Using Indirect Inference to Solve the Initial Conditions Problem

1997 ◽  
Author(s):  
Mark Yuying An ◽  
Ming NMI1 Liu
Keyword(s):  
Initial Conditions ◽  
Indirect Inference ◽  
Initial Conditions Problem

scholarly journals Axion hilltops, Kahler modulus quintessence and the swampland criteria

2019 ◽  
Vol 34 (28) ◽  
pp. 1950164 ◽  
Author(s):  
Maxim Emelin ◽  
Radu Tatar
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Effective Field ◽  
Fine Tuning ◽  
De Sitter ◽  
Moduli Stabilization ◽  
Nonperturbative Effect ◽  
Initial Conditions Problem ◽  
Field Excursion ◽  
Hubble Time

We study the interplay among extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of nonperturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessence that satisfies the swampland criteria. Using a single nonperturbative effect, the maximum along the axion direction provides such a runaway direction, which is unstable in the axion directions, sensitive to initial conditions and too steep to allow for a Hubble time of expansion without violating the field excursion criterion. Adding a second nonperturbative effect generates a saddle point in the potential satisfying the refined de Sitter criterion, which solves the steepness problem and improves the initial conditions problem although some fine-tuning remains required.

scholarly journals A plausible solution to the problem of initial conditions for inflation

2019 ◽  
Vol 28 (15) ◽  
pp. 1950165
Author(s):  
Suratna Das ◽  
Raghavan Rangarajan
Keyword(s):  
Correlation Length ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Initial Condition ◽  
Inflaton Field ◽  
Condition Problem ◽  
Initial Conditions Problem ◽  
Thermal Correlation

We propose yet another solution to the initial condition problem of inflation associated with homogeneity beyond the horizon at the onset of inflation, in cases where inflation is preceded by a radiation era. One may argue that causality will allow for smoothness over the causal horizon scale [Formula: see text], but for thermal inflationary scenarios, the background inflaton field will only be correlated over the thermal correlation length [Formula: see text] which is much smaller than [Formula: see text]. We argue, with examples, that if the number of relativistic degrees of freedom in the preinflationary era is very large [Formula: see text] then the thermal correlation length can be of the order of the causal horizon size alleviating the initial conditions problem of inflation.

Variational Solution for an Initial Conditions Problem

1997 ◽  
Vol 50 (11S) ◽  
pp. S50-S55 ◽  
Author(s):  
C. P. Filipich ◽  
M. B. Rosales
Keyword(s):  
Finite Number ◽  
Classical Solution ◽  
Time Domain ◽  
Initial Conditions ◽  
Boundary Value ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impulse Load ◽  
Initial Conditions Problem ◽  
The Time Domain

An initial conditions problem is addressed by first transforming it into a boundary value one. An appropriate functional and an extremizing sequence are proposed. The methodology has been previously named WEM (Whole Element Method) by the authors. In the present paper, this name is justified since division of the time domain is avoided even when loads with finite number of impulses of arbitrary duration are involved. The method is theoretically founded by theorems and corolaries. Their statements are included in the work. A numerical example of an undamped single degree of freedom (SDOF) system subjected to a rectangular impulse load is carried out. Comparison is made with the well-known classical solution.

State-Dependent Demand Estimation with Initial Conditions Correction

2020 ◽  
Vol 57 (5) ◽  
pp. 789-809
Author(s):  
Andrey Simonov ◽  
Jean-Pierre Dubé ◽  
Günter Hitsch ◽  
Peter Rossi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Initial Conditions ◽  
Brand Choice ◽  
State Dependence ◽  
The State ◽  
Data Sets ◽  
True Parameter ◽  
State Dependent ◽  
Initial Conditions Problem

The authors analyze the initial conditions bias in the estimation of brand choice models with structural state dependence. Using a combination of Monte Carlo simulations and empirical case studies of shopping panels, they show that popular, simple solutions that misspecify the initial conditions are likely to lead to bias even in relatively long panel data sets. The magnitude of the bias in the state dependence parameter can be as large as a factor of 2–2.5. The authors propose a solution to the initial conditions problem that samples the initial states as auxiliary variables in a Markov chain Monte Carlo procedure. The approach assumes that the joint distribution of prices and consumer choices is in equilibrium, which is plausible for the mature consumer packaged goods products commonly used in empirical applications. In Monte Carlo simulations, the approach recovers the true parameter values even in relatively short panels. Finally, the authors propose a diagnostic tool that uses common, biased approaches to bound the values of the state dependence and construct a computationally light test for state dependence.

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