Aspects of astrophysical mass loss

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Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n+1 Endogenous Variables

This paper analyzes the behavior of posterior distributions under the Jeffreys prior in a simultaneous equations model. The case under study is that of a general limited information setup with n + 1 endogenous variables. The Jeffreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact finite sample distribution of the corresponding LIML estimator. A stronger correspondence is established in the special case of a just-identified orthonormal canonical model, where the posterior density under the Jeffreys prior is shown to have the same functional form as the density of the finite sample distribution of the LIML estimator. The work here generalizes that of Chao and Phillips (1997), which gives analogous results for the special case of two endogenous variables.Cauchy tails, exact finite sample distributions, Jeffreys prior, just identification, limited information, posterior density, simultaneous equations model

Prognostic and surrogate markers for outcome in the treatment of pulmonary tuberculosis

Phase III trials for new tuberculosis treatment regimens require large numbers of participants and can take over five years to complete. A surrogate marker for poor outcome (failure at end of treatment or recurrence following successful treatment), the established endpoint in such trials, could shorten trial duration and reduce trial size. Culture results after two months of treatment have shown the most promise but, prior to this research, no formal evaluation had been performed. In this thesis, culture results during treatment are evaluated as prognostic and surrogate markers for poor outcome using data on 6974 patients from twelve tuberculosis treatment randomised controlled multi-arm trials conducted in East Africa and East Asia. A strong association was found between culture results during treatment and poor outcome. Nevertheless, culture results were not good patient-specific predictors of poor outcome with low sensitivities and specificities. Existing meta-analytic methods for evaluating surrogate markers are not wholly suited to this setting of multi-arm trials with binary true and surrogate endpoints. Extending these methods, the two month culture was found to be a good surrogate marker using data from Hong Kong trials and the three month culture was found to be a good surrogate marker using data from East African trials. These results are an indication that cultures during treatment do capture some of the treatment effect. Further work is needed in understanding the differences between the Hong Kong and East African trials. The meta-analytic methods for evaluating surrogate markers in this thesis included a graphical representation that permitted a clear visual evaluation of the surrogate. Methods developed in this thesis for modelling the relationship between the treatment effects on the true and surrogate endpoints were not satisfactory. The deficiencies were not overcome with the two extensions proposed. Further work is needed in developing a more appropriate model

Uniform Inference in Panel Autoregression

This paper considers estimation and inference concerning the autoregressive coefficient (ρ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. The main objective is to construct confidence intervals for ρ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. It is shown that a properly normalized statistic based on the Anderson-Hsiao IV procedure, which we call the M statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. In the unit root case confidence intervals based on this procedure are unsatisfactorily wide and uninformative. To sharpen the intervals a new procedure is developed using information from unit root pretests to select alternative confidence intervals. Two sequential tests are used to assess how close ρ is to unity and to correspondingly tailor intervals near the unit root region. When ρ is close to unity, the width of these intervals shrinks to zero at a faster rate than that of the confidence interval based on the M statistic. Only when both tests reject the unit root hypothesis does the construction revert to the M statistic intervals, whose width has the optimal N^{-1/2}T^{-1/2} rate of shrinkage when the underlying process is stable. The asymptotic properties of this pretest-based procedure show that it produces confidence intervals with at least the prescribed coverage probability in large samples. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings

Bayesian Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys’ Prior

This paper studies the use of the Jeffreys’ prior in Bayesian analysis of the simultaneous equations model (SEM). Exact representations are obtained for the posterior density of the structural coefficient beta in canonical SEM’s with two endogenous variables. For the general case with m endogenous variables and an unknown covariance matrix, the Laplace approximation is used to derive an analytic formula for the same posterior density. Both the exact and the approximate formulas we derive are found to exhibit Cauchy-like tails analogous to comparable results in the classical literature on LIML estimation. Moreover, in the special case of a two-equation, just-identified SEM in canonical form, the posterior density of beta is shown to have the same infinite series representation as the density of the finite sample distribution of the corresponding LIML estimator. This paper also examines the occurrence of a nonintegrable asymptotic cusp in the posterior distribution of the reduced form parameter Pi, first documented in Kleibergen and van Dijk (1994). This phenomenon is explained in terms of the jacobian of the mapping from the structural model to the reduced form. This interpretation assists in understanding the success of the Jeffreys’ prior in resolving this proble

Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure

The current practice for determining the number of cointegrating vectors, or the cointegrating rank, in a vector autoregression (VAR) requires the investigator to perform a sequence of cointegration tests. However, as was shown in Johansen (1992), this type of sequential procedure does not lead to consistent estimation of the cointegrating rank. Moreover, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rarely known, Simulation studies by Toda and Phillips (1994) and Chao (1993), on the other hand, have shown that test performance of these procedures can be adversely affected by lag misspecification. This paper addresses these issues by extending the analysis of Phillips and Ploberger (1996) on the Posterior Information Criterion (PIC) to a partially nonstationary vector autoregressive process with reduced rank structure. This extension allows lag length and cointegrating rank to be jointly selected by the criterion, and it leads to the consistent estimation of both. In addition, we also evaluate the finite sample performance of PIC relative to existing model selection procedures, BIC and AIC, through a Monte Carlo study. Results here show PIC to perform at least as well and sometimes better than the other two methods in all the cases examined

Cyclic pyrrole-imidazole polyamides targeted to the androgen response element

Hairpin pyrrole−imidazole (Py-Im) polyamides are a class of cell-permeable DNA-binding small molecules that can disrupt transcription factor−DNA binding and regulate endogenous gene expression. The covalent linkage of antiparallel Py-Im ring pairs with an γ-amino acid turn unit affords the classical hairpin Py-Im polyamide structure. Closing the hairpin with a second turn unit yields a cyclic polyamide, a lesser-studied architecture mainly attributable to synthetic inaccessibility. We have applied our methodology for solution-phase polyamide synthesis to cyclic polyamides with an improved high-yield cyclization step. Cyclic 8-ring Py-Im polyamides 1−3 target the DNA sequence 5′-WGWWCW-3′, which corresponds to the androgen response element (ARE) bound by the androgen receptor transcription factor to modulate gene expression. We find that cyclic Py-Im polyamides 1−3 bind DNA with exceptionally high affinities and regulate the expression of AR target genes in cell culture studies, from which we infer that the cycle is cell permeable

Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure

The current practice for determining the number of cointegrating vectors, or the cointegrating rank, in a vector autoregression (VAR) requires the investigator to perform a sequence of cointegration tests. However, as was shown in Johansen (1992), this type of sequential procedure does not lead to consistent estimation of the cointegrating rank. Moreover, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rarely known, Simulation studies by Toda and Phillips (1994) and Chao (1993), on the other hand, have shown that test performance of these procedures can be adversely affected by lag misspecification. This paper addresses these issues by extending the analysis of Phillips and Ploberger (1996) on the Posterior Information Criterion (PIC) to a partially nonstationary vector autoregressive process with reduced rank structure. This extension allows lag length and cointegrating rank to be jointly selected by the criterion, and it leads to the consistent estimation of both. In addition, we also evaluate the finite sample performance of PIC relative to existing model selection procedures, BIC and AIC, through a Monte Carlo study. Results here show PIC to perform at least as well and sometimes better than the other two methods in all the cases examined.Cointegrating rank, information criterion, order selection, PIC, reduced rank regression, vector autoregression

Atomic Carbon in M82

We report observations of C I(^3P_1 - ^3P_0) emission at 492 GHz toward the starburst galaxy M82. Both the C I/C II intensity ratio and the C/CO column density ratio are a factor of 2-5 higher than observed toward Galactic photodissociation regions (PDRs) or predicted by PDR models. We argue that current PDR models are insufficient to explain the observations, and propose that some of the emission is due to atomic carbon existing within molecular clouds. Employing new chemical models, which use a fast H_3^+ dissociative recombination rate, we find that enhanced cosmic-ray flux supplied by supernova remnants in the M82 starburst lead to an enhanced atomic carbon abundance and elevated temperatures deep within the molecular clouds, resulting in a higher C I emissivity than found in previous PDR models