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

Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions

We study the issue of the spin-chirality decoupling/coupling in the ordering of the Heisenberg spin glass by performing large-scale Monte Carlo simulations on a one-dimensional Heisenberg spin-glass model with a long-range power-law interaction up to large system sizes. We find that the spin-chirality decoupling occurs for an intermediate range of the power-law exponent. Implications to the corresponding $d$-dimensional short-range model is discussed.Comment: 5 pages, 4 figures, to appear in Physical Review Letter

Universal theory of nonlinear Luttinger liquids

One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a linear one, which leads to a linear hydrodynamic theory. We show that to describe the measurable dynamic response functions one needs to take into account the nonlinearity of the generic spectrum and thus of the resulting quantum hydrodynamic theory. This nonlinearity leads, for example, to a qualitative change in the behavior of the spectral function. The universal theory developed in this article is applicable to a wide class of one-dimensional fermionic, bosonic, and spin systems.Comment: final published version with supporting online materia

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper

Assessing banks’ resilience: A complementary approach to stress testing using fair values from banks’ financial statements

For more than a decade, supervisory banking authorities in Europe and the United States have sought to assess the resilience of banks to adverse economic episodes to safeguard the financial system's stability. They rely on regulatory capital measures like Common Equity Tier 1 (CET1) relative to risk-weighted assets in the aftermath of potential economic crises. We propose a new measure of banks' resilience based on financial statements. The fair value margin (FVM) is estimated as the difference between the fair value of assets and the book value of liabilities, scaled by the book value of equity. We find that FVM is positively associated with the surplus or shortfall of CET1 resulting from the stress testing results from 2014, 2016 and 2018. To corroborate the relevance of FVM for supervisory authorities, we compare the ability of the loan component of FVM to predict future credit losses with the capital surplus/shortfall metric derived from the stress test. The findings indicate that the fair value of loans predicts net charge-offs better than stress test outcomes. Therefore, we suggest that FVM could be used as a readily available and relatively low-cost tool to assess bank resilience, thus complementing the stress test exercises