The Living Thing / Notebooks :

Indirect inference

A.k.a the “auxiliary method”. Also possibly a.k.a Approximate Bayesian Computation? (Should work out if that is so.)

Here be economists and ecologists.

Maybe this will solve my current weird intractable model issues?

There is an R package for at least some versions of it: pomp

Quoting Cosma:

[…] your model is too complicated for you to appeal to any of the usual estimation methods of statistics. […] there is no way to even calculate the likelihood of a given data set \(x_1,x_2,...x_t\equiv x_t\) under parameters \(\theta\) in closed form, which would rule out even numerical likelihood maximization, to say nothing of Bayesian methods […] Yet you can simulate; it seems like there should be some way of saying whether the simulations look like the data.

This is where indirect inference comes in […] Introduce a new model, called the “auxiliary model”, which is mis-specified and typically not even generative, but is easily fit to the data, and to the data alone. (By that last I mean that you don’t have to impute values for latent variables, etc., etc., even though you might know those variables exist and are causally important.) The auxiliary model has its own parameter vector \(\beta\), with an estimator \(\hat{\beta}\). These parameters describe aspects of the distribution of observables, and the idea of indirect inference is that we can estimate the generative parameters \(\theta\) by trying to match those aspects of observations, by trying to match the auxiliary parameters.

Surely those conditions in themselves don’t necessarily rule out Bayesian methods? But anyway that’s the drift. I clearly have more to learn here.

Aaaron King’s lab at UMichigan does a lot of this. . Read this stuff: =================

Arva14
Arvanitis, S. (2014) A simple example of an indirect estimator with discontinuous limit theory in the MA(1) model. Journal of Time Series Analysis, 35(6), 536–557. DOI.
BHIK09
Bretó, C., He, D., Ionides, E. L., & King, A. A.(2009) Time series analysis via mechanistic models. The Annals of Applied Statistics, 3(1), 319–348. DOI.
CaFe08
Cauchemez, S., & Ferguson, N. M.(2008) Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London. Journal of The Royal Society Interface, 5(25), 885–897. DOI.
CRGT03
Chernov, M., Ronald Gallant, A., Ghysels, E., & Tauchen, G. (2003) Alternative models for stock price dynamics. Journal of Econometrics, 116(1–2), 225–257. DOI.
ClBj04
Clark, J. S., & Bjørnstad, O. N.(2004) Population time series: process variability, observation errors, missing values, lags, and hidden states. Ecology, 85(11), 3140–3150. DOI.
COMG07
Cook, A. R., Otten, W., Marion, G., Gibson, G. J., & Gilligan, C. A.(2007) Estimation of multiple transmission rates for epidemics in heterogeneous populations. Proceedings of the National Academy of Sciences, 104(51), 20392–20397. DOI.
CoKa12
Cox, D. R., & Kartsonaki, C. (2012) The fitting of complex parametric models. Biometrika, 99(3), 741–747. DOI.
CrKr12
Creel, M., & Kristensen, D. (2012) Estimation of dynamic latent variable models using simulated non-parametric moments. The Econometrics Journal, 15(3), 490–515. DOI.
CrKr13
Creel, M., & Kristensen, D. (2013) Indirect Likelihood Inference (revised) (UFAE and IAE Working Paper No. 93113). . Unitat de Fonaments de l’Anàlisi Econòmica (UAB) and Institut d’Anàlisi Econòmica (CSIC)
CzRo10
Czellar, V., & Ronchetti, E. (2010) Accurate and robust tests for indirect inference. Biometrika, 97(3), 621–630. DOI.
DrGR07
Dridi, R., Guay, A., & Renault, E. (2007) Indirect inference and calibration of dynamic stochastic general equilibrium models. Journal of Econometrics, 136(2), 397–430. DOI.
Efro10
Efron, B. (2010) The Future of Indirect Evidence. Statistical Science, 25(2), 145–157. DOI.
FaTa08
Fackler, P., & Tastan, H. (2008) A framework for indirect inference. . Working paper
FoNg15
Forneron, J.-J., & Ng, S. (2015) The ABC of Simulation Estimation with Auxiliary Statistics. arXiv:1501.01265 [stat].
GaHT97
Gallant, A. R., Hsieh, D., & Tauchen, G. (1997) Estimation of stochastic volatility models with diagnostics. Journal of Econometrics, 81(1), 159–192. DOI.
GaHT99
Gallant, A. R., Hsu, C.-T., & Tauchen, G. (1999) Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance. The Review of Economics and Statistics, 81(4), 617–631. DOI.
GaTa96
Gallant, A. R., & Tauchen, G. (1996) Which Moments to Match?. Econometric Theory, 12(04), 657–681. DOI.
GaTa97
Gallant, A. R., & Tauchen, G. (1997) Estimation of continuous-time models for stock returns and interest rates. Macroeconomic Dynamics, 1(01), 135–168. DOI.
GeRo03
Genton, M. G., & Ronchetti, E. (2003) Robust Indirect Inference. Journal of the American Statistical Association, 98(461), 67–76. DOI.
GiRe01
Gibson, G. J., & Renshaw, E. (2001) Likelihood estimation for stochastic compartmental models using Markov chain methods. Statistics and Computing, 11(4), 347–358. DOI.
GoMo93
Gourieroux, C., & Monfort, A. (1993) Simulation-based inference: A survey with special reference to panel data models. Journal of Econometrics, 59(1–2), 5–33. DOI.
GoMR93
Gourieroux, C., Monfort, A., & Renault, E. (1993) Indirect Inference. Journal of Applied Econometrics, 8, S85–S118.
HeIK10
He, D., Ionides, E. L., & King, A. A.(2010) Plug-and-play inference for disease dynamics: measles in large and small populations as a case study. Journal of The Royal Society Interface, 7(43), 271–283. DOI.
IBAK11
Ionides, E. L., Bhadra, A., Atchadé, Y., & King, A. (2011) Iterated filtering. The Annals of Statistics, 39(3), 1776–1802. DOI.
IoBK06
Ionides, E. L., Bretó, C., & King, A. A.(2006) Inference for nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 103(49), 18438–18443. DOI.
JiTu04
Jiang, W., & Turnbull, B. (2004) The Indirect Method: Inference Based on Intermediate Statistics—A Synthesis and Examples. Statistical Science, 19(2), 239–263. DOI.
KEMW05
Kendall, B. E., Ellner, S. P., McCauley, E., Wood, S. N., Briggs, C. J., Murdoch, W. W., & Turchin, P. (2005) Population cycles in the pine looper moth: Dynamical tests of mechanistic hypotheses. Ecological Monographs, 75(2), 259–276.
NiPö09:
Nickl, R., & Pötscher, B. M.(2009) Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference. Mathematical Methods of Statistics 19, 327–364.
RoSt01
Roberts, G. O., & Stramer, O. (2001) On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm. Biometrika, 88(3), 603–621. DOI.
ShKR11
Shrestha, S., King, A. A., & Rohani, P. (2011) Statistical Inference for Multi-Pathogen Systems. PLoS Comput Biol, 7(8), e1002135. DOI.
Smit93
Smith, A. A.(1993) Estimating nonlinear time-series models using simulated vector autoregressions. Journal of Applied Econometrics, 8(S1), S63–S84. DOI.
Smit08
Smith, A. A.(2008) Indirect Inference. In The New Palgrave Dictionary of Economics. Palgrave Macmillan
WoSL14
Wong, R. K. W., Storlie, C. B., & Lee, T. C. M.(2014) A Frequentist Approach to Computer Model Calibration. arXiv:1411.4723 [stat].
Wood10
Wood, S. N.(2010) Statistical inference for noisy nonlinear ecological dynamic systems. Nature, 466(7310), 1102–1104. DOI.
Zhao10
Zhao, L. (2010) A model of limit-order book dynamics and a consistent estimation procedure. . Citeseer