API

setprogress!(progress::Bool)

Enable progress logging in Turing if progress is true, and disable it otherwise.

Flat()

The flat distribution is the improper distribution of real numbers that has the improper probability density function

\[f(x) = 1.\]

FlatPos(l::Real)

The positive flat distribution with real-valued parameter l is the improper distribution of real numbers that has the improper probability density function

\[f(x) = \begin{cases} 0 & \text{if } x \leq l, \\ 1 & \text{otherwise}. \end{cases}\]

BinomialLogit(n, logitp)

The Binomial distribution with logit parameterization characterizes the number of successes in a sequence of independent trials.

It has two parameters: n, the number of trials, and logitp, the logit of the probability of success in an individual trial, with the distribution

\[P(X = k) = {n \choose k}{(\text{logistic}(logitp))}^k (1 - \text{logistic}(logitp))^{n-k}, \quad \text{ for } k = 0,1,2, \ldots, n.\]

See also: Binomial

OrderedLogistic(η, c::AbstractVector)

The ordered logistic distribution with real-valued parameter η and cutpoints c has the probability mass function

\[P(X = k) = \begin{cases} 1 - \text{logistic}(\eta - c_1) & \text{if } k = 1, \\ \text{logistic}(\eta - c_{k-1}) - \text{logistic}(\eta - c_k) & \text{if } 1 < k < K, \\ \text{logistic}(\eta - c_{K-1}) & \text{if } k = K, \end{cases}\]

where K = length(c) + 1.

LogPoisson(logλ)

The Poisson distribution with logarithmic parameterization of the rate parameter describes the number of independent events occurring within a unit time interval, given the average rate of occurrence $\exp(\log\lambda)$.

The distribution has the probability mass function

\[P(X = k) = \frac{e^{k \cdot \log\lambda}}{k!} e^{-e^{\log\lambda}}, \quad \text{ for } k = 0,1,2,\ldots.\]

See also: Poisson

BernoulliLogit(logitp=0.0)

A Bernoulli distribution that is parameterized by the logit logitp = logit(p) = log(p/(1-p)) of its success rate p.

\[P(X = k) = \begin{cases} \operatorname{logistic}(-logitp) = \frac{1}{1 + \exp{(logitp)}} & \quad \text{for } k = 0, \\ \operatorname{logistic}(logitp) = \frac{1}{1 + \exp{(-logitp)}} & \quad \text{for } k = 1. \end{cases}\]

External links:

• Bernoulli distribution on Wikipedia

See also Bernoulli

predict([rng::AbstractRNG,] model::Model, chain::MCMCChains.Chains; include_all=false)

Execute model conditioned on each sample in chain, and return the resulting Chains.

If include_all is false, the returned Chains will contain only those variables sampled/not present in chain.

Details

Internally calls Turing.Inference.transitions_from_chain to obtained the samples and then converts these into a Chains object using AbstractMCMC.bundle_samples.

Example

julia> using Turing; Turing.setprogress!(false);
[ Info: [Turing]: progress logging is disabled globally

julia> @model function linear_reg(x, y, σ = 0.1)
           β ~ Normal(0, 1)

           for i ∈ eachindex(y)
               y[i] ~ Normal(β * x[i], σ)
           end
       end;

julia> σ = 0.1; f(x) = 2 * x + 0.1 * randn();

julia> Δ = 0.1; xs_train = 0:Δ:10; ys_train = f.(xs_train);

julia> xs_test = [10 + Δ, 10 + 2 * Δ]; ys_test = f.(xs_test);

julia> m_train = linear_reg(xs_train, ys_train, σ);

julia> chain_lin_reg = sample(m_train, NUTS(100, 0.65), 200);
┌ Info: Found initial step size
└   ϵ = 0.003125

julia> m_test = linear_reg(xs_test, Vector{Union{Missing, Float64}}(undef, length(ys_test)), σ);

julia> predictions = predict(m_test, chain_lin_reg)
Object of type Chains, with data of type 100×2×1 Array{Float64,3}

Iterations        = 1:100
Thinning interval = 1
Chains            = 1
Samples per chain = 100
parameters        = y[1], y[2]

2-element Array{ChainDataFrame,1}

Summary Statistics
  parameters     mean     std  naive_se     mcse       ess   r_hat
  ──────────  ───────  ──────  ────────  ───────  ────────  ──────
        y[1]  20.1974  0.1007    0.0101  missing  101.0711  0.9922
        y[2]  20.3867  0.1062    0.0106  missing  101.4889  0.9903

Quantiles
  parameters     2.5%    25.0%    50.0%    75.0%    97.5%
  ──────────  ───────  ───────  ───────  ───────  ───────
        y[1]  20.0342  20.1188  20.2135  20.2588  20.4188
        y[2]  20.1870  20.3178  20.3839  20.4466  20.5895

julia> ys_pred = vec(mean(Array(group(predictions, :y)); dims = 1));

julia> sum(abs2, ys_test - ys_pred) ≤ 0.1
true

ordered(d::Distribution)

Return a Distribution whose support are ordered vectors, i.e., vectors with increasingly ordered elements.

Specifically, d is restricted to the subspace of its domain containing only ordered elements.

Notes on ordered being un-normalized

The resulting ordered distribution is un-normalized. This is not a problem if used in a context where the normalizing factor is irrelevant, but if the value of the normalizing factor impacts the resulting computation, the results may be inaccurate.

For example, if the distribution is used in sampling a posterior distribution with MCMC and the parameters of the ordered distribution are themselves sampled, then the normalizing factor would in general be needed for accurate sampling, and ordered should not be used. However, if the parameters are fixed, then since MCMC does not require distributions be normalized, ordered may be used without problems.

A common case is where the distribution being ordered is a joint distribution of n identical univariate distributions. In this case the normalization factor works out to be the constant n!, and ordered can again be used without problems even if the parameters of the univariate distribution are sampled.