estimate_calcium: Estimate underlying calcium concentration based on estimated...
In FastLZeroSpikeInference: Fast Nonconvex Deconvolution of Calcium Imaging Data

Description Usage Arguments Details Value See Also Examples

Estimate underlying calcium concentration based on estimated spikes

1	estimate_calcium(fit)

fit

object created by running estimate_spikes

This algorithm solves the optimization problems

AR(1) model:

minimize_c1,...,cT 0.5 sum_t=1^T ( y_t - c_t )^2 + lambda sum_t=2^T 1_[c_t != max(gam c_t-1, EPS)]

for the global optimum, where y_t is the observed fluorescence at the tth timestep.

Constrained AR(1) model:

minimize_c1,...,cT 0.5 sum_t=1^T ( y_t - c_t )^2 + lambda sum_t=2^T 1_[c_t != max(gam c_t-1, EPS)]

subject to c_t >= max(gam c_t-1, EPS), t = 2, ..., T

We introduce the constant EPS > 0, to avoid arbitrarily small calcium concentrations that would result in numerical instabilities. In practice, this means that the estimated calcium concentration decays according to the AR(1) model for values greater than EPS and is equal to EPS thereafter.

When estimating the spikes, it is not necessary to explicitly compute the calcium concentration. Therefore, if only the spike times are required, the user can avoid this computation cost by setting the estimate_calcium boolean to false. Because estimating the calcium requires additional computation time, we suggest estimating the calcium only if it is needed.

Given the set of estimated spikes produced from the estimate_spike, the calcium concentration can be estimated with the estimate_calcium function (see examples below).

For additional information see:

1. Jewell, Hocking, Fearnhead, and Witten (2018) <arXiv:1802.07380> and

2. Jewell, Sean; Witten, Daniela. Exact spike train inference via l0 optimization. Ann. Appl. Stat. 12 (2018), no. 4, 2457–2482. doi:10.1214/18-AOAS1162. https://projecteuclid.org/euclid.aoas/1542078052

Returns a list with elements:

spikes the set of estimated spikes

estimated_calcium estimated calcium concentration

change_pts the set of changepoints

cost the cost at each time point

n_intervals the number of intervals at each point

Estimate spikes: estimate_spikes estimate_calcium

Simulate: simulate_ar1

sim <- simulate_ar1(n = 500, gam = 0.95, poisMean = 0.009, sd = 0.05, seed = 1)
plot(sim)

## Fits for a single tuning parameter

# AR(1) model
fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1)
print(fit)

# compute fitted values from prev. fit
fit <- estimate_calcium(fit)
plot(fit)

# or
fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1, estimate_calcium = TRUE)
plot(fit)

# Constrained AR(1) model
fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1, constraint = TRUE,
                                                    estimate_calcium = TRUE)
print(fit)
plot(fit)