X-ray emission but ultimately conclude that the fundamental plane can empirically describe all such sources. We end with advice for how to use this as a tool for estimating black hole masses.Comment: ApJ Accepted. Online interactive version of Figure 7 available at http://kayhan.astro.lsa.umich.edu/supplementary_material/fp