Table 1.

A summary of the models and estimation methods described in the review.

Model	Estimator	Multiple filters	References
Linear-Gaussian	ML (Linear regression)	No	Theunissen et al., 2000
$\widehat{r}={\mathbf{\text{k}}}^{\mathsf{\text{T}}}\mathbf{\text{s}},r˜Normal$	Ridge regression	No	Machens et al., 2004
	ARD/ASD	No	Sahani and Linden, 2003a
	ALD	No	Park and Pillow, 2011b
Linear-Nonlinear Poisson	STA	No	Bussgang, 1952; Chichilnisky, 2001
r = f(kTs), r ~ Poisson
	MID	Yes	Sharpee et al., 2004
	STC	Yes	Brenner et al., 2000
r = $f$(kTs), r ~ Poisson	ML (Poisson GLM)	No	Truccolo et al., 2005
Linear-Nonlinear Bernoulli	ML (Bernoulli GLM)	No	–
r = $f$(kTs), r ~ Bernoulli
r = f(kTs), r ~ Bernoulli	CbRF	No	Meyer et al., 2014a
General count model	ML	Yes	Williamson et al., 2015
$\widehat{r}$ = ∑j fj(kTs),
r ∈ {0, 1, 2, …}
Gain control model $\widehat{r}=f\left(\frac{{\mathbf{\text{k}}}_0^{\mathsf{\text{T}}}\mathbf{\text{s}}-u\left(\mathbf{\text{s}}\right)}{v\left(\mathbf{\text{s}}\right)}\right)$	STC Logistic regression	No No	Schwartz et al., 2002; Rabinowitz et al., 2011
Input nonlinearity model $\widehat{r}=f\left({\mathbf{\text{k}}}^{\mathsf{\text{T}}}{\displaystyle {\sum }_{i=1}^B{b}_i{g}_i\left(s\right)}\right)$	ML	No	Ahrens et al., 2008b
Context model $\widehat{r}={\displaystyle {\sum }_i{k}_{i}g\left(s_i\right)}{\text{Context}}_i$	ML	Yes	Ahrens et al., 2008a; Williamson et al., 2016
LNLN cascade $\widehat{r}=f\left({\displaystyle {\sum }_{n=1}^N{W}_n{g}_n\left({\mathbf{\text{k}}}^{\mathsf{\text{T}}}\mathbf{\text{s}}\right)}\right)$	ML	Yes	Butts et al., 2007, 2011; Schinkel-Bielefeld et al., 2012; McFarland et al., 2013
$\widehat{r}=f\left({\displaystyle {\sum }_{c,n,i}{w}_{c,n}{b}_{c,i}{g}_i\left({\mathbf{\text{k}}}_{c,n}^{\mathsf{\text{T}}}\mathbf{\text{s}}\right)}\right)$	ML	Yes	Lehky et al., 1992; Vintch et al., 2015; Harper et al., 2016
Generalized quadratic model $\widehat{r}=f\left({\mathbf{\text{k}}}^{{\left(1\right)}^{\mathsf{\text{T}}}}\mathbf{\text{s}}+{\mathbf{\text{s}}}^{\mathsf{\text{T}}}{\mathbf{\text{K}}}^{\left(2\right)}\mathbf{\text{s}}\right)$	Orthogonalized Wiener kernels	Yes	Rieke et al., 1997; Pienkowski and Eggermont, 2010
	Information-theoretic	Yes	Fitzgerald et al., 2011a; Rajan et al., 2013
$\widehat{r}=f\left({\mathbf{\text{k}}}^{{\left(1\right)}^{\mathsf{\text{T}}}}\mathbf{\text{s}}+{\mathbf{\text{s}}}^{\mathsf{\text{T}}}{\mathbf{\text{K}}}^{\left(2\right)}\mathbf{\text{s}}\right)$	ML	Yes	Rajan et al., 2013
	Maximum expected likelihood	Yes	Park et al., 2013
Time-varying model	Recursive least-squares filtering	No	Stanley, 2002
$\widehat{r}=f\left({\mathbf{\text{k}}}_t^{\mathsf{\text{T}}}\mathbf{\text{s}}\right)$	ML	No	Brown et al., 2001; Eden et al., 2004
	Adaptive prior	No	Meyer et al., 2014b

Red colored quantities indicate model parameters that are fixed prior to parameter estimation.