27,960 research outputs found
Splitting of liftings in products of probability spaces
We prove that if (X,\mathfrakA,P) is an arbitrary probability space with
countably generated \sigma-algebra \mathfrakA, (Y,\mathfrakB,Q) is an arbitrary
complete probability space with a lifting \rho and \hat R is a complete
probability measure on \mathfrakA \hat \otimes_R \mathfrakB determined by a
regular conditional probability {S_y:y\in Y} on \mathfrakA with respect to
\mathfrakB, then there exist a lifting \pi on (X\times Y,\mathfrakA \hat
\otimes_R \mathfrakB,\hat R) and liftings \sigma_y on (X,\hat \mathfrakA_y,\hat
S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and
every y\in Y, [\pi(E)]^y=\sigma_y\bigl([\pi(E)]^y\bigr). Assuming the absolute
continuity of R with respect to P\otimes Q, we prove the existence of a regular
conditional probability {T_y:y\in Y} and liftings \varpi on (X\times
Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R), \rho' on (Y,\mathfrakB,\hat Q)
and \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every
E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y,
[\varpi(E)]^y=\sigma_y\bigl([\varpi(E)]^y\bigr) and \varpi(A\times
B)=\bigcup_{y\in\rho'(B)}\sigma_y(A)\times{y}\qquadif A\times
B\in\mathfrakA\times\mathfrakB. Both results are generalizations of Musia\l,
Strauss and Macheras [Fund. Math. 166 (2000) 281-303] to the case of measures
which are not necessarily products of marginal measures. We prove also that
liftings obtained in this paper always convert \hat R-measurable stochastic
processes into their \hat R-measurable modifications.Comment: Published at http://dx.doi.org/10.1214/009117904000000018 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Forecasting real housing price growth in the Eighth District states
The authors consider forecasting real housing price growth for the individual states of the Federal Reserve's Eighth District. They first analyze the forecasting ability of a large number of potential predictors of state real housing price growth using an autoregressive distributed lag (ARDL) model framework. A number of variables, including the state housing price-to-income ratio, state unemployment rate, and national inflation rate, appear to provide information that is useful for forecasting real housing price growth in many Eighth District states. Given that it is typically difficult to determine a priori the particular variable or small set of variables that are the most relevant for forecasting real housing price growth for a given state and time period, the authors also consider various methods for combining the individual ARDL model forecasts. They find that combination forecasts are quite helpful in generating accurate forecasts of real housing price growth in the individual Eighth District states.Housing - Prices ; Federal Reserve District, 8th
The long-run relationship between consumption and housing wealth in the Eighth District states
Federal Reserve District, 8th ; Consumption (Economics) ; Housing
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity
This paper develops necessary and sufficient conditions for the preservation
of asymptotic convergence rates of deterministically and stochastically
perturbed ordinary differential equations with regularly varying nonlinearity
close to their equilibrium. Sharp conditions are also established which
preserve the asymptotic behaviour of the derivative of the underlying
unperturbed equation. Finally, necessary and sufficient conditions are
established which enable finite difference approximations to the derivative in
the stochastic equation to preserve the asymptotic behaviour of the derivative
of the unperturbed equation, even though the solution of the stochastic
equation is nowhere differentiable, almost surely
Patient adherence to cognitive behavioural therapy for obsessive-compulsive disorder: a systematic review and meta-analysis
Whilst cognitive behavioural therapy (CBT) is the treatment of choice for obsessive-compulsive disorder (OCD), around half of the participants do not experience remission following treatment. As yet, there is no comprehensive systematic review of the extent to which patient non-adherence presents a challenge to the overall benefit of CBT for OCD. The aim of this systematic review and meta-analysis was to identify the magnitude, moderators and reasons for poor patient adherence to CBT for OCD in terms of: (1) treatment refusal, (2) treatment dropout, (3) session at- tendance/module completion, and (4) between-session CBT task adherence. Sociodemographic and clinical variables, treatment and study design characteristics were examined as moderators of adherence. The systematic search identified 123 studies including 5627 participants taking part in CBT or control conditions. A pooled rate of 15.6% of eligible patients refused CBT and a further 15.9% of treatment starters dropped out from treatment. Group CBT had significantly lower dropout rates than individually-delivered CBT. No other significant moderators were found. Most studies reported moderate to good adherence to between-session CBT tasks, which had a significant medium to large association with post-treatment OCD symptom reduction. Recommendations for enhanced measurement and re- porting of patient adherence to CBT for OCD are made along with clinical implications of findings
The Geoff Egan Memorial Lecture 2011. Artefacts, art and artifice: reconsidering iconographic sources for archaeological objects in early modern Europe
A first systematic analysis of historic domestic material culture depicted in contemporaneous Western painting and prints, c.1400-1800. Drawing on an extensive data set, the paper proposes to methodologies and hermeneutics for historical analysis and archaeological correspondence
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