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Diffstat (limited to 'utils/slice_sampler.h')
| -rw-r--r-- | utils/slice_sampler.h | 191 |
1 files changed, 191 insertions, 0 deletions
diff --git a/utils/slice_sampler.h b/utils/slice_sampler.h new file mode 100644 index 00000000..aa48a169 --- /dev/null +++ b/utils/slice_sampler.h @@ -0,0 +1,191 @@ +//! slice-sampler.h is an MCMC slice sampler +//! +//! Mark Johnson, 1st August 2008 + +#ifndef SLICE_SAMPLER_H +#define SLICE_SAMPLER_H + +#include <algorithm> +#include <cassert> +#include <cmath> +#include <iostream> +#include <limits> + +//! slice_sampler_rfc_type{} returns the value of a user-specified +//! function if the argument is within range, or - infinity otherwise +// +template <typename F, typename Fn, typename U> +struct slice_sampler_rfc_type { + F min_x, max_x; + const Fn& f; + U max_nfeval, nfeval; + slice_sampler_rfc_type(F min_x, F max_x, const Fn& f, U max_nfeval) + : min_x(min_x), max_x(max_x), f(f), max_nfeval(max_nfeval), nfeval(0) { } + + F operator() (F x) { + if (min_x < x && x < max_x) { + assert(++nfeval <= max_nfeval); + F fx = f(x); + assert(std::isfinite(fx)); + return fx; + } + return -std::numeric_limits<F>::infinity(); + } +}; // slice_sampler_rfc_type{} + +//! slice_sampler1d() implements the univariate "range doubling" slice sampler +//! described in Neal (2003) "Slice Sampling", The Annals of Statistics 31(3), 705-767. +// +template <typename F, typename LogF, typename Uniform01> +F slice_sampler1d(const LogF& logF0, //!< log of function to sample + F x, //!< starting point + Uniform01& u01, //!< uniform [0,1) random number generator + F min_x = -std::numeric_limits<F>::infinity(), //!< minimum value of support + F max_x = std::numeric_limits<F>::infinity(), //!< maximum value of support + F w = 0.0, //!< guess at initial width + unsigned nsamples=1, //!< number of samples to draw + unsigned max_nfeval=200) //!< max number of function evaluations +{ + typedef unsigned U; + slice_sampler_rfc_type<F,LogF,U> logF(min_x, max_x, logF0, max_nfeval); + + assert(std::isfinite(x)); + + if (w <= 0.0) { // set w to a default width + if (min_x > -std::numeric_limits<F>::infinity() && max_x < std::numeric_limits<F>::infinity()) + w = (max_x - min_x)/4; + else + w = std::max(((x < 0.0) ? -x : x)/4, (F) 0.1); + } + assert(std::isfinite(w)); + + F logFx = logF(x); + for (U sample = 0; sample < nsamples; ++sample) { + F logY = logFx + log(u01()+1e-100); //! slice logFx at this value + assert(std::isfinite(logY)); + + F xl = x - w*u01(); //! lower bound on slice interval + F logFxl = logF(xl); + F xr = xl + w; //! upper bound on slice interval + F logFxr = logF(xr); + + while (logY < logFxl || logY < logFxr) // doubling procedure + if (u01() < 0.5) + logFxl = logF(xl -= xr - xl); + else + logFxr = logF(xr += xr - xl); + + F xl1 = xl; + F xr1 = xr; + while (true) { // shrinking procedure + F x1 = xl1 + u01()*(xr1 - xl1); + if (logY < logF(x1)) { + F xl2 = xl; // acceptance procedure + F xr2 = xr; + bool d = false; + while (xr2 - xl2 > 1.1*w) { + F xm = (xl2 + xr2)/2; + if ((x < xm && x1 >= xm) || (x >= xm && x1 < xm)) + d = true; + if (x1 < xm) + xr2 = xm; + else + xl2 = xm; + if (d && logY >= logF(xl2) && logY >= logF(xr2)) + goto unacceptable; + } + x = x1; + goto acceptable; + } + goto acceptable; + unacceptable: + if (x1 < x) // rest of shrinking procedure + xl1 = x1; + else + xr1 = x1; + } + acceptable: + w = (4*w + (xr1 - xl1))/5; // update width estimate + } + return x; +} + +/* +//! slice_sampler1d() implements a 1-d MCMC slice sampler. +//! It should be correct for unimodal distributions, but +//! not for multimodal ones. +// +template <typename F, typename LogP, typename Uniform01> +F slice_sampler1d(const LogP& logP, //!< log of distribution to sample + F x, //!< initial sample + Uniform01& u01, //!< uniform random number generator + F min_x = -std::numeric_limits<F>::infinity(), //!< minimum value of support + F max_x = std::numeric_limits<F>::infinity(), //!< maximum value of support + F w = 0.0, //!< guess at initial width + unsigned nsamples=1, //!< number of samples to draw + unsigned max_nfeval=200) //!< max number of function evaluations +{ + typedef unsigned U; + assert(std::isfinite(x)); + if (w <= 0.0) { + if (min_x > -std::numeric_limits<F>::infinity() && max_x < std::numeric_limits<F>::infinity()) + w = (max_x - min_x)/4; + else + w = std::max(((x < 0.0) ? -x : x)/4, 0.1); + } + // TRACE4(x, min_x, max_x, w); + F logPx = logP(x); + assert(std::isfinite(logPx)); + U nfeval = 1; + for (U sample = 0; sample < nsamples; ++sample) { + F x0 = x; + F logU = logPx + log(u01()+1e-100); + assert(std::isfinite(logU)); + F r = u01(); + F xl = std::max(min_x, x - r*w); + F xr = std::min(max_x, x + (1-r)*w); + // TRACE3(x, logPx, logU); + while (xl > min_x && logP(xl) > logU) { + xl -= w; + w *= 2; + ++nfeval; + if (nfeval >= max_nfeval) + std::cerr << "## Error: nfeval = " << nfeval << ", max_nfeval = " << max_nfeval << ", sample = " << sample << ", nsamples = " << nsamples << ", r = " << r << ", w = " << w << ", xl = " << xl << std::endl; + assert(nfeval < max_nfeval); + } + xl = std::max(xl, min_x); + while (xr < max_x && logP(xr) > logU) { + xr += w; + w *= 2; + ++nfeval; + if (nfeval >= max_nfeval) + std::cerr << "## Error: nfeval = " << nfeval << ", max_nfeval = " << max_nfeval << ", sample = " << sample << ", nsamples = " << nsamples << ", r = " << r << ", w = " << w << ", xr = " << xr << std::endl; + assert(nfeval < max_nfeval); + } + xr = std::min(xr, max_x); + while (true) { + r = u01(); + x = r*xl + (1-r)*xr; + assert(std::isfinite(x)); + logPx = logP(x); + // TRACE4(logPx, x, xl, xr); + assert(std::isfinite(logPx)); + ++nfeval; + if (nfeval >= max_nfeval) + std::cerr << "## Error: nfeval = " << nfeval << ", max_nfeval = " << max_nfeval << ", sample = " << sample << ", nsamples = " << nsamples << ", r = " << r << ", w = " << w << ", xl = " << xl << ", xr = " << xr << ", x = " << x << std::endl; + assert(nfeval < max_nfeval); + if (logPx > logU) + break; + else if (x > x0) + xr = x; + else + xl = x; + } + // w = (4*w + (xr-xl))/5; // gradually adjust w + } + // TRACE2(logPx, x); + return x; +} // slice_sampler1d() +*/ + +#endif // SLICE_SAMPLER_H |