@article {Paninski2010,
	title = {A new look at state-space models for neural data.},
	journal = {Journal of computational neuroscience},
	volume = {29},
	number = {1-2},
	year = {2010},
	pages = {107{\textendash}26},
	abstract = {<p>State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in state-space models with non-Gaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way, we point out connections to some related standard statistical methods, including spline smoothing and isotonic regression. Finally, we note that the computational methods reviewed here do not in fact depend on the state-space setting at all; instead, the key property we are exploiting involves the bandedness of certain matrices. We close by discussing some applications of this more general point of view, including Markov chain Monte Carlo methods for neural decoding and efficient estimation of spatially-varying firing rates.</p>},
	keywords = {1 introduction, Action Potentials, Action Potentials: physiology, Animals, Computer Simulation, for inference in state-space, forward-backward methods, hidden markov model, models, neural coding, Neurological, Neurons, Neurons: physiology, Retinal Ganglion Cells, Retinal Ganglion Cells: physiology, state-space models, Statistical, Synapses, Synapses: physiology, tridiagonal matrix},
	issn = {1573-6873},
	doi = {10.1007/s10827-009-0179-x},
	url = {http://www.ncbi.nlm.nih.gov/pubmed/19649698},
	author = {Paninski, Liam and Ahmadian, Yashar and Gil, Daniel and Shinsuke, Ferreira and Rahnama, Kamiar and Michael, Rad and Vogelstein, Joshua T and Wu, Wei and Ferreira, Daniel Gil and Koyama, Shinsuke and {Rahnama Rad}, Kamiar and Vidne, Michael}
}
@article {VogelsteinPaninski09,
	title = {Spike inference from calcium imaging using sequential Monte Carlo methods.},
	journal = {Biophys J},
	volume = {97},
	number = {2},
	year = {2009},
	pages = {636{\textendash}655},
	publisher = {Department of Neuroscience, The Johns Hopkins School of Medicine, Baltimore, Maryland, USA. joshuav@jhu.edu},
	abstract = {<p>As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies, the signals of interest{\textendash}spike trains and/or time varying intracellular calcium concentrations{\textendash}are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing sequential Monte Carlo methods (particle filters) based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing error bars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence (e.g., refractoriness) of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate temporal superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation maximization with only a very limited amount of data (e.g., approximately 5-10 s or 5-40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.</p>},
	keywords = {Animals, Biological, Calcium, cytology/metabolism, Fluorescence, Inbred C57BL, Intracellular Space, metabolism, Mice, models, Monte Carlo Method, Neurons, Probability, Time Factors},
	doi = {10.1016/j.bpj.2008.08.005},
	url = {http://dx.doi.org/10.1016/j.bpj.2008.08.005},
	author = {Vogelstein, Joshua T and Watson, Brendon O and Packer, Adam M and Yuste, Rafael and Jedynak, Bruno and Paninski, Liam}
}
