Package 'flipped'

Compute probability of observations given an exponential decay model

Description

Compute probability of observations given an exponential decay model

Usage

d_coin_multiplicative(
  nheads,
  nflips,
  multiplier,
  log = FALSE,
  possibilities = get_possibilities(nheads, nflips),
  outside_bounds_is_NA = FALSE
)

Arguments

nheads	Number of heads
nflips	Total number of flips (heads and tails)
multiplier	How much to multiply by each flip
log	If TRUE return log transformed probabilities.
possibilities	All possible sequences of flips that lead to the observed number of heads
outside_bounds_is_NA	If TRUE, if any probability of heads is outside the bounds of probability, the function returns NA. Otherwise, it sets the value to the nearer bound.

Value

The likelihood of the data (or log likelihood if log=TRUE)

---

Compute probability of observations given an exponential decay model The idea is that the coin before handling has 100% chance of heads, but each time it is picked up that probability will decrease (maybe it is bent by the statistician's mighty thumb). After halflife times handling it, the probability of heads is 50%, and it keeps dropping from there.

Description

Compute probability of observations given an exponential decay model The idea is that the coin before handling has 100% chance of heads, but each time it is picked up that probability will decrease (maybe it is bent by the statistician's mighty thumb). After halflife times handling it, the probability of heads is 50%, and it keeps dropping from there.

Usage

dcoin_exponential_decay(
  nheads,
  nflips,
  halflife,
  log = FALSE,
  possibilities = get_possibilities(nheads, nflips)
)

Arguments

nheads	Number of heads
nflips	Total number of flips (heads and tails)
halflife	How many flips to get to 50% heads
log	If TRUE return log transformed probabilities.
possibilities	All possible sequences of flips that lead to the observed number of heads

Value

The likelihood of the data (or log likelihood if log=TRUE)

---

Compute probability of observations given a vector of probability of heads

Description

Compute probability of observations given a vector of probability of heads

Usage

dcoin_from_probability(
  pheads,
  nheads,
  nflips,
  log = FALSE,
  possibilities = get_possibilities(nheads, nflips),
  diff_value = NULL
)

Arguments

pheads	Vector with the probability of a heads on flip 1, 2, etc.
nheads	Number of heads
nflips	Total number of flips (heads and tails)
log	If TRUE return log transformed probabilities.
possibilities	All possible sequences of flips that lead to the observed number of heads
diff_value	If not NULL, the final likelihood will be abs(likelihood - diff_value) for minimizing a function

Value

The likelihood of the data (or log likelihood if log=TRUE)

---

Compute probability of observations given linear change model This is essentially stats::dbinom() but allowing for the probability of heads to linearly change from the starting value. By default it increases by 10% per flip, but this can be set to other values.

Description

The idea is that the coin before handling has some probability of heads, but each time it is picked up that probability could change (maybe it is bent by the statistician's mighty thumb). The slope gives the amount of change in this probability each flip: for example, a coin that starts fair and which has a slope of 0.01 has a probability of heads of 0.51 (0.50 + 0.01) on its first flip, 0.52 on its second, and so forth. If the act of flipping has absolutely no effect on the probability of heads, slope can be set to be zero, though using stats::dbinom() for this particular edge case should be faster.

Usage

dcoin_linear(
  nheads,
  nflips,
  preflip_prob = 0.5,
  slope = 0.1,
  log = FALSE,
  outside_bounds_is_NA = FALSE
)

Arguments

nheads	Number of heads
nflips	Total number of flips (heads and tails)
preflip_prob	Probability of heads before the coin is handled
slope	How much the probability changes each time the coin is flipped
log	If TRUE return log transformed probabilities.
outside_bounds_is_NA	If TRUE, if any probability of heads is outside the bounds of probability, the function returns NA. Otherwise, it sets the value to the nearer bound.

Details

Of course, if all we have is the total number of heads and total number of flips, we do not know if it was HTT, THT, or TTH. For the particular case of a slope set to exactly zero the order does not matter, but in the general case it will. For example, if the probability of heads increases with each flip, HTT is less likely than TTH even though each has one heads out of three flips. The current code looks at all possibilities exhaustively, but more efficient ways to calculate this undoubtedly exist. Pull requests are welcome. It also means this may be slow as the number of flips increases.

For some slopes and preflip probabilities,the probabilities of heads on a given flip may be outside the 0 to 1 bounds. By default, if this happens the function returns NA. If outside_bounds_is_NA is FALSE, it moves the probabilities to the nearer bound.

Value

The likelihood of the data (or log likelihood if log=TRUE)

---

Find congruent models to a simple binomial model This will find the parameter values for other models that equal the likelihood for a simple binomial model. This may not be the MLE for these other models

Description

Find congruent models to a simple binomial model This will find the parameter values for other models that equal the likelihood for a simple binomial model. This may not be the MLE for these other models

Usage

find_congruent_models(
  nheads,
  nflips,
  slopes = c(0, 0.1, -0.05),
  stopval = 1e-04
)

Arguments

nheads	Number of heads
nflips	Total number of flips (heads and tails)
slopes	Vector of slopes to use
stopval	How large a difference in probability is considered close enough between the flat model and others

Value

A list containing the parameter estimates with likelihoods for each model and the probabilities for heads at each model

---

Exhaustively get all possible sets of outcomes that result in a specified number of heads out of a certain number of flips

Description

This grows very large with the number of flips. It will throw an error if you try too many flips.

Usage

get_possibilities(nheads, nflips)

Arguments

nheads	Number of heads
nflips	Total number of flips (heads and tails)

Value

data.frame with each potential trial as a row. 1=heads, 0=tails.

---

Compute the probability of heads with each flip given an exponential model The model assumes 100% chance of heads before a coin is picked up and it drops exponentially each time the coin is handled.

Description

Compute the probability of heads with each flip given an exponential model The model assumes 100% chance of heads before a coin is picked up and it drops exponentially each time the coin is handled.

Usage

prob_heads_exponential_decay(nflips, halflife)

Arguments

nflips	Total number of flips (heads and tails)
halflife	How many flips to get to 50% heads

Value

Vector of probability of heads for the first flip, second flip, etc.

---

Compute the probability of heads with each flip given a linear change model.

Description

Compute the probability of heads with each flip given a linear change model.

Usage

prob_heads_linear(nflips, preflip_prob = 0.5, slope = 0.1)

Arguments

nflips	Total number of flips (heads and tails)
preflip_prob	Probability of heads before the coin is handled
slope	How much the probability changes each time the coin is flipped

Value

Vector of probability of heads for the first flip, second flip, etc.

---

Compute the probability of heads with each flip given a multiplier model The model assumes 50% chance of heads before a coin is picked up and it changes as a percentage of the previous value each flip. i.e., the probability of heads is 101% of the probability the previous flip with a multiplier of 1.01.

Description

Compute the probability of heads with each flip given a multiplier model The model assumes 50% chance of heads before a coin is picked up and it changes as a percentage of the previous value each flip. i.e., the probability of heads is 101% of the probability the previous flip with a multiplier of 1.01.

Usage

prob_heads_multiplicative(nflips, multiplier, outside_bounds_is_NA = FALSE)

Arguments

nflips	Total number of flips (heads and tails)
multiplier	Factor to multiply the previous probability by
outside_bounds_is_NA	If TRUE, if any probability of heads is outside the bounds of probability, the function returns NA. Otherwise, it sets the value to the nearer bound.

Value

Vector of probability of heads for the first flip, second flip, etc.

---

Computes the likelihood for a range of values using an exponential coin model

Description

Computes the likelihood for a range of values using an exponential coin model

Usage

profile_exponential_decay_model(
  nheads,
  nflips,
  param_range = c(0, nflips * 10),
  number_of_steps = 1000,
  log = FALSE
)

Arguments

nflips	Total number of flips (heads and tails)
param_range	Range of parameters to try
number_of_steps	How many values of the parameter to try

Value

vector of likelihoods

Examples

nheads <- 8
nflips <- 10
exp_results <- profile_exponential_decay_model(nheads, nflips)
plot(x=exp_results$preflip_prob, y=exp_results$likelihood, type="l")
best_param <- exp_results$halflife[which.max(exp_results$likelihood, na.rm=TRUE)]
print(best_param)

---

Computes the likelihood for a range of values using a linear coin model

Description

Computes the likelihood for a range of values using a linear coin model

Usage

profile_linear_model(
  nheads,
  nflips,
  param_range = c(0, 1),
  slope = 0.1,
  number_of_steps = 1000,
  log = FALSE,
  outside_bounds_is_NA = FALSE
)

Arguments

nflips	Total number of flips (heads and tails)
param_range	Range of parameters to try
slope	How much the probability changes each time the coin is flipped
number_of_steps	How many values of the parameter to try

Value

vector of likelihoods

Examples

nheads <- 8
nflips <- 10
linear_results <- profile_linear_model(nheads, nflips)
plot(x=linear_results$preflip_prob, y=linear_results$likelihood, type="l")
dbinom_proportions <- seq(from=0, to=1, length.out=1000)
lines(dbinom_proportions, dbinom(nheads, nflips, dbinom_proportions), col="red")
best_param <- linear_results$preflip_prob[which.max(linear_results$likelihood, na.rm=TRUE)]
print(best_param)

---

Compute probability of observations across many potential vectors This will try (1/stepsize)^nflips possible vectors, computing the probability of the observation for each

Description

Compute probability of observations across many potential vectors This will try (1/stepsize)^nflips possible vectors, computing the probability of the observation for each

Usage

try_many_vectors(
  nheads,
  nflips,
  number_samples = 1000,
  stopval = 1e-05,
  log = FALSE,
  possibilities = get_possibilities(nheads, nflips)
)

Arguments

nheads	Number of heads
nflips	Total number of flips (heads and tails)
number_samples	How many vectors to sample
stopval	How large a difference in probability is considered close enough between the flat model and others
log	If TRUE return log transformed probabilities.
possibilities	All possible sequences of flips that lead to the observed number of heads

Value

The likelihood of the data (or log likelihood if log=TRUE)

---