FastLZeroSpikeInference (version 2018.12.10)

estimate_spikes: Estimate spike train, underlying calcium concentration, and changepoints based on a fluorescence trace.

Description

Estimate spike train, underlying calcium concentration, and changepoints based on a fluorescence trace.

Usage

estimate_spikes(dat, gam, lambda, constraint = FALSE,
  estimate_calcium = FALSE, EPS = 1e-04)

Arguments

dat

fluorescence data

gam

a scalar value for the AR(1) decay parameter

lambda

tuning parameter lambda

constraint

boolean specifying constrained or unconstrained optimization problem (see below)

estimate_calcium

boolean specifying whether to estimate the calcium

EPS

double specifying the minimum calcium value

Value

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

Details

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

See Also

Estimate spikes: estimate_spikes estimate_calcium

Simulate: simulate_ar1

Examples

# NOT RUN {
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)

# }