scholarly journals Characterizing and Communicating the Balance of Risks of Macroeconomic Forecasts: A Predictive Density Approach for Colombia

2021 ◽  
Author(s):  
Juan C. Méndez-Vizcaíno ◽  
Alexander Guarín ◽  
César Anzola-Bravo ◽  
Anderson Grajales-Olarte
Keyword(s):  
Probability Distribution ◽  
General Equilibrium ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Dsge Models ◽  
Predictive Density ◽  
Macroeconomic Forecasting ◽  
Equilibrium Relationships ◽  
Predictive Densities

Since July 2021, Banco de la República strengthened its forecasting process and communication instruments, by involving predictive densities on the projections of its models, PATACON and 4GM. This paper presents the main theoretical and empirical elements of the predictive density approach for macroeconomic forecasting. This model-based methodology allows to characterize the balance of risks of the economy, and quantify their effects through a joint probability distribution of forecasts. We estimate this distribution based on the simulation of DSGE models, preserving the general equilibrium relationships and their macroeconomic consistency. We also illustrate the technical criteria used to represent the prospective factors of risk through the probability distributions of shocks.

scholarly journals Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging

2019 ◽  
Vol 23 ◽  
pp. 271-309
Author(s):  
Joseph Muré
Keyword(s):  
Probability Distribution ◽  
Gibbs Sampler ◽  
Prediction Interval ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Distributions ◽  
Stationary Probability Distribution ◽  
Gibbs Sampling Algorithm ◽  
Correlation Parameters

Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.

scholarly journals Tests for quantum contextuality in terms of Q-entropies

2014 ◽  
Vol 14 (11&12) ◽  
pp. 996-1013
Author(s):  
Alexey E. Rastegin
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Theoretic Approach ◽  
Entropic Inequalities ◽  
Information Theoretic ◽  
The Family ◽  
Information Theoretic Approach ◽  
New Inequalities

The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser--Horne--Shimony--Holt (CHSH) and Klyachko--Can--Binicio\v{g}lu--Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.

Joint probability of storm surge and wave along Hainan Island based on bi-variate copulas analysis

2020 ◽  
Author(s):  
Meng Cheng ◽  
Weihua Fang
Keyword(s):  
Probability Distribution ◽  
Storm Surge ◽  
Wave Height ◽  
Significant Wave Height ◽  
Probability Distributions ◽  
Joint Probability ◽  
Hainan Island ◽  
Joint Probability Distribution ◽  
Significant Wave ◽  
Surge Height

<p>Tropical cyclones (TCs) often bring multiple hazards to offshore and onshore areas, including wind, rainfall, riverine flood, wave and storm surge. These hazards usually interact with each other and cause greater amplified hazard intensity. In the coastal areas, wave may damage coastal defense system like sea walls and dykes, and overtopping storm surge could hence become severe flooding due to the breach of the dykes. The probability distributions of wave and surge, as univariate respectively, have been studies and used in the design in various research. However, far less investigations on their joint probability distribution have been carried out in the past.</p><p>In this study, the dataset of hourly surge height, and significant wave height of 89 TC events impacting along Hainan Island during 1949~2013 was obtained, which are simulated numerically with ADCIRC and SWAN respectively. Following that, 4 types of probability distributions for univariate were used to fit the marginal distribution of storm surge and wave. Secondly, Frank, Clayton and Gumbel Copula were tried to construct the joint probability distribution of wave and surge, and the optimal Copula was determined by K-S test and AIC, BIC criteria. Based on the optimal Copula selected for each area of interest, the joint return period of wave and surge was estimated.</p><p>The results show that, 1) the annual maximum value of the storm surge height and significant wave height of Hainan Island has a relatively obvious geographical distribution regularity. 2) GEV and Gumbel are the most optimal distribution for storm surge height and significant wave height respectively. 3) Clayton Copula is the best model for fitting joint probability of storm surge and wave. The estimated joining probability distribution can help the determination of design standard, and typical TC disaster scenario development.</p>

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

scholarly journals Analytical theory of turbulent diffusion

1961 ◽  
Vol 11 (2) ◽  
pp. 257-283 ◽  
Author(s):  
P. H. Roberts
Keyword(s):  
Probability Distribution ◽  
Turbulent Diffusion ◽  
Similarity Theory ◽  
Probability Distributions ◽  
Joint Probability ◽  
Relative Displacement ◽  
Initial Position ◽  
Joint Probability Distribution ◽  
Variable Diffusion ◽  
High Reynolds

Recently Kraichnan (1959) has propounded a theory of homogeneous turbulence, based on a novel perturbation method, that leads to closed equations for the velocity covariance. In the present paper, this method is applied to the theory of turbulent diffusion and closed equations are derived for the probability distributions of the positions of marked fluid elements released in a turbulent flow.Two topics are discussed in detail. The first is the probability distribution, at timet, of the displacement of an element from its initial position. In homogeneous flows, this distribution is found to resemble that for classical diffusion but with a variable coefficient of diffusion which is proportional to$v^2_0 t$for$t \ll l|v_0$and which approaches a constant value [eDot ]lv0fortt[Gt ]l/v0(l= macroscale,v0= r.m.s. turbulent velocity).The second topic treated is the joint probability distribution of the displacements of two fluid elements. Particular attention is focused upon the probability distribution of relative displacement, i.e. Richardson's distance-neighbour function. This is found to be Gaussian for separationsrwhich are large ([Gt ]l). For smaller separations (r[Lt ]l), its behaviour at high Reynolds numbers is found to be quite well expressed in terms of a variable diffusion coefficientK(r,t), as suggested by Richardson (1926). For all but extremely short times,K(r,t) is found to depend only onrand on the form of the inertial range spectrumE(k). On assuming$E(r) \propto v^2_0 l(kl)^{- \frac {3}{2}}$as results from Kraichnan's approximation (1959), one finds$E(r) \propto v_0 l(r|l)^{ \frac {3}{2}}$. On the basis of similarity arguments of the Kolmogorov type, which give$E(r) \propto v^2_0 l(kl)^{- \frac {5}{2}}$, one finds$E(r) \propto v_0 l(r|l)^{ \frac {4}{3}}$as, in fact, Richardson originally proposed. The dispersionr2is proportional to$l^2(v_0 t|l)^4$on Kraichnan's theory; while$\langle r^2 \rangle \propto l^2 (v_0 t|l)^3$on the similarity theory. This illustrates that the behaviour of$\langle r^2 \rangle$is very sensitive to the spectrum.

CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS

2018 ◽  
Vol 107 (3) ◽  
pp. 302-318
Author(s):  
JONATHAN BORWEIN ◽  
PHIL HOWLETT
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Marginal Distributions ◽  
Joint Probability Distributions

In modelling joint probability distributions it is often desirable to incorporate standard marginal distributions and match a set of key observed mixed moments. At the same time it may also be prudent to avoid additional unwarranted assumptions. The problem is to find the least ordered distribution that respects the prescribed constraints. In this paper we will construct a suitable joint probability distribution by finding the checkerboard copula of maximum entropy that allows us to incorporate the appropriate marginal distributions and match the nominated set of observed moments.

Statistical Analysis for the Duration and Time Intervals of Tropical Cyclones, Hong Kong

2019 ◽  
Author(s):  
Shanshan Tao ◽  
Jialing Song ◽  
Zhifeng Wang ◽  
Yong Liu ◽  
Sheng Dong
Keyword(s):  
Hong Kong ◽  
Tropical Cyclone ◽  
Probability Distribution ◽  
Tropical Cyclones ◽  
Conditional Probability ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Time Intervals

Abstract Hong Kong is impacted by tropical cyclones from April to December each year. The duration of tropical cyclones is one key factor to impact the normal operation of port or coastal engineering, and longer time interval between two tropical cyclones can provide longer operation or construction time. Therefore, it is quite important to study on the long-term laws of the duration and time intervals of tropical cyclones which attacked Hong Kong. The Hong Kong Observatory issues the warning signals to warn the public of the threat of winds associated with a tropical cyclone. Choose the tropical cyclones with warning signal No. 3 or above as the research object. A statistical study was conducted on the duration of each tropical cyclone, the time interval between every two continuous tropical cyclones during the year, and the time interval between the last cyclone of each year and the first cyclone of the following year. Poisson compound extreme value distributions are constructed to calculate the return values, which can make people know how long a tropical cyclone with a fixed duration or time interval occurs once in statistical average sense. Based on bivariate copulas, the joint probability distribution of duration and time intervals of tropical cyclones are presented. Then when the duration of a tropical cyclone is known, the conditional probability that the time interval before the next tropical cyclone occurs is greater than a certain value can be calculated. The results provide corresponding conditional probability distributions. Similarly, for the sum of the duration of tropical cyclones each year, and the time interval between the last cyclone of each year and the first cyclone of the following year, their joint probability distribution and conditional probability distributions are also presented. The conditional probability can provide the probabilistic prediction of the length of the stationary period (with no impact of tropical cyclones).

scholarly journals STATISTICAL PROPERTIES OF THE INTERBEAT INTERVAL CASCADE IN HUMAN HEARTS

2006 ◽  
Vol 17 (04) ◽  
pp. 571-580 ◽  
Author(s):  
FATEMEH GHASEMI ◽  
J. PEINKE ◽  
M. REZA RAHIMI TABAR ◽  
MUHAMMAD SAHIMI
Keyword(s):  
Probability Distribution ◽  
Diffusion Coefficients ◽  
Probability Distributions ◽  
Joint Probability ◽  
Planck Equation ◽  
Statistical Properties ◽  
Kolmogorov Equation ◽  
Joint Probability Distribution ◽  
Conditional Probability Distribution ◽  
And Diffusion

Statistical properties of interbeat intervals cascade in human hearts are evaluated by considering the joint probability distribution P (Δx2, τ2; Δx1, τ1) for two interbeat increments Δx1and Δx2of different time scales τ1and τ2. We present evidence that the conditional probability distribution P (Δx2, τ2| Δx1, τ1) may be described by a Chapman–Kolmogorov equation. The corresponding Kramers–Moyal (KM) coefficients are evaluated. The analysis indicates that while the first and second KM coefficients take on well-defined and significant values, the higher-order coefficients in the KM expansion are small. As a result, the joint probability distributions of the increments in the interbeat intervals are described by a Fokker–Planck equation, with the first two KM coefficients acting as the drift and diffusion coefficients. The method provides a novel technique for distinguishing two classes of subjects, namely, healthy ones and those with congestive heart failure, in terms of the drift and diffusion coefficients which behave differently for two classes of the subjects.

Sign in / Sign up

Export Citation Format

Share Document