Simple procedures for finding mean first passage times in Markov chains

The derivation of mean first passage times in Markov chains involves the solution of a family of linear equations. By exploring the solution of a related set of equations, using suitable generalized inverses of the Markovian kernel I – P, where P is the transition matrix of a finite irreducible Markov chain, we are able to derive elegant new results for finding the mean first passage times. As a by-product we derive the stationary distribution of the Markov chain without the necessity of any further computational procedures. Standard techniques in the literature, using for example Kemeny and Snell’s fundamental matrix Z, require the initial derivation of the stationary distribution followed by the computation of Z, the inverse I – P + eπT where eT = (1, 1, …,1) and πT is the stationary probability vector. The procedures of this paper involve only the derivation of the inverse of a matrix of simple structure, based upon known characteristics of the Markov chain together with simple elementary vectors. No prior computations are required. Various possible families of matrices are explored leading to different related procedures

Bounds on expected coupling times in Markov chains

In the author’s paper “Coupling and Mixing Times in Markov Chains” (RLIMS, 11, 1- 22, 2007) it was shown that it is very difficult to find explicit expressions for the expected time to coupling in a general Markov chain. In this paper simple upper and lower bounds are given for the expected time to coupling in a discrete time finite Markov chain. Extensions to the bounds under additional restrictive conditions are also given with detailed comparisons provided for two and three state chains

Stationary distributions and mean first passage times of perturbed Markov chains

Stationary distributions of perturbed finite irreducible discrete time Markov chains are intimately connected with the behaviour of associated mean first passage times. This interconnection is explored through the use of generalized matrix inverses. Some interesting qualitative results regarding the nature of the relative and absolute changes to the stationary probabilities are obtained together with some improved bounds

Detection of leukocytes stained with acridine orange using unique spectral features acquired from an image-based spectrometer

A leukocyte differential count can be used to diagnosis a myriad blood disorders, such as infections, allergies, and efficacy of disease treatments. In recent years, attention has been focused on developing point-of-care (POC) systems to provide this test in global health settings. Acridine orange (AO) is an amphipathic, vital dye that intercalates leukocyte nucleic acids and acidic vesicles. It has been utilized by POC systems to identify the three main leukocyte subtypes: granulocytes, monocytes, and lymphocytes. Subtypes of leukocytes can be characterized using a fluorescence microscope, where the AO has a 450 nm excitation wavelength and has two peak emission wavelengths between 525 nm (green) and 650 nm (red), depending on the cellular content and concentration of AO in the cells. The full spectra of AO stained leukocytes has not been fully explored for POC applications. Optical instruments, such as a spectrometer that utilizes a diffraction grating, can give specific spectral data by separating polychromatic light into distinct wavelengths. The spectral data from this setup can be used to create object-specific emission profiles. Yellow-green and crimson microspheres were used to model the emission peaks and profiles of AO stained leukocytes. Whole blood was collected via finger stick and stained with AO to gather preliminary leukocyte emission profiles. A MATLAB algorithm was designed to analyze the spectral data within the images acquired using the image-based spectrometer. The algorithm utilized watershed segmentation and centroid location functions to isolate independent spectra from an image. The output spectra represent the average line intensity profiles for each pixel across a slice of an object. First steps were also taken in processing video frames of manually translated microspheres. The high-speed frame rate allowed objects to appear in multiple consecutive images. A function was applied to each image cycle to identify repeating centroid locations. The yellow-green (515 nm) and crimson (645 nm) microspheres exhibited a distinct separation in colorimetric emission with a peak-to-peak difference of 36 pixels, which is related to the 130 nm peak emission difference. Two AO stained leukocytes exhibited distinct spectral profiles and peaks across different wavelengths. This could be due to variations in the staining method (incubation period and concentration) effecting the emissions or variations in cellular content indicating different leukocyte subtypes. The algorithm was also effective when isolating unique centroids between video frames. We have demonstrated the ability to extract spectral information from data acquired from the image-based spectrometer of microspheres, as a control, and AO stained leukocytes. We determined that the spectral information from yellow-green and crimson microspheres could be used to represent the wavelength range of AO stained leukocytes, thus providing a calibration tool. Also, preliminary spectral information was successfully extracted from yellow-green microspheres translated under the linear slit using stationary images and video frames, thus demonstrating the feasibility of collecting data from a large number of objects

Identifying asymmetric, multi-period Euler equations estimated by non-linear IV/GMM

In this article, the identification of instrumental variables and generalized method of moment (GMM) estimators with multi-period perceptions is discussed. The state space representation delivers a conventional first order condition that is solved for expectations when the Generalized Bézout Theorem holds. Here, it is shown that although weak instruments may be enough to identify the parameters of a linearized version of the Quasi-Reduced Form (Q-RF), their existence is not sufficient for the identification of the structural model. Necessary and sufficient conditions for local identification of the Quasi-Structural Form (Q-SF) derive from the product of the data moments and the Jacobian. Satisfaction of the moment condition alone is only necessary for local and global identification of the Q-SF parameters. While the conditions necessary and sufficient for local identification of the Q-SF parameters are only necessary to identify the expectational model that satisfies the regular solution. If the conditions required for the decomposition associated with the Generalized Bézout Theorem are not satisfied, then limited information estimates of the Q-SF are not consistent with the full solution. The Structural Form (SF) is not identified in the fundamental sense that the Q-SF parameters are not based on a forward looking expectational model. This suggests that expectations are derived from a forward looking model or survey data used to replace estimated expectations

Multifactor consumption based asset pricing model of the UK stock market: The US stock market as a wealth reference

Copyright @ 2011 University of BirminghamHere a multifactor model of UK stock returns is developed, replac- ingHere a multifactor model of UK stock returns is developed, replacing the conventional consumption habit reference by a relation that depends on US wealth. Two step Instrumental Variables and Generalized Method of Moments estimators are applied to reduce the impact of weak instruments. The standard errors are corrected for the generated regressor problem and the model is found to explain UK excess returns by UK consumption growth and expected US excess returns. Hence, controlling for nominal effects by subtracting a risk free rate and conditioning on real US excess returns provides an appealing explanation of the equity premium puzzle. US excess returns. Hence, controlling for nominal e¤ects by subtracting a risk free rate and conditioning on real US excess returns provides an appealing explanation of the equity premium puzzle

Identification and Identifiability of non-linear IV/GMM Estimators

In this article, the identi¯cation of instrumental variables and generalised method of moment (GMM) estimators is discussed. It is common that representations of such models are derived from the solution to linear quadratic optimisation problems. Here, it is shown that even though the rank condition on the Jacobian and the instrument set is valid, that the transversality condition may not be satis¯ed by the estimated model. Further, acceptance of the transversality condition does occur when identi ¯cation fails or the forward model vanishes. As a result the parameters of such models irrespective of any correction for serial correlation may not be identi¯ed in a fundamental sense. This suggests that either forward looking models should be estimated directly or more complex non-linear restrictions should be imposed

Mechanism of operation of the TFE-bonded gas-diffusion electrode

Mathematical analytical model predicts the performance of an electrode as a function of certain measurable physical characteristics. Concept assumes the catalyst particles form porous electrically conductive agglomerates which are completely flooded with electrolyte